Steven J. Miller                                                       Professor of Mathematics, Williams College                18 Hoxsey St, Williamstown, MA (sjm1 AT williams.edu) NOTE: At some point my pages will be migrating to https://sites.williams.edu/sjm1/   [Click here for general advice] curriculum vita (click here for annotated bibliography)  teaching statement Takeaways (all classes)  Possible thesis / colloquium projects Opportunities in Mathematics (REUs, gradschool) photos of Cam and Kayla

If there are several versions of a talk, the later version is usually the more 'complete' (ie, correct) version.

1. From Pythagoras to Pi: Part I: https://youtu.be/JHvmP-1KXYc (slides here). Given to 7th grade son who is in Algebra I. 41 minutes
2. From Pythagoras to Pi: Part II: https://youtu.be/ISo8kXDP-6U (slides here). Given to 7th grade son who is in Algebra I. 27 minutes
3. What do you MEAN? https://youtu.be/jBKZaCxpgSE (word file here, pdf here) (3/19/2020): Comfort with Algebra sufficient: 40 minutes
4. Shoe size and age: https://youtu.be/aDxdDifvlKM (word file here, pdf here) (3/20/2020): Just need to be able to multiply and add, say grade 1 or 2 and up: 20 minutes
5. Mono-variants: https://youtu.be/PbZhVLXyatY (powerpoint  here, pdf here) (3/23/2020):  Grade 5 and up: 28 minutes
6. I Love Rectangles Game: https://youtu.be/JHtrzARHwHU (powerpoint  here, pdf here) (3/24/2020): Aimed for K, should be good for all ages. 13 minutes
7. From Pascal to Calculus: Part I: https://youtu.be/dv15VTyEWyQ (powerpoint  here, pdf here) (3/25/2020): For those knowing Algebra I (equations of lines): 52 minutes
8. From Pascal to Calculus: Part II: https://youtu.be/D6OnleQJ1XM (powerpoint  here, pdf here) (3/26/2020): For those knowing Algebra I (equations of lines): 40 minutes
9. Games: Tic Tac Toe, Chocolate Bar, Coins, Devil: https://Mathyoutu.be/4Kvx-JHBvs0 (slides here) (3/27/2020): Much of it can be done with K, 2nd and higher to be safe: 38 minutes
10. Induction and Sums: Part I: Induction https://youtu.be/3orVsQECaag (powerpoint  here, pdf here) (3/30/2020): Assuming Algebra I: 32 minutes
11. Induction and Sums: Part II: Geometric Series Formula https://youtu.be/CJjglF65x6g (powerpoint  here, pdf here): (3/31/2020): Assuming Algebra I: 25 minutes
12. Induction and Sums: Part III: From the Geometric Series Formula to Primes https://youtu.be/UWNM8EtzoMI  (powerpoint  here, pdf here)  (4/4/2020): Assuming Algebra: 22 minutes
13. The Three Hat Problem and Error Correcting Codes:https://youtu.be/oMeKf7AhAa4 (powerpoint  here, pdf here)  (4/6/2020): Aimed for 3rd Grade and up: 26 minutes
14. How to Attack Problems I: We WILL Cross That Bridge: https://youtu.be/JH6uxmgWoFQ (powerpoint  here, pdf here)  (4/8/2020): Aimed for 4th Grade and up: 20 minutes
15. How to Attack Problems II: Legal 21: https://youtu.be/dlBVLlt4PPA (powerpoint  here, pdf here)  (4/9/2020): Aimed for 4th/5th Grade and up: 14 minutes
16. Polynomials and Applications: Part I: Lecture 1:  Lines: https://youtu.be/NNxBhUTzexA (powerpoint  here, pdf here)  (4/10/2020): Aimed at 6th/7th grade and up: 9 minutes
17. Polynomials and Applications: Part 2: Lecture 2: Introduction to Quadratics: Plotting, Simple Examples and Roots: https://youtu.be/bkIWsNcw-bU (powerpoint  here, pdf here)  (4/13/2020): Aimed at 7th grade and up: 17 minutes
18. Polynomials and Applications: Part 2: Lecture 3: Introduction to Quadratics: Plotting, Simple Examples and Roots:   https://youtu.be/u8Xx7r0VrJ4 (powerpoint  here, pdf here)  (4/14/2020): Aimed at 7th grade and up: 18 minutes.
19. Polynomials and Applications: Part 2: Lecture 4: Application 1: Trajectories: https://youtu.be/hAw9vSNMzhg  (powerpoint  here, pdf here)  (4/15/2020): Aimed at 7th grade and up: 24 minutes.
20. Polynomials and Applications: Part 3: Lecture 5: Application 2: Fibonacci Numbers: https://youtu.be/WB9gLTASXCw (powerpoint  here, pdf here)  (4/16/2020): Aimed at 7th grade and up: 24 minutes.
21. Polynomials and Applications: Part 4: Lecture 6: Application 3: Recurrence Relations and Gambling! https://youtu.be/Esa2TYwDmwA  (4/17/2020): Aimed at 7th grade and up: 7 minutes
22. Polynomials and Applications: Part 5: Lecture 6: Application 4: Finding Trajectories (revisited)  https://youtu.be/7bfeNy4XW5I  (powerpoint  here, pdf here) (4/21/2020): Aimed at 7th grade and up: 10 minutes
23. Polynomials and Applications: Part 6: Lecture 7: Application 5: Codes: https://youtu.be/wSEXv5PXxu0  (powerpoint  here, pdf here) (4/24/2020): Aimed at 7th grade and up: 11 minutes
24. Introduction to Probability: Part 1: The Factorial Function:  https://youtu.be/Un3tWIX-kDY  (powerpoint  here, pdf here) (4/27/2020): Aimed at 7th grade and up: 13 minutes
25. Introduction to Probability: Part 2: Permutations:  https://youtu.be/hhYtkpcQQAY   (powerpoint  here, pdf here) (4/29/2020): Aimed at 7th grade and up: 11 minutes
26. Introduction to Probability: Part 3: Combinations: https://youtu.be/8w8HWvhWM34  (powerpoint  here, pdf here) (4/29/2020): Aimed at 7th grade and up: 19 minutes
27. Introduction to Probability: Part 4: Darth Vader Problem: https://youtu.be/qsUYmXGgngE  (powerpoint  here, pdf here) (5/4/2020): Aimed at 7th grade and up: 19 minutes
28. Introduction to Probability: Part 5: Double Sixes Problem: https://youtu.be/zJTaXORiH9o  (powerpoint  here, pdf here) (5/6/2020): Aimed at 7th grade and up: 15 minutes (re-recorded; no TAs)
29. Introduction to Probability: Part 6: Long Suits: https://youtu.be/-iWWLLlCRy4  (powerpoint  here, pdf here) (5/8/2020): Aimed at 7th grade and up: 18 minutes
30. Introduction to Probability: Part 7: Long Suits: https://youtu.be/ke5RLxIW6v4   (powerpoint  here, pdf here) (5/11/2020): Aimed at 7th grade and up: 18 minutes
31. Introduction to Probability: Part 8: All trump, Poker: https://youtu.be/InhvzliUb4I  (powerpoint  here, pdf here) (5/13/2020): Aimed at 7th grade and up: 15 minutes
32. Introduction to Probability: Part 9: Advanced Combinatorics: https://youtu.be/WFcEQeCoG5k (powerpoint  here, pdf here) (5/19/2020): Aimed at 7th grade and up: 16 minutes

• Talks Online

• Random Matrix Theory and $$L$$-Functions
• Random Matrix Theory and $$L$$-Functions I: Analytic Number Theory Seminar, Ohio State (10/20/03):   pdf
• Random Matrix Theory and $$L$$-Functions II: Analytic Number Theory Seminar, Ohio State (10/27/03): pdf
• From Random Matrix Theory to $$L$$-Functions: Special Number Theory Seminar, Tel Aviv (12/23/04):    pdf (see also the expanded talk given in Utah in 2009 below)
• Identifying Symmetry Groups of Zeros of Families of $$L$$-Functions:  Number Theory and Random Matrix  Theory Workshop, CMS Summer 2005, Waterloo (6/1/05):    ps   pdf;  tabbed version ps dvi
• Identifying and breaking the symmetry group of zeros of families of $$L$$-functions: Number Theory Seminar, CUNY Lehman (10/20/06):   pdf
• A Symplectic Test of the $$L$$-Functions Ratios Conjecture: Algebra Seminar, Brown University (9/17/07):   paper.pdf   AMS Special Session on $$L$$-functions and automorphic forms, Courant (20 minute version, 3/16/08):   pdf   tabbed version  pdf    Johns Hopkins University (50 minute version, 4/4/08):   pdf (untabbed version: pdf); Cornell University (50 minute version, 6/5/08): pdf (untabbed version: pdf).
• From Random Matrix Theory to $$L$$-Functions: Graduate Workshop on Zeta Functions, $$L$$-Functions and their Applications, Utah Valley University, June 2, 2009: pdf   I've created a webpage with links to talks and papers related to this conference; click here for these papers and links.
• Random Matrix Theory and Number Theory: Progress report from 2009 SMALL REU at Williams College (final presentation of my students John Goes, Steven Jackson, David Montague, Eve Ninsuwan, Ryan Peckner and Vincent Pham): Williams College (8/11/09): pdf
• Low Lying Zeros of Number Field $$L$$-Functions (presented by Ryan Peckner).  Young Mathematicians Conference,  Ohio State (8/29/09):  pdf
• Tests of the $$L$$-Functions Ratios Conjecture. Maine - Quebec Number Theory Conference (10/3/09):   pdf  Rutgers University (expanded version, 3/2/10):   pdf
• The n-level density of zeros of quadratic Dirichlet $$L$$-functions (presented by Jake Levinson), Young Mathematicians Conference, August 19, 2011. pdf
• Low-lying zeros of cuspidal Maass forms (presented by Oleg Lazarev and Liyang Zhang), Young Mathematicians Conference, August 20, 2011. pdf Maine-Quebec Number Theory Conference, October 2, 2011. pdf
• Determinantal Expansions in Random Matrix Theory and Number Theory (with Nicholas Triantafillou), Maine-Quebec Number Theory Conference, September 29, 2012. pdf (trimmed pdf)
• Low-lying zeros of cuspidal Maass forms (blackboard talk given by Levent Alpoge), Maine-Quebec Number Theory Conference, September 29, 2012.
• Low-lying zeros of GL(2) $$L$$-functions, University of Michigan, October 22, 2012.  part 1     part 2
• Low-lying zeros of GL(2) $$L$$-functions, AMS Special Session on Arithmetic Statistics, I, Joint Meetings SD, January 10, 2013 (includes excised orthogonal ensemble for elliptic curves and results for holomorphic cuspidal newforms and Maass forms). pdf  Expanded Version: Quebec-Vermont Number Theory Seminar, Concordia University, March 21, 2013pdf
• Newman's Conjecture for Automorphic and Function Field $$L$$-functions (presented by Alan Chang), Maine-Quebec Number Theory Conference (10/5/13).  pdf; CANT May 28, 2014  pdf (video online here).
• The $$n$$-Level Density of Dirichlet $$L$$-Functions (presented by Kyle Pratt and Minh-Tam Trinh), Maine-Quebec Number Theory Conference (10/5/13).  pdf
• Problems in the theory of low-lying zeros, Simons Symposium on Families of Automorphic Forms and the Trace Formula, Puerto Rico, January 27, 2014. pdf
Results in the theory of low-lying zeros, Simons Symposium on Families of Automorphic Forms and the Trace Formula, Puerto Rico, January 28, 2014. pdf
• Biases in Moments of Satake Parameters and Models for L-function Zeros (with Kevin Yang), Maine-Quebec Number Theory Conference, October 3, 2015pdf
• Biases in Moments of Satake Parameters and in Zeros near the Central Point in Families of L-Functions, Computational Aspects of L-functions, ICERM, Providence, RI (11/10/15).   pdf
• Gaps Between Zeros of GL(2) L-functions, Southern New England Conference on Quadratic Forms and Modular Forms, June 2, 2016.   pdf
• Extending Agreement in the Katz-Sarnak Density Conjecture (joint with Peter Cohen and Roger Van Peski), Quebec-Maine Number Theory Conference, October 8, 2016.   pdf
• One-level density for holomorphic cusp forms of arbitrary level, 31st Annual Workshop on Automorphic Forms, ETSU, Mar 6, 2017.   pdf
• Lower Order Biases in Fourier Coefficients of Elliptic Curve and Cuspidal Newform families (with Jared Lichtman, Eric Winsor and Jianing Yang), Maine-Qu\'ebec Number Theory Conference, October 14, 2017.   pdf   MASON VI, March 17, 2023.  pdf
• Variance of Gaussian Primes Across Sectors and The Hecke L-Function Ratios Conjecture (with Yujin Kim and Shannon Sweitzer), Maine-Qu\'ebec Number Theory Conference, October 14, 2017.   pdf
• Lower Order Terms for the Variance of Gaussian Primes across Sectors (given by Ezra Waxman), 32nd Autormorphic Forms Workshop, Tufts University, May 22, 2018.  pptx  pdf
• Optimal Test Functions for n-Level Densities and Applications to Central Point Vanishing (with Charles Devlin VI), Maine-Qu\'ebec Number Theory Conference, October 5, 2019.   pdf (video: https://youtu.be/I4j374CQgfg)
• How Low Can We Go? Understanding Zeros of L-Functions Near The Central Point, New York Number Theory Seminar, February 18, 2021.   pdf
• The Katz-Sarnak Density Conjecture and Bounding Central Point Vanishing of L-Functions, Second Int'l Webinar: Recent Developments in Number Theory, School of Applied Sciences (Mathematics), Kalinga Institute of Industrial Technology University, Bhubaneswar, India, October 3, 2021.   pdf (video: https://youtu.be/dsdMFl0yPfw) University of Rochester, November 5, 2021  pdf  (video: https://youtu.be/zDJasLIaXhY)
• The Katz-Sarnak Density Conjecture and Bounding Central Point Vanishing of L-Functions (expanded version with improved bounds), Upstate New York Number Theory Conference, Rochester, NY April 2, 2023.  pdf (video: https://youtu.be/Be3zNr4kKVw) (20 minute version) 35th Automorphic Forms Workshop, LSU May 23, 2023.  pdf
• Combinatorics in Analyzing L-Function Coefficients and Applications to Low-Lying Zeros, Special Session in Number Theory in Celebration of the 70th Birthday of Ram Murty, CMS Summer Meeting, 4 June 2023.   pdf (video:  )
• Upper Bounds for the Lowest First Zero in Families of Cuspidal Newforms, 36th Automorphic Forms Workshop, Oklahoma State University, May 21, 2024.  pdf (talk: https://youtu.be/imMo7_yUDxs)
• Group Theory in Compound Families of L-Functions, Zassenhaus Groups and Friends Conference, Texas State University, June 2, 2024.  pdf

• Random Matrix Theory and Elliptic Curves
• 1 and 2 Level Density Functions for Families of Elliptic Curves: Evidence for the Underlying Group Symmetries.
(Thesis defense) Princeton (5/26/02), Number Theory Seminar  Ohio State (5/30/02):  pdf    Boston University (2/10/03):  pdf
• Evidence for a Spectral Interpretation of the Zeros of Families of Elliptic Curves. Joint meeting of the AMS and UMI Pisa (6/13/02): pdf   title  Shorter version (20 minutes): AMS Sectional, Salt Lake City (10/27/02):  dvi   pdf
• Random Matrix Theory and Elliptic Curves: Evidence for the Underlying Group Symmetries (with three appendices). Johns Hopkins University  (3/3/04):   pdf   An alternate version:   Five College Number Theory Seminar, Amherst, MA,  (4/20/04):   pdf
• Random Matrix Theory models for zeros near the central point (and applications to elliptic curves) (45 minutes) Workshop on Spectral Theory and Automorphic Forms, Montreal, May 2004.  ps.   An alternate version (60 minutes):  Boston University (2/10/03): ps  Brown University (9/13/04 - expanded):  dvi   pdf   Another alternate version:  (120 minutes)  Fellowship of the Ring Seminar, Brandeis University (4/1/05):  ps  pdf; tabbed version ps dviAnother alternate version  (30 minutes), Advances in Number Theory and Random Matrix Theory, Rochester, NY (6/7/06):   pdf;   tabbed version pdf paper the talk is based on (to appear in Experimental Mathematics)
• How the Manhattan Project helps us understand primes and elliptic curves (with appendices on Dirichlet $$L$$-Fns, Random Graphs and a bibliography). Colloquium, University of Connecticut (3/24/05): ps  pdf; tabbed version ps dvi.
• From the Manhattan Project to Number Theory: How nuclear physics helped us understand primes: Theoretical Physics Seminar, Brown University (4/12/06): pdf; relevant papers: Investigations of Zeros Near the Central Point of Elliptic Curve $$L$$-Functions (to appear in Experimental Mathematics pdf  (data available online).
• Finite conductor models for zeros near the central point of elliptic curve $$L$$-functions (with Eduardo Duenez, Duc Khiem Huynh and Jon P. Keating). $$L$$-functions, ranks of elliptic curves and random matrix theory workshop, Banff (7/12/07):   slides:  pdf (my part);   pdf (Duenez);   ppt (Keating);   pdf (Huynh)   pdf (combined).   AMS Special Session on Number Theory, Wesleyan University, Middletown, CT (10/11/08):   pdf  Conference on Modular Forms and Related Topics, Beirut, May 28, 2018. pdf    CNTA XV, Universite Laval, July 9, 2018.  pdf   University of Maine, March 29, 2023.   pdf  University of Maryland, March 29, 2023 pdf (talk here: https://youtu.be/cNsSR5PloTY)
• Finite conductor models for zeros near the central point of elliptic curve $$L$$-functions (with Eduardo Duenez, Duc Khiem Huynh and Jon P. Keating). (This is an expanded version, and includes results towards an average version of the Birch and Swinnerton-Dyer Conjecture, as well as the results from Duc Khiem's thesis on modeling the first zero of quadratic twists by Jacobi ensembles with discretization and lower order terms included.) University of Rochester:  pdf    Five College Number Theory Seminar:   pdf    Williams College (abridged 40 minute version):   pdf     Maine - Quebec Number Theory Conference (20 minute version, full theory, 10/1/11):   pdf      Brown University (10/24/11):   pdf
• Closed-form moments in elliptic curve families and low-lying zeros, Simons Symposium on Families of Automorphic Forms and the Trace Formula, Puerto Rico, January 31, 2014.
• From Sato-Tate Distributions to Low-Lying Zeros, Frobenius distributions of curves, CIRM, February 2014 pdf (and alsothe SouthEastern Regional Meeting on Numbers (SERMON XXVII), Wofford College, April 26, 2014 pdf): YouTube version of SERMON talk here: http://youtu.be/VBzVAvZ6k6A
• From the Manhattan Project to Elliptic Curves: The  Ohio State University, March 24, 2014. pdf  UMass Boston, February 4, 2014. pdf   Washinigton State University, October 12, 2015. pdf MASON IV (3/7/20). pdf  (video here: https://youtu.be/p15X3ERNvLs)
• Finite conductor models for zeros near the central point of elliptic curve L-functions: Yale University, April 15, 2014. pdf  Boston College, April 30, 2015. pdf (includes Bias Conjecture)    Duke University (9/7/16)  pdf
• Results on GL(2) $$L$$-Functions: Biases in Coefficients and Gaps Between Zeros, Families of Automorphic Forms and the Trace Formula, Banff International Research Station, Dec 1, 2014: video online here  (slides here). Brown University, Number Theory Seminar, April 2, 2018. pdf
• Large Gaps Between Zeros of GL(2) L-Functions (with Owen Barrett and Karl Winsor), 29th Automorphic Forms Workshop, University of Michigan, March 2, 2015.  pdf
• Generalizing repulsion of elliptic curve zeros near the central point to other GL(2) forms (with Owen Barrett), 29th Automorphic Forms Workshop, University of Michigan, March 2, 2015.  pdf
• Biases in the second moments of Fourier coefficients in one-parameter families of elliptic curves (with Blake Mackall and Karl Winsor), 29th Automorphic Forms Workshop, University of Michigan, March 3, 2015.  pdf    AMS Special Session on Analytic Number Theory and Automorphic Forms, Washington State University, April 23, 2017.   pdf
• Biases in Second Moments of Elliptic Curves (Aditya Jambhale and Akash L. Narayanan), Maine-Quebec Number Theory Conference, September 30, 2023.  pdf
• Machine Learning in Elliptic Curves and Beyond: From Conjectures to Theorems to Conjectures, Hybrid Conference on AI-Math, Institute of Mathematics and Statistics, State University of Rio de Janeiro, RJ, Brazil, February 28, 2024.  pdf  AMS Special Session on Artificial Intelligence in Mathematics, Milwaukee, April 20, 2024.   pdf

• Elliptic Curves
• Ranks of One-Parameter Families of Elliptic Curves Over Q(T) and Thoughts on the Excess Rank Question (with five appendices). Boston College (3/10/03):  dvi   pdf
• Constructing 1-Parameter Families of Elliptic Curves over Q(T) with Moderate Rank. AMS Sectional, Boulder, CO (10/4/03): pdf
• The effect of zeros of elliptic curve $$L$$-functions at the central point on nearby zeros. AMS Sectional, Lawrenceville, NJ (4/18/04):  pdf  Expanded Version: Algebra Seminar, Brown University (10/24/05):  pdf   tabbed version dvi
• Towards an Average'' Version of the Birch and Swinnerton-Dyer Conjecture (presented by John Goes).  Young Mathematicians Conference,  Ohio State (8/29/09):  pdf
• Biases in Moments of Elliptic Curve, 30th Automorphic Forms Workshop, Wake Forest University, March 8, 2016 pdf
• Rank and Bias in Families of Hyperelliptic Curves, Quebec-Maine Number Theory Conference, October 7, 2018.   pdf
• Rank and Bias in Families of Curves via Nagao's Conjecture, AMS Special Session on A Showcase of Number Theory at Undergraduate Institutions, JMM, Baltimore (1/17/19): pdf   33rd Automorphic Forms Workshop, Duquesne University (3/8/19): pdf
• Applications of Moments of Dirichlet Coefficients in Elliptic Curve Families, Murmurations in Arithmetic, ICERM, July 7, 2023: pdf

• Random Matrix Ensembles
• Eigenvalue Statistics for Ensembles of Random Matrices (especially Toeplitz Ensembles & Diophantine Obstructions). Probability and Ergodic Theory  Seminar, Ohio State (10/30/03): pdf   Boston University (6/7/04 expanded):   pdf     Brown University (9/15/04 expanded):   pdf
• On the probability that random graphs are Ramanujan. Expanders and Ramanujan Graphs: Construction and Applications, AMS National Meeting, San Diego (1/9/08):  pdf
• Eigenvalue statistics for Toeplitz ensembles. ICM Satellite Meeting in Probability & Stochastic Processes, Bangalore, India (August, 2010):   pdf
• The Limiting Eigenvalue Density for the Ensemble of m-Circulant Matrices (presented by Gene Kopp and Murat Kologlu, SMALL progress report (8/4/10):   pdf    Expanded Version: Young Mathematicians Conference,  Ohio State (8/28/10):  pdf
• Eigenvalue Statistics of Toeplitz and Block m-Circulant Ensembles (presented with Murat Kologlu), AMS Special Session on Random Processes, Worcester, MA (4/9/11):   pdf
• Painleve VI and Tracy-Widom Distributions in Random Graphs, Random Matrix Theory and Number Theory, AMS Special Session on Random Processes, Worcester, MA (4/9/11):   pdf
• Distributions of Eigenvalues of Weighted, Structured Matrix Ensembles (presented by Olivia Beckwith and Karen Shen), Young Mathematicians Conference, August 19, 2011. pdf
• Eigenvalue Statistics for Toeplitz and Circulant Ensembles, Analysis and Probability Seminar, UConn, March 2, 2012. pdf  Expanded version July 3, 2012 (with Gene Kopp, Murat Kologlu and Karen Shen) at the second Institute of Mathematical Sciences Asia Pacific Rim Meeting, Tsukuba, Japan. pdf (zipped files for slides here)
• Random Matrix Ensembles with Split Limiting Behavior} (joint with Peter Cohen, Yen Nhi Truong Vu and Roger Van Peski), International Conference of The Indian Mathematics Consortium in cooperation with American Mathematical Society, Banaras Hindu University, December 15, 2016. pdf  Joint Meetings of the AMS/MAA, Atlanta, January 5, 2017.  pdf

• Benford's Law (see the compilation page I made for my Bentley talk for links to papers and other resources) (see also colloquium talks)
• Benford's Law, Values of $$L$$-functions and the 3x+1 Problem. Boston College (10/19/04), University of Michigan (11/15/04), University of Arizona (1/11/06), Brown University (3/20/06): slides  paper.pdf.   Number Theory Special Session, AMS Sectional Meeting, WPI, Worcester, MA (4/25/09, 20min version):   pdf        Mathematica programs:  Just the 3x+1 Map      Benford Investigations        Some Numerical Simulations:  Data
• Benford's Law and Order Statistics. Brown University (2/1/06)   paper.pdf
• Poisson Summation and Benford's Law: From values of $$L$$-functions to the 3x+1 problem to products of random variables. University of Bristol (12/12/07); Workshop on the Theory and Applications of Benford's Law, Santa Fe, NM (12/18/07):  pdf
• The logarithmic link between economic, hydrologic, and seismic statistics (with Mark Nigrini), Workshop on the Theory and Applications of Benford's Law, Santa Fe, NM (12/17/07):
• Chains of distributions and Benford's Law (with Dennis Jang, Jung Uk Kang, Alex Kruckman and Jun Kudo), Workshop on the Theory and Applications of Benford's Law, Santa Fe, NM (12/17/07):  pdf
• Benford's Law: Why the IRS might care about the 3x+1 problem and ζ(s) (general introduction to the subject),  Western New England College (2/11/08):   pdf (untabbed version pdf); Smith College (10/7/08):   pdf;  Williams College, Bronfman Science Lunch (10/21/08, 20min version):   pdf    Central Connecticut State University (9/25/09):   pdf;   Bentley University (2/1/10):   pdf    (untabbed version: pdf; click here for links to papers and other resources)  Five Colleges Number Theory Seminar, Amherst (1/31/12, 50min version, more number theoretic):   pdf
• Theory and applications of Benford's law to fraud detection, or: Why the IRS should care about number theory! IRS (Boston Offices, 3/28/08):  pdf (untabbed version pdf). Williams College, SMALL Summer Colloquium (6/23/10, 40min version):   pdf.     Hampshire College Summer Program (7/14/2011) pdf.     Smith College Sigma Xi talk (11/15/11) pdf.   Mount Holyoke College (2/1/12)   pdf     Math 161, Brown University (11/12/12): pdf (video of the talk is available here)
• Theory and Applications of Benford's Law (Iranian Elections, Climate Data and the Weibull) (Tory Cuff and Allie Lewis presenters), SMALL report, August 3, 2010:  pdf
• Benford's law and dependent random variables (presented by Thealexa Becker), WIMIN Conference, Smith College (9/24/11) pdf
• Benford's Law, Values of $$L$$-Functions and the $$3x+1$$ Problem, or: Why the IRS cares about Number and Ergodic Theory, Ergodic Theory Seminar, University of Illinois, March 26, 2013.   pdf
• Benford's Law: Why the IRS cares about Algebra and Number Theory (and why you should too!),  SMALL Faculty Seminar, July 22, 2015.  pdf  SACNAS, Washington, DC, October 2015.  pdf  PME Induction Ceremony, Holy Cross, April 20, 2016.  pdf   Duke University, September 7, 2016.  pdf   Washington State University, April 21, 2017.   pdf
• Can math detect fraud? CSI: Mathematics: The natural behavior of numbers. Science Cafe, Northampton, September 26, 2016.   pdf    (Video: https://youtu.be/42vYLnY8tnA)
• Benford's Law and the 3x+1 Problem, or: Why the IRS cares about Discrete Dynamical Systems. AMS Northeastern Sectional, Discrete Dynamical Systems, April 22, 2018.   pdf
• Benford's Law: Why the IRS and others care about Number Theory (and you should too!), Cross-domain Conference on Benford's Law application, Stresa, Italy, July 10, 2019.   pdf   PIMS Distinguished Lecture, UNBC, November 14, 2019 (changed to 11/4/2020: video here: https://youtu.be/NSuXJRIFcXc).  pdf  Vassar College pdf  (video: https://youtu.be/fm3s-xjcnAE). UConn Math Club (9/16/20) pdf.  New York Number Theory Seminar (6/16/22)  pdf.  Texas State REU (7/1/22) pdf  University of Pittsburgh (11/11/22)   pdf
• Benford's Law and Random Integer Decomposition with Congruence Stopping Condition, MAA Southeastern Sectional Meeting, Special Session on the Theory of Integer Sequences, University of Tennessee, Saturday, March 16, 2024 (video here: https://youtu.be/FIjIFsmDk0c).   pdf.
• See also some of the talks in the Additive Number Theory section and the colloquium section.

• Additive Number Theory: More Sum Than Difference Sets, Ramsey Theory, Ramanujan Primes, ...
• When almost all sets are difference dominated. Analysis Seminar, Brown University (9/12/07)   paper.pdf; Williams College (9/12/08):   pdf    Wesleyan University (11/20/08):   pdf   Workshop on  Combinatorial and Additive Number Theory (CANT 2009), CUNY Graduate Center, New York, May 2009: pdf
• Explicit constructions of infinite families of MSTD sets (presented by Dan Scheinerman), Number Theory Session, Joint Mathematical Meetings, Washington, DC (1/05/09):   pdf
• The Circle Method and Class Groups of Quadratic Fields (Carlos Dominguez, presenter), SMALL report, August 4, 2010.   pdf    Expanded Version: Young Mathematicians Conference,  Ohio State (8/27/10):  pdf
• Constructing explicit families of generalized families of MSTD sets (with Sean Pegado and Luc Robinson), May 26, 2011 at CANT 2011: pdf
• Constructing Generalized Sum-Dominant Sets (presented by Geoff Iyer and Liyang Zhang), Young Mathematicians Conference, August 19, 2011. pdf; Maine-Quebec Number Theory Conference, October 2, 2011. pdf; May 23, 2012 at CANT 2012: pdf
• The Distribution of Generalized Ramanujan Primes (presented by Nadine Amersi and Ryan Ronan), Young Mathematicians Conference, August 20, 2011. pdf; May 24, 2012 at CANT 2012: pdf
• The Distribution of the Number of Missing Sums in Sumsets (presented by Oleg Lazarev), Young Mathematicians Conference, August 21, 2011. pdf.   May 23, 2012 at CANT 2012: pdf
• Most Sets are Balanced in Finite Groups (presented by Kevin Vissuet), Special Session on Additive and Combinatorial Number Theory, AMS Sectional, Akron, Ohio, October 21, 2012  pdf
• When Almost All Sets Are Difference Dominated, Number Theory Seminar, University of Illinois, March 25, 2013.   pdf
• When Almost All Generalized Sumsets Are Difference-Dominated (given by Ginny Hogan), CANT, May 21, 2013. pdf
• Coordinate Sum and Difference Sets of $$d$$-dimensional Modular Hyperbolas (given by Amanda Bower), CANT, May 21, 2013. pdf
• Sums and Differences of Correlated Random Sets (given by Thao Do), Garden State Undergraduate Math Conference, April 5, 2014. pdf
• Continued Fraction Digit Averages and Maclaurin's Inequalities, CANT, May 28, 2014. pdf (talk online here), Quebec-Maine Number Theory Conference, Sept 28, 2014 pdf   AMS Special Session on Continued Fractions, JMM 2015, January 12, 2015.  pdf
• MSTD Subsets and Properties of Divots in the Distribution of Missing Sums (with Victor Xu and Xiaorong Zhang), CANT May 26, 2016  pdf
• When almost all sets are difference dominated in Z/nZ (given by Adam Lott), Integers Conference, University of West Georgia, October 7, 2016.   pdf
• A geometric perspective on the MSTD question (given by Carsten Peterson), Integers Conference, University of West Georgia, October 7, 2016.  pdf
• Ramsey Theory over Number Fields, Finite Fields and Quaternions, CANT, May 26, 2017 pdf
• Within-perfect & near-perfect numbers (with Kevin Kwan), CANT May 22, 2018  pdf
• Phase Transitions in the Distribution of Missing Sums and a Powerful Family of MSTD Sets, Integers 2018, Augusta, Georgia, October 4, 2018.   pdf
• Recent progress in sumsets, generalized Schreier sets, generalized Zeckendorf decompositions, and prime and square-free walks (with Joshua Ackerman, Tudor Popescu, Zimu Xiang), CANT May 23, 2019
• Distribution of missing differences in diffsets (given by Fei Peng), CANT June 5, 2020  pdf
• Distribution of missing sums in correlated sumsets (given by Dylan King), CANT June 5, 2020  pdf
• Large sets are sumsets (given by Ben Baily and Henry Fleischmann), Combinatorial and Additive Number Theory, May 2022.  pdf
• Schreier multisets and the s-step Fibonacci sequences, Integers Conference, University of Georgia, May 18, 2023.

• Additive Number Theory: Zeckendorf Decompositions (images for Zeckendorf / gaps)
• Cookie Monster Meets the Fibonacci Numbers. Mmmmmm -- Theorems!  Workshop on  Combinatorial and Additive Number Theory (CANT 2010), CUNY Graduate Center, New York, May 2010: pdf (untabbed version pdf); Hampshire College Summer Program (expanded version, 7/15/10):   pdf; Smith College (1/28/11, 30 minute version):  pdf   Special Session on Undergraduate Research, Holy Cross, 4/9/10 (presented by Murat Kologlu)   pdf; expanded version from May 26, 2011 for CANT 2011: pdf  expanded version with gaps for Algebra Seminar, UConn (2/7/12)   pdf  AMS Special Session on Difference Equations, Washington, DC (4/27/12, 20 minutes) pdf    University of Michigan (11/30/17)  pdf Williams and Texas State REUs (7/8/20)  pdf
• From the Fibonacci Numbers to a Central Limit Type Theorem (presented by Yinghui Wang). SMALL report, August 4, 2010.  pdf   Expanded Version: Young Mathematicians Conference,  Ohio State (8/28/10):  pdf  Even more expanded version: Williams College Seminar October 1, 2010.   pdf
• Gaps between summands in generalized Zeckendorf decompositions (presented by Olivia Beckwith), Young Mathematicians Conference, August 19, 2011. pdf
• To Infinity and Beyond:  Gaps Between Summands in Zeckendorf Decompositions, May 22, 2012 at CANT 2012: pdf
• Distribution of Summands in Generalized Zeckendorf Decompositions (presented by Rachel Insoft and Philip Tosteson), AMS Sectional Meeting, Rochester, September 22, 2012: pdf  AMS Sectional Meeting, Rochester, September 22, 2012: pdf  Special Session on Additive and Combinatorial Number Theory, AMS Sectional, Akron, Ohio, October 21, 2012  pdf
• Distribution of summands in generalized Zeckendorf decompositions, AMS Session on Number Theory, I, Joint Meetings San Diego, January 9, 2013. pdf
• Mind the Gap: Distribution of Gaps in Generalized Zeckendorf Decompositions, CANT, May 21, 2013. pdf  Williams Math/Stats Faculty Seminar (9/12/13), Maine - Quebec Number Theory Conference (10/5/13), AMS Special Session on Difference Equations (10/12/13).  pdf  Expanded version dealing with Kentucky Sequence: 16th International Fibonacci Conference, Rochester, NY (7/25/2014): pdf

• Coin Flips, Fibonacci Numbers and Gaps! (given by Phil Tosteson), AMS Special Session on Difference Equations, March 29, 2014. pdf
• Introduction to Zeckendorf Decompositions, AIM, July 7, 2014; Progress Report Images July 9, 2014 (pdf); Final report July 11, 2014 (pdf).
• From Fibonacci Quilts to Benford's Law through Zeckendorf Decompositions, AMS Special Session on Difference Equations, JMM 2015, January 10, 2015.   pdf  CANT May 19, 2015.  pdf
• From the Kentucky Sequence to Benford's Law through Zeckendorf Decompositions, AMS Special Session on Difference Equations, Washington, DC, March 7, 2015.   pdf
• The Fibonacci Quilt Sequence (presented by Pari Ford), AMS Special Session on Difference Equations, Washington, DC, March 7, 2015.   pdf
• Convergence rates in generalized Zeckendorf decomposition problems (with Ray Li, Zhao Pan and Huanzhong Xu), CANT May 26, 2016  pdf
• Convergence Rates in Generalized Zeckendorf Decompositions (with Zhao Pan and Huanzhong Xu), 17th International Fibonacci Confernece, Caen, France (6/28/2016): pdf
• On Summand Minimality of Generalized Zeckendorf Decompositions (given by Chi Huynh, Carsten Peterson and Nhi Truong), AMS Contributed Paper Session on Undergraduate Research, JMM Atlanta 2017.   pdf
• Generalizations of Zeckendorf's Theorem to Two-Dimensional Sequences (with Joshua Siktar), AMS Special Session on Discrete Neural Networking and Applications, I, JMM, San Diego, January 11, 2018. pdf
• Distributions in Generalized Zeckendorf Decompositions (with Yujin Kim, Shannon Sweitzer, Eric Winsor and Jianing Yang), AMS Special Session on Discrete Neural Networking and Applications, I, JMM, San Diego, January 11, 2018.  pdf.
• Monovariants to Zeckendorf Decompositions and Games, The Eighteenth International Conference on Fibonacci Numbers and Their Applications, Dalhousie University, July 2, 2018.   pdf
• Gaps Of Summands of The Zeckendorf Lattice, presented by SMALL 2019 and Eureka 2018, 19th International Fibonacci Conference, July 21, 2020.
• Completeness of Positive Linear Recurrence Sequences, presented by SMALL 2020, 19th International Fibonacci Conference, July 21, 2020.
• Generalizing Zeckendorf's Theorem to non-constant coefficient recurrences, presented by Eureka 2020 and Polymath REU (pdf), 19th International Fibonacci Conference, July 22, 2020.
• Asymptotic Analysis For Lattice Walks Derived From Zeckendorf Decompositions, presented by CMU students and Eureka 2019, 19th International Fibonacci Conference, July 23, 2020.   pdf
• Generalizing Zeckendorf's Theorem to Homogeneous Linear Recurrences, presented by Thomas Martinez, 19th International Fibonacci Conference, July 23, 2020.
• The Generalized Bergman game (given by Faye Jackson and Luke Reifenberg), Combinatorial and Additive Number Theory, May 2022pdf
• Why I love Monovariants: From Zombies to Conway's Soldiers via the Golden Mean, 7th Number Theory Meeting - Torino, September 28, 2023.  pdf  Kansas State University, November 8, 2023: pdf  Western New England PME Induction Ceremony, April 26, 2024: pdf
• The theory of normalization constants and Zeckendorf decompositions, Combinatorial and Additive Number Theory 2024, Cuny Graduate Center, May 22, 2024.

• Additive Number Theory: Erdos Distance Problems (images for Zeckendorf / gaps)
• Classification of Crescent Configurations on Four and Five Points (given by Chi Huynh), Integers Conference, University of West Georgia, October 7, 2016. pdf  AMS-MAA-SIAM Special Session on Research in Mathematics by Undergraduates and Students in Post-Baccalaureate Programs, III, Joint Math Meetings, Atlanta, January 2017  (given by Becky Durst, Chi Huynh, Max Hlavacek)   pdf
• Crescent Configurations In Non-Euclidean Norms, (given by Dylan King and Cathy Wahlenmayer), Maine-Qu\'ebec Number Theory Conference, October 5, 2019.
• Angle variants of the Erdos distinct distance problem (given by Henry Fleischmann and Ethan Pesikof), Combinatorial and Additive Number Theory, May 2022.
• Erdos Distinct Angle Problems (given by Henry Fleischmann and Ethan Pesikoff),   Combinatorial and Additive Number Theory, May 2022.  pdf

• Computers, Dynamical Systems and Mathematics Education
• Computers in Undergraduate Education and Zeros of  Elliptic Curves. Minnesota (8/10/02): pdf   Expanded Version:    pdf
• Statistical Investigations as a Tool in Undergraduate Mathematics Research: Poster and Workshop Sessions
International Conference on Statistics Honolulu, Hawaii (6/5/03 and 6/7/03):  pdf
• NSF Workshop on Computation in Algebra, Number Theory and Combinatorics. Washington DC (9/21/02): ps  and  ps
• The Pythagorean Won-Loss Theorem: An introduction to modeling. Great Activities for an Introductory Statistics Class, AMS National Meeting, San Diego, (1/7/08):  pdf
• Workshop on Mathematicians in Mathematics Education, participant, Institute for Mathematics Education, Tucson, Arizona, March 20 - 22, 2008.
• Progress Report: Statistics in Function Fields, Sage Days 21, Seattle, Washington, May 27, 2010.   pdf
• Introduction to Matlab: IAS Women in Mathematics: May 18, 2011. Click here for files.
• Virus dynamics on star graphs (presented by Thealexa Becker), WIMIN Conference, Smith College (9/24/11) pdf; expanded version at AMS Special Session on Difference Equations, University of Maryland, March 29, 2014. pdf
• Why more is better: the power of multiple proofs, ATMIM Spring Conference, Assabet Valley Regional Technical High School, Grade 9 - 12 Session (3/23/13)   pdf
• From M&Ms to Mathematics, or, How I learned to answer questions and help my kids love math, ATMIM Spring Conference, Assabet Valley Regional Technical High School, Keynote Address (3/23/13)   pdf     HCSSiM, July 17++, 2013.   pdf; Dr. Philip O. Coakley Middle School, Norwood, MA, June 9, 2014.   pdf.   Maine-Quebec Number Theory Conference, October 3, 2015pdf  Math League, College of New Jersey, July 25, 2016 and July 20, 2017.   pdf   Prospective Days, Williams College, August 11, 2017.   pdf
• Why Cookies And M&Ms Are Good For You (Mathematically), Stuyvesant High School, May 9, 2014.   pdf (talk online here)
• YouTube University: The Benefits of Recording Lectures, Blended Learning Conference, May 22, 2014.  pdf  (talk online here)
• Challenges and Opportunities for Graduate School Bound Liberal Arts Students, AMS Committee on Education, Washington, DC, October 30, 2015.   slides pdf     handout pdf
• Building YouTube University Brick by Brick, AMS-MAA Special Session on Innovative Ideas in Enhancing Success in Mathematics Classes, Joint Meetings of the AMS-MAA, Seattle, January 6, 2015.  pdf
• Balancing responsibilities in academia, panelist at the 30th Automorphic Forms Workshop, Wake Forest University, March 7, 2016.
• Results and Research in REUs: Cookie Monster Meets the Fibonacci Numbers. Mmmmmm -- Theorems! Florida Institute of Technology, May 20, 2016.  pdf
• Springboards to Mathematics: From Zombies to Zeckendorf, Math League Summer Program, College of New Jersey, July 25, 2016.  pdf
• Portable Lecture Capture, LACOL Teaching with Tech 2017 Lightning Round, Vassar College, June 15, 2017.  pdf   (powerpoint slides here)
• Where's my remote? Shared upper level math courses across schools, LACOL 2017 Session 7, Vassar College, June 16, 2017.  pdf (video here: http://lacol.net/shared-math/)
• YouTube University: Shared upper level math courses across schools, AMS-MAA Special Session: Novel Methods of Enhancing Success in Mathematics Classes, Joint Mathematics Meeting, San Diego, January 2018.   pdf
• Where's the Remote? Upper-Level Math/Stats Hybrid Course Sharing for the Liberal Arts (with Jingchen (Monika) Hu),  EDUCAUSE Learning Initiative (ELI) Annual Meeting, New Orleans, January 30, 2018.   pdf
• Exploration into a Framework for Digitally Shared Courses (with Liz Evans, Lioba Gerhardi and Monika Hu), LACOL Workshop, Carlton College, June 1, 2018.
• From M&Ms to Modern Mathematics: Introduction to Plotting, Logarithms and Patterns, Williamstown Elementary School, October 1, 2018.   pdf
• The Explicit Sato-Tate Conjecture in Arithmetic Progressions, Quebec-Maine Number Theory Conference, October 7, 2018.   pdf
• Summer Data Science (online): By and for the liberal arts, panelist in discussion on an online class co-teaching, LACOL Data Science Workshop, June 6, 2019.
• YouTube University II: Shared upper level math courses across schools, Joint Math Meetings, AMS Special Session on Pedagogical Innovations That Lead to Successful Mathematics, Denver, Jan 16, 2020.   pdf (online: https://youtu.be/rjn1sn3WLZg)
• Extending P y t h a g o r a s, Williams College 3/9/20: pdf
• From Zombies to Fibonaccis: An Introduction to the Theory of Games, Michigan Math Circle, April 23 and 30,  2020.   pdf (part I)  pdf (part II)   NJ Math Camp, July 17, 2023.  pdf

• Engaging students in research in the covid pandemic, Cross Atlantic Representation Theory and Other Topics ONline (CARTOON), May 30, 2020.  pdf
• All I need to know about probability I learned from Darth Vader and James Bond, Hampshire College Institute for Summer Studies in Mathematics, August 3, 2020. (powerpoint  here, pdf here)
• Analyzing Virus Dynamics on k-level Starlike Graphs (with Akihiro Takigawa), Spring 2021 AMS Eastern Sectional Meeting: Special Session on Applications and Asymptotic Properties of Discrete Dynamical Systems: A Session in Honor of the Retirement of Orlando Merino.  pdf
• CUR-Goldwater Faculty Mentor Award, May 12, 2021, Expanded Version. https://youtu.be/NGS5mHJcnlQ (powerpoint  here, pdf here)
• Computational Thinking Modules: From Data to Results (through chocolate!), STANYS (Science Teachers of New York State) Conference: November 7, 2021: https://youtu.be/xYy_LAy-gHo (powerpoint  here, pdf here).
• The Fibonacci Sequence and Math Outreach (joint with Cameron and Kayla Miller, Anna Mello and her classes, and SMALL 2022), the 20th International Fibonacci Conference, Sarajevo, July 29, 2022: (powerpoint  here, pdf here).
• Modeling Beyond the Classroom: Linking Students and Industry, Integrating Math Modeling and Interdisciplinarity into Your Classroom, MathFest, August 5, 2022: https://youtu.be/G1ttDfUzaqA   (powerpoint  here, pdf here).  COMAP Contributed Paper Session: Integrating Modeling into Established Courses: Joint Math Meetings: Boston: Jan 7, 2023   (powerpoint  here, pdf here).
• From Zombies to Sports: An Introduction to the Theory of Games, Michigan Math Circle, April 23 and 30,  2020.   pdf (part I)  pdf (part II)   NJ Math Camp, July 17, 2023.  pdf
• AMS Expects that every Mathematician will do their ODEs: From the Battle of Trafalgar to Calculus (or Nelson to Newton), AMS Special Session on Modeling to Motivate the Teaching of Mathematics of Differential Equations JMM, San Francisco, January 3, 2024.  pdf (video here: https://youtu.be/rRBWahHdMS4  SIMIODE EXPO 2024: February 11, 2024.  pdf

• Colloquium / General Talks (mostly Random Matrix Theory and Number Theory)
• How the Manhattan Project helped us understand primes. Colloquium, University of Cincinatti (10/16/03) and Ohio State (10/1/03):  pdf. An alternate version (with appendices on Dirichlet $$L$$-Fns, Elliptic Curves and a bibliography): Colloquium, Colby College (3/8/05): ps pdf; tabbed version ps dvi.   Another alternate version  (with appendices on Dirichlet $$L$$-Fns, Random Graphs and a bibliography). Colloquium, University of Connecticut (3/24/05): ps   pdf; tabbed version ps dvi
• From Nuclear Physics to Number Theory: How the Manhattan Project helped us understand Primes: SUMS Conference, Brown University (2/12/05): ps  pdf; tabbed version ps  dvi  This is similar to the above colloquia, but aimed more at undergraduates.
• $$L$$-functions and Random Matrix Theory. Brown University (10/6/06). See  pdf  for a more extensive version.
• From the Manhattan Project to Number Theory: How Nuclear Physics Helps Us Understand Primes (20 minutes). Bronfman Science Lunch, Williams College (6/23/09): pdf (20 minute version) pdf (expanded version). Wellesley College (2/2/10):  pdf (25 minute version)
• Heuristics and Ballpark Estimates: From the 3x+1 problem to counting primes and birthdays: PROMYS, Boston University (7/28/09)
• Pythagoras at the Bat: an Introduction to Statistics and Mathematical Modeling: Wellesley (9/21/09):   pdf
• How low can we go? Lower order terms in CLTs from Benford's Law to Elliptic Curves (25 minute version). NES MAA Fall 2009 Meeting (11/21/09):   pdf   (no tab pdf)
• Great Expectations, or: Expect More, Work Less. Wellesley (2/3/10):   pdf
• The Riemann Hypothesis at 150: From Primes to Nuclei and Many Things Between. Williams College (11/18/09)  Blackboard talk, but see the following page for relevant papers on the subject.
• From the Manhattan Project to Elliptic Curves. Smith College (1/28/11)   pdf   Dartmouth College, January 28, 2013.  pdf   (no tab version: pdf)
• From Cookie Monster to the IRS: Some Fruitful Interactions between Probability, Combinatorics and Number Theory.  UNC Charlotte (2/1/11)   pdf
• Cookie Monster Meets the Fibonacci Numbers. Mmmmmm -- Theorems!  Pi Mu Epsilon Induction Ceremony, College of the Holy Cross (5/5/11)   pdf   Smith College (9/13/11)   pdf (click here for the talk) Amherst College (9/21/11) and Mount Holyoke College (10/5/11)   pdf    SUMS, Brown University (3/10/12; presented by Louis Gaudet, alternate 18 minute version emphasizing gaps)   pdf    Colby College (3/28/12)  pdf  Summer Science Lecture Series, Williams College (6/19/12, 20 minutes)   pdf;   Williams College (9/14/12),  Middlebury College  (9/28/12), Wesleyan College (10/19/12) and Brown University (11/12/12)   pdf  Expanded Version for Yale University with data for longest gap part (4/14/14): pdf (video here: http://youtu.be/5e6HsfxqVSE),  Yale University (with rectangle game) (2/23/24)  pdf (video here)

• Biases: From Benford's Law to Additive Number Theory via the IRS and Physics. SMALL Summer REU, Williams College (6/22/11)   pdf
• Number Theory and Random Matrix Theory Progress Report (Nadine Amersi, Thealexa Becker, Olivia Beckwith, Geoffrey Iyer, Oleg Lazarev, Karen Shen, Alec Greaves-Tunnell, Ryan Ronan, Liyang Zhang). SMALL End of Summer Progress Report, Williams College (8/2/11)   pdf (zipped file here). This work was also presented at a poster session. Poster 1 (RMT, Maass forms, Viruses), Poster 2 (Benford, MSTD, c-Ramanujan).
• From Random Matrix Theory to Number Theory, SMALL colloquium, July 25, 2012 (similar to Utah graduate talk).   pdf
• Number Theory and Probability: SMALL '13 Projects, Williams College, June 19, 2013.   pdf
• The Latke-Hamantaschen Debate: The Primacy of Three, Williams College, March 19, 2014.   pptx    pdf   (YouTube clip: http://www.youtube.com/watch?v=tt4_4YajqRM
• , Williams College, March 20, 2014 (supplemental lecture for multivariable calculus).
• Some Results on Low-Lying Zeros of L-Functions, Williams College, July 16, 2014 (SMALL colloquium).  pdf
• Why more is better: the power of multiple proofs, Hampshire College, July 31, 2014.  pdf
• He's just going through a phase: Miller's SMALL students and Phase Transitions, Williams College, October 10, 2014.  pdf
• From Fibonacci Quilts to Benford's Law through Zeckendorf Decompositions, Williams College, Science Talk, November 11, 2014.  pdf
• Why the IRS cares about the Riemann Zeta Function and Number Theory (and you should too!), Williams College talk to the faculty February 12, 2015 (http://youtu.be/JmBXZCbbwas, slides here), Carnegie Mellon 3/25/15 and Winona State University 3/30/15:  pdf
• Extending the Pythagorean Formula, Williams College (4/8/15):  http://youtu.be/idIHcgapMG4 (slides here).  Modified version (all slides, no blackboard: 20 minutes Williams Summer Science Talk): http://youtu.be/8HtABCG6ACg  (slides here). Expanded version (all slides, 50 minutes: Hampshire College Summer Studies in Mathematics, 7/28/2015):  (slides here) Washington State University (10/12/15) (see Hampshire College slides), Window on Williams (10/16/15).  pdf   Hampshire College (8-3-16).  pdf   Williams SMALL REU, July 26, 2017 and TCNJ Math Camp, July 29, 2017.   pdf   Williams March 9, 2020  https://www.youtube.com/watch?v=EH6PUS2OwUY&t=931s
• Success and/or Significance, A musician and mathematician discuss beauty, perfection, and faith in the liberal arts, Veritas forum, Williams College, April 14, 2016.  pdf   pptx (with videos)
• From the Manhattan Project to Elliptic Curves: Introduction to Random Matrix Theory, SMALL Faculty Talk, Williams College, July 27, 2016  pdf    SUMS, Brown University, March 18, 2017.  pdf. SMALL Faculty Talk, Williams College, July 5, 2017.  pdf  Analysis Seminar, Virginia Tech, April 6, 2018.  pdf.   SMALL Faculty Talk, Williams College, June 13, 2018.  pdf.   Yale University, October 8, 2018.   pdf   Math Club at U(M), January 21, 2021.  pdf  (video here: https://youtu.be/j4imqkJ7Eg8)
• Secrets of the Tax System with Steve Miller: Keep More of Your MOOLA:  Williams College 9/16/2016: (slides here)
• Egg Drop Mathematics: It's all it's cracked up to be: Math League Summer Program, July 17 and 29, 2017; July 14, 2019. University of Michigan, November 30, 2017. REU in Computational Statistics, UNC Greenesboro, July 10, 2023,  TCNJ Math Camp, July 18 and 25, 2023.  pdf

• From C to Shining C: Complex Dynamics from Combinatorics to Coastlines, Maritime Studies Program of Williams College and Mystic Seaport, Mystic, CT, October 20, 2017.   pdf  (video here: https://youtu.be/TMILk79N_Bs) Michigan Math Circle, April 30, 2020.  pdf   Hampshire College 8/8/2022 (video: https://youtu.be/GO3EbWUesBQpdf
• SNAP DECISIONS: Management Lessons from Legos, Lever, North Adams, January 25, 2018.  ppt  pdf
• From Zombies to Fibonaccis: An Introduction to the Theory of Games. TCNJ Math Camp, July 16 and 29 (Part I) and 17 and 30 (Part II), 2018.   pdf   Hampshire College, July 24, 2018.  pdf
• The German Tank Problem: Math/Stats At War, University of Connecticut Math Department Awards Dinner, April 26, 2019.   pdf   Hampshire College, July 8, 2019.   pdf (Hampshire College talk: https://youtu.be/IOcI2c3QQbw)   Yale University, September 27, 2019.   pdf (video: https://youtu.be/nZJUbwC_bTw).  The Christie Lecture, NES/MAA Fall 2019 Meeting, 11/22/2019.   pdf  (video: https://youtu.be/I3ngtIYjw3w).  PROMYS August 7, 2020 pdf  UNC Greensboro REU, June 9, 2022 pdf
• Inrtoduwtion to Erorr Dwtetcion and Czorrectmon, TCNJ Math Camp, July 14, 2019. MathFest, August 1, 2019.   pdf  (video: https://youtu.be/RPWMAqPhv6w); 50 minute video from class: https://youtu.be/YOs8QYU3Wq8   Hampshire College, June 30, 2021. University of Michigan, October 1, 2021.  pdf (video: https://youtu.be/tuL0K1XtGBE)
• VCTAL CRYPTOGRAPHY LECTURES: June 19-20, 2019: Burlington, VT: See VCTAL Lectures Burlington 2019: Introduction to cryptography, error detection / correction.
• Of the Origin and Design of Eigenvalues in General, with Concise Remarks on the English Constitution. Dearborn REU (6/24/19) and SMALL REU (7/3/19). pdf
• Why I love Monovariants: From Zombies to Conway's Soldiers via the Golden Mean. Math Club, University of Michigan, September 10, 2020.   pdf  (video: https://youtu.be/LWWc4q3e-RY) Williams College, October 13, 2021.  pdf (video: https://youtu.be/b6CrLgHawm8).  Baruch College, August 4, 2022.   pdf
• Lessons I've learned (many the hard way), Baruch REU July 6, 2021 and Polymath Jr REU July 8, 2021. Williams College (10/13/21)  pdf (video: )
• From Monovariants to Zeckendorf Decompositions and Games, and Random Matrix Theory, Williams College (7/14/21) and Texas Tech (7/29/21). pdf (video: https://youtu.be/Kayru_V75V8)
• Classifying GOATS (like Brady, Russell and Ruth) by their tails (joint with Rick Cleary), MathFest August 5, 2021 pdf
• Connections of Class Numbers to the Group Structure of Generalized Pythagorean Triples (with Thomas Jaklitsch, Thomas Martinez, and Sagnik Mukherjee), International Conference on Class Groups of Number Fields 2021 pdf  https://youtu.be/BbeFny-C5sU
• Why I love Monovariants: From Zombies to Conway's Soldiers to Fibonacci Games, AMS Eastern Sectional, UMass Amherst 10/1/22    pdf  (video from version given in Math 409: 9/26/33: https://youtu.be/p2-QfjgitQ8University of Pittsburgh 11/10/22 pdf    University of Maryland 3/29/23 pdf  (talk online: https://youtu.be/n5I39r_CyuA)   YPMD III, 17-1/17 mod 10, 17*119, Math Camp (New Jersey) 7/25/23, Williams College 7/26/23   pdf
• Problem Child: Using Problems as a Springboard to Research, MathFest: Problem Creation and Problem Solving Session, August 5, 2023   pdf
• Math/Stat Thesis Showcase, Williams College, April 12, 2024   pdf

• Baseball / Sabermetrics Talks
• The Pythagorean Won-Loss Formula in Baseball (An Introduction to Statistics and Modeling) (60 minute version) Brown University (9/28/05) and (12/7/05): slides(tab) slide(no tab)  paper_pdf. Shorter 15 minute version: 2006 Hudson River Undergraduate Mathematics Conference (4/8/06): slides(tab)   slides(no tab)Pythagoras at the Bat: An Introduction to Statistics and Modeling (20 minute version): Society For American
• Baseball Research, Boston Meeting, Boston, MA (5/20/06): slides(tab)   slides(no tab)   paper_pdf.   Williams College (40 minute version, 1/15/08):   pdf.   Holy Cross (50 minute version, 2/7/08):  pdf. Western New England College (40 minute version, 1/15/08):   pdf.   Connecticut Smoky Joe Wood SABR Chapter, Hamden, CT (30 minute version, 2/16/08)   pdf.    PROMYS Program, Boston University (40 minute version, 7/25/08):   pdf.    Bennington College (2/27/09):   pdf      Hampshire College (7/22/09):   pdf        Wellesley (9/21/09):   pdf     Awards Night, University of Connecticut (4/12/10):   pdf        Virginia Tech (3/28/11):  pdf       UMass Amherst (10/19/11) and Fitchburg State University (11/3/11):   pdf     Boston College (3/29/12)  pdf  Science Days  talk to Prospective Williams Students (8/15/14) pdf  and 8/12/16 pdf  and 8/10/18  pdf University of Vermont (12/2/16, with an intro on undergraduate research)  pdf  Developer Thursdays at Cloud85 (6/8/17):  pdf   University of Michigan (11/29/17):  pdf  San Francisco (to Williams Northern California Alumni Society, expanded version with xSLG) (1/4/24) pdf   Siena College (head-to-head added) (2/8/24): pdf  Western New England (head-to-head expanded): (4/26/24):  pdf

• Pythagoras on the Ice: Hockey Conference, Babson (10/1/16):   pdf

• Webpages with talks / posters by students and colleagues at conferences
• Joint Meeting of the AMS/MAA, 2012: Boston, January 4 to 7, 2012: click here for a webpage with all the talks, or click here for notes on the Panel on Undergraduate Research.
• Young Mathematicians Conference: Ohio State, July 27-29, 2012: click here for a webpage with all the talks.
• SMALL 2012 posters: Poster 1 (Gaps, Phase Transitions)        Poster 2 (RMT, Maass)
• SMALL 2012: end of summer talk, Williams College, August 7, 2012.
• Joint Meetings of the AMS/MAA, 2013: San Diego, January 9 to 12, 2013: click here for a webpage with all the talks.
• SMALL 2013: UMass Amherst 7/30/13    Williams 7/31/13    YMC August 2013: Click here for talks and posters.
• AMS Special Session on Difference Equations: Baltimore 2014: homepage for session, including links to talks available on YouTube.
• 2014 SMALL PANTHers Group: (Projects supervised with Caroline Turnage-Butterbaugh, Nathan McNew and Ben Weiss)
• Biases in Elliptic Curve Families (Blake Mackall, Christina Rapti, Karl Winsor): Yale REU Conference, July 25, 2014: pdf
• A Benford Walk Down Wall Street (Xixi Edelsbrunner, Karen Huan, Blake Mackall, Jasmine Powell, Madeleine Weinstein): Yale REU Conference, July 25, 2014: pdf
• Complex Ramsey Theory (Andrew Best, Karen Huan, Nathan McNew, Jasmine Powell, Kimsy Tor, Madeleine Weinstein): Yale REU Conference, July 25, 2014: pdf
• Large gaps between zeros of GL(2) L-functions (Owen Barrett, Brian McDonald, Patrick Ryan, Karl Winsor): Yale REU Conference, July 25, 2014: pdf (talk),  pdf (poster)
• Benfordness of Zeckendorf Decompositions (Andrew Best, Patrick Dynes, Xixi Edelsbunner, Brian McDonald, Kimsy Tor and Madeleine Weinstein): 16th International Conference on Fibonacci Numbers and Their Applications, July 25, 2014: pdf     Fall Southeastern Sectional Meeting of the AMS, Special Session on Difference Equations, March 7, 2014: pdf
• Cookie Monster Meets the Fibonacci Numbers --- Mmmm, Theorems! (Andrew Best, Patrick Dynes, Xixi Edelsbunner, Brian McDonald, Kimsy Tor and Madeleine Weinstein): 16th International Conference on Fibonacci Numbers and Their Applications, July 25, 2014: pdf
• 2014 Quebec-Maine Number Theory Conference
• SMALL 2015
• UConn REU Conference: A Ramsey Theoretic Approach to Function Fields and Quaternions (Megumi Asada, Sarah Manski), July 28, 2015.  pdf
• Large Gaps Between Zeros of L-Functions Associated to GL(2) Cusp Forms (given by David Burt & Blaine Talbut), Maine-Quebec Number Theory Conference, October 3, 2015. pdf
• A Ramsey Theoretic Approach to Finite Fields and Quaternions (given by Sarah Manski), Maine-Quebec Number Theory Conference, October 3, 2015. pdf
• Biases in Moments of Satake Parameters and Models for $L$-function Zeros (with Kevin Yang), Maine-Quebec Number Theory Conference, October 3, 2015. pdf
• From M\&Ms to Mathematics, or, how I learned to answer questions and help my kids love math (joint with Cam and Kayla Miller), Maine-Quebec Number Theory Conference, October 3, 2015. pdf (see also https://www.youtube.com/watch?v=BXVRxLk8PKs&feature=youtu.be )
• SMALL 2016 and Carnegie Mellon 2016
• Williams College Summer Science Poster Session (if presented at Ohio State as well, just listed there) and/or Williams Summer REU Conferencce
• RMT Poster: Checkerboard Matrices and Limiting Spectral Distributions: Peter Cohen, Max Hlavacek, Carsten Sprunger, Paula Burkhardt, Kevin Yang,
Jonathan Dewitt, Nhi Truong, and Roger Van Peski
• Zeckendorf Poster: Summand Minimality of Generalized Zeckendorf Representations of Non-Negative Linear Recurrence Relations: Katherine Cordwell, Max Hlavacek, Ngoc Yen Chi Huynh, Carsten Peterson, and Yen Nhi Truong Vu
• Distance Talk: Optimal point sets determining few distinct triangles: Alyssa Epstein and Adam Lott: Williams College REU Conference: July 29, 2016
• Distance Poster: Classification of All Crescent Configurations on Four and Five Points: Rebecca Durst and Magda Hlavacek
• Young Mathematicians Conference: Ohio State August 19-21, 2016 (the posters were also presented at Williams College)
• Integer Complexity Poster: Some Bounds on Integer Complexity: Katherine Cordwell and Aaditya Sharma
• MSTD Poster: When almost all sets are difference dominated in $$\mathbb{Z}/n\mathbb{Z}$$: Adam Lott
• $$L$$-Functions Poster: Second Moments of Satake Parameters of Convolutions of Families of $$L$$-functions: Andrew Kwon
• Zeckendorf Talk: A Collection of Central Limit Type Theorems in Generalized Zeckendorf Decompositions: Ray Li
• Distance Talk: Classification of All Crescent Configurations on Four and Five Points: Rebecca Durst and Magda Hlavacek
• RMT Talk: Deviations from large eigenvalues of a special matrix ensemble: Carsten Sprunger and Peter Cohen
• $$L$$-Functions and RMT Talk: Extending agreement in the Katz-Sarnak Density Conjecture: Peter Cohen and Carsten Sprunger
• $$L$$-Functions Talk: The Langlands Program: Beyond Endoscopy: Oscar Gonzalez and Chung Hang Kwan (paper here)
• Zeckendorf Talk: On Summand Minimality of Generalized Zeckendorf Decompositions: Katherine Cordwell and Magda Hlavacek
• Number Theory Talk: Near-perfect, within-perfect, and order-a-abundant numbers: Adam Lott and Chung Hang Kwan
• SMALL 2017
• SMALL 2018 (plus CMU)
• (Maria R Ross and Casimir M Kothari), Young Mathematicians Conference, Columbus, Ohio, August 10, 2018. pdf
• (Madeleine L Farris), Young Mathematicians Conference, Columbus, Ohio, August 10, 2018. pdf
• (Mengxi Wang and Lily Shao), Young Mathematicians Conference, Columbus, Ohio, August 10, 2018. pdf
• (Noah Luntzlara and Hunter Wieman), Young Mathematicians Conference, Columbus, Ohio, August 11, 2018. pdf
• (Ben C Logsdon and Trajan A Hammonds), Young Mathematicians Conference, Columbus, Ohio, August 11, 2018. pdf
• (Hung Viet Chu and Lily Shao),  Young Mathematicians Conference, Columbus, Ohio, August 11, 2018. pdf
• (Joshua Siktar), Young Mathematicians Conference, Columbus, Ohio, August 12, 2018.
• (poster; Mengxi Wang and Noah Luntzlara), Young Mathematicians Conference, Columbus, Ohio, August, 2018. pdf
• (poster; Trajan A Hammonds and Casimir M Kothari),  Young Mathematicians Conference, Columbus, Ohio, August, 2018. pdf
• SMALL 2019
• Erdos Distance Problem
• Crescent Configurations In Non-Euclidean Norms Speakers: Sara Fish, Dylan King, Catherine Wahlenmayer, Conference for New England REU. 7/23/19.   pdf  Young Mathematicians Conference, August 9, 2019   pdf   Maine-Qu\'ebec Number Theory Conference, October 5, 2019.
• Convolutions
• Extensions of Autocorrelation Inequalities with Applications to Additive Combinatorics, Young Mathematicians Conference, August 10, 2019   pdf
• L-functions
• Zeros of L-Functions near the Central Point and Optimal Test Functions Speakers: Charles Devlin, Conference for New England REU. 7/23/19.   pdf    Young Mathematicians Conference, August 9, 2019   pdf   Maine-Qu\'ebec Number Theory Conference, October 5, 2019.   pdf
• MSTD
• Distribution of Missing Sums in Correlated Sumsets Speakers: Thomas Martinez, Dylan King and Chenyang Sun, Conference for New England REU. 7/23/19.   pdf    Young Mathematicians Conference, August 10, 2019.   pdf    Poster at Harvy Mudd September 2019.   pdf    Shenandoah Undergraduate Mathematics and Statistics Conference, September 21, 2019  pdf
• Random Matrix Theory
• ABBA and the Random Matrix Discotheque Speakers: Keller Blackwell and Wanqiao Xu (Joint work with Neelima Borade, Charles Devlin VI, Renyuan Ma, and Leticia Mattos da Silva), Conference for New England REU. 7/23/19.   pdf  Joint Math Meetings, Denver, January 15, 2020.   pdf
• Spies and Traitors: Random Matrix Kaleidoscopes and their Turncoat Eigenvalues Speakers: Neelima Borade and Renyuan Ma, Conference for New England REU. 7/23/19.   pdf    Young Mathematicians Conference, August 10, 2019.   pdf   Poster at the Joint Mathematics Meetings, Denver January 17, 2020   pdf
• When Bands Play in Random Matrix Theory, Young Mathematicians Conference, August 10, 2019.   pdf  (poster)  pdf  (talk)
• Zeckendorf
• Generalizing Zeckendorf's Theorem to Homogeneous Linear Recurrences Speakers: Clayton Mizgerd, Thomas Martinez and Chenyang Sun, Conference for New England REU. 7/23/19.   pdf;  20th International Fibonacci Conference, July (pre-recorded), 2022.
• Fibonacci Quilt Game Speakers: Alexandra Newlon, Neelima Borade, Annie Xu, Catherine Wahlenmayer, Conference for New England REU. 7/23/19.   pdf. Poster at YMC at Ohio State: Aug 2010: pdf  (zipped files here Women in Mathematics in New England, September 21, 2019.   Women in Mathematics in New England, September 21, 2019.     pdf    Undergraduate Mathematics Symposium, University of Illinois  (11/2/19).     pdf    JMM Poster, January 2019.   pdf
• Distribution of gaps in Zeckendorf Decompositions from d-dimensional Lattices: Neelima Borade and Annie Xu, Young Mathematicians Conference, August 10, 2019.   pdf
• SMALL / POLYMATH 2020
• Erdos Distance Problem
• Tinkering with Lattices: A New Take on the Erdos Distance Problem (Elena Kim, Fernando Trejos Suarez, Jason Zhao), Young Mathematicians Conference, August 2020. https://youtu.be/vP9cqGTwQcU. Also Quebec-Maine Number Theory Conference, September 26, 2020.
• MSTD
• Constructions of Generalized MSTD Sets in Higher Dimensions (Elena Kim, John Lentfer, John Haviland, Phuc Lam, Fernando Trejos Suarez), Young Mathematicians Conference, August 2020. Video: https://youtu.be/znYNJYFgE48
• More Sums Than Differences Sets in Finite Non-Abelian Groups (John Haviland, John Lentfer, Elena Kim, Phuc Lam, Fernando Trejos Suarez), Young Mathematicians Conference, August 2020. https://youtu.be/_K9KoDVlv1Q
• Optimal Test Functions
• Determining optimal test functions for 2-level densities (Ela Boldyriew, Fangu Chen, Jason Zhao), Young Mathematicians Conference, August 2020. https://youtu.be/2sqlbz06J1U Quebec-Maine Number Theory Conference, September 26, 2020 (Jason Zhao):
• Prime Walks
• Prime Walks to Infinity in Z[sqrt(2)] (Daniel Sarnecki and Bencheng Li), Northeast REU Math Conference and Young Mathematicians Conference, August 2020. Video: https://youtu.be/cXnM0E-11qg; also PAJAMAS September 20, 2020: pdf  (video here)
• Walking to Infinity Along Some Number Theory Sequences (Tudor Popescu, Saam Rasool, Ploy Wattanawanichkul).  PAJAMAS September 19, 2020: pdf (video here)
• RMT
• Split limiting behavior of random matrices with prescribed discrete spectra (Yuxin Lin, Jiahui Yu, Fangu Chen), Young Mathematicians Conference, August 2020. https://youtu.be/7fg5ub5j7uI
• Virus Propagation
• Extending Virus Dynamics to k-level Star-Like Graphs (Akihiro Takigawa, Jack Murphy, Rodrigo Bravo), Young Mathematicians Conference, August 2020. https://youtu.be/vyuYEgQcchY
• Zeckendorf
• Juggling Coefficients in Complete Recurrent Sequences (Ela Boldyriew, Phuc Lam, John Lentfer), Young Mathematicians Conference, August 2020. https://www.youtube.com/watch?v=Au4lKJlthZ4&feature=youtu.be
• Analytic Approaches to Completeness of Generalized Fibonacci Sequences (Fernando Trejos, John Lentfer, John Haviland, Ela Boldyriew, Phuc Lam), Young Mathematicians Conference, August 2020. https://www.youtube.com/watch?v=R_PYpJpb9wU&feature=emb_logo
• Bounding the Zeroing Algorithm: A Tool for Investigating Linear Recurrence Relations (Jack Murphy), Young Mathematicians Conference, August 2020.s://youtu.be/j0npXDk4KGI
• Zeckendorf Games (Kevin Ke, Carl Ye, Vashisth Tiwari), Northeast REU Math Conference and Young Mathematicians Conference, August 2020. https://www.youtube.com/watch?v=usOXOlY0tlE
• Juggling Coeffcients in Complete Recurrent Sequences (given by Elzbieta  Boldyriew, John Haviland, Phuc Lam, John Lentfer and Fernando Trejos Suarez), CANT 2021, 5/26/21.  pdf (video here)
• SMALL / POLYMATH 2021
• Benford's Law
• Benfordness of the Riemann Mapping Function for the Reciprocal of the Mandelbrot Set (given by Filippo Beretta, Jesse Dimino, Weike Fang), Young Mathematicians Conference, Ohio State, August 2021.
• Erdos Distance Problems
• Thresholds for the Existence of Similar Area Configurations (given by Ben Bailey and Arian Nadjimzadah), Young Mathematicians Conference, Ohio State, August 2021.
• Extending Erdos Distinct Distance Problems to Angles (given by Henry Fleischmann Hongyi Hu), Young Mathematicians Conference, Ohio State, August 2021.  pdf
• Erdos Distinct Distance Problem (given by Henry Fleischmann and Ethan Pesikoff), AMS Special Session on Distance Problems in Continuous, Discrete and Finite Field Settings, Joint Math Meetings, Jan 7, 2023.
• Fibonacci/Zeckendorf
• Complexity of the Zeckendorf Graph Game (given by Ben Baily, Faye Jackson, Ethan Pesikoff), Young Mathematicians Conference, Ohio State, August 2021.
• A Stochastic Central Limit Theorem and Applications to Integer Decompositions (given by Ben Bailey, Alicia Smith-Reina, Yingzi Yang), Young Mathematicians Conference, Ohio State, August 2021.
• The Bergman Game (given by Faye Jackson, Ethan Pesikoff, Luke Reifenberg), Young Mathematicians Conference, Ohio State, August 2021.  20th International Fibonacci Conference, July 26, 2022.
• Winning Strategy of Two-Player, Multiplayer and Multialliance Generalized Zeckendorf Game (given by ), Young Mathematicians Conference, Ohio State, August 2021.
• Sums of Reciprocals of Recurrence Relations (given by Sophia Davis, Alicia Reina Smith and Eliel Sosis), 20th International Fibonacci Conference, July 28, 2022. https://youtu.be/jfaS-3pqi_k
• General Number Theory
• Reducibility of Sets in Generalized Settings (given by Justine Dell, Henry Fleischmann, Faye Jackson), Young Mathematicians Conference, Ohio State, August 2021.  pdf
• Extending Support in calculating the n-level density of low lying zeros of families of L-functions (given by Justine Dell, Simran Khunger, Alexander Shashkov, Stephen Willis), Young Mathematicians Conference, Ohio State, August 2021. Maine-Quebec Number Theory October 5, 2021. pdf  Upstate Number Theory Conference, Union College, October 24, 2021.   pdf
• One-level density of a family of L-functions over function fields (given by Dang Dang, Hari Iyer, Sanford Lu), Young Mathematicians Conference, Ohio State, August 2021.
• Prime walk (Walking to Infinity Along Some Number Theory Sequences) (given by Fei Peng, Tudor Popescu), Young Mathematicians Conference, Ohio State, August 2021.
• A Novel Generalization of Diophantine $m$-tuples in Finite Fields (given by Arjun Nigam, Kyle Onghai, Dishant Saikia, Lalit Sharma), Young Mathematicians Conference, Ohio State, August 2021.
• Random Matrix Theory
• Closed form densities for the limiting spectral measure of random circulant Hankel matrices (given by Teresa Dunn, Henry Fleischmann, Alexander Shashkov), Young Mathematicians Conference, Ohio State, August 2021.  pdf
• SMALL / POLYMATH / OTHER 2022
• Benford's Law
• Benfordness of lower-dimensional spaces resulting from hyper-box fragmentation (given by Livia Betti and Zoe McDonald), Young Mathematicians Conference August 14, 2022.  pdf
• Benfordness of measurements resulting from box fragmentation (given by Livia Betti and Zoe McDonald), The International Conference on Advances in Interdisciplinary Statistics
and Combinatorics, October 8, 2022.  pdf
• A New Benford Test for Clustered Data with Applications to American Elections (given by Katie Anderson), International Conference on Advances in Interdisciplinary Statistics and Combinatorics, October 8, 2022. pdf
• CGDS
• Distinct Angles and Angle Chains in Three Dimensions (given by Ruben Ascoli and Jacob Lehmann Duke), Young Mathematicians Conference August 14, 2022. pdf (poster at williams: pdf)
• Learning Spheres and Chains in F_q^d (given by Wyatt Milgrim and Ryan Jeong), Young Mathematicians Conference August 14, 2022.    pdf  Symposium for Undergraduate Mathematics Research (SUMR), SUNY New Paltz, September 10, 2022. pdf
• Distinct Angles and Angle Chains in $\textbf{R}^3$} (given by Ruben Ascoli), AMS Special Session on Distance Problems in Continuous, Discrete and Finite Field Settings, Joint Math Meetings, Jan 7, 2023.  pdf
• VC-Dimension and Distance Chains in F_q^d (given by Wyatt Milgrim), AMS Special Session on Distance Problems in Continuous, Discrete and Finite Field Settings, Joint Math Meetings, Jan 7, 2023.  pdf
• Generalized German Tank Problem
• Generalizing the German Tank Problem: Math/Stats at War! (given by Anthony Lee), AISC Conference at UNC Greensboro, October 8, 2022.  pdf
• Fibonacci/Zeckendorf
• Continuing Analysis of the Zeckendorf Game (given by SMALL 2022), 20th International Fibonacci Conference, July 28, 2022.   pdf
• Generalized (c-k)-nacci Zeckendorf Game (given by Carl Ye), 20th International Fibonacci Conference, July (pre-recorded), 2022.       pdf
• Generalizing Minimality Properties of Far-Difference Fibonacci Decompositions (given by Andrew Keisling and Jacob Lehmann), Young Mathematicians Conference August 13, 2022.
• On Zeckendorf Related Partitions Using the Lucas Sequence (given by David Luo), 20th International Fibonacci Conference, July 28, 2022.  pdf
• Random and Maximal Lengths of Zeckendorf Games (given by Guilherme Dantas and Prakod Ngamlamai), Young Mathematicians Conference August 14, 2022.   pdf
• S-Legal Index Difference Decompositions (given by SMALL 2022), 20th International Fibonacci Conference, July 28, 2022.    pdf and Joint Math Meetings January 2023   pdf (and MASON VI, March 18, 2023).
• Short-Range and Random Differences in the Number of Summands of Zeckendorf Decompositions (given by SMALL 2022), 20th International Fibonacci Conference, July 25, 2022.
• Short-Range Differences of the Number of Summands of Zeckendorf Decompositions (given by Guilherme Dantas, Xuyan Liu and Jack Miller, Young Mathematicians Conference August 14, 2022.  pdf
• The Far Difference Game (given by SMALL 2022), 20th International Fibonacci Conference, July 25, 2022.     pdf
• The Far Difference Game (given by SMALL 2022), Young Mathematicians Conference, August 14. 2022, pdf
• Walking to Infinity on the Fibonacci Sequence (given by Nawapan Wattanawanichkul), 20th International Fibonacci Conference, July (pre-recorded), 2022.     pdf
• The Accelerated Zeckendorf Game (given by Ajmain Yamin), Hunter College Math Colloquium, March 16, 2023. pdf
• L-Functions
• An alternative method for calculating Bessel integrals appearing in L-function zero statistics (given by Astrid Lilly and Santiago Velazquez), Young Mathematicians Conference, August 13, 2022.  pdf
• Bounding ranks of cuspidal newforms through excised orthogonal ensembles (given by Astrid Lilly and Xuyan Liu), Young Mathematicians Conference, August 13, 2022.    pdf
• An excised orthogonal model for families of cusp forms (Andrew Keisling, Xuyan Lu, Annika Mauro Zoe McDonald, Santiago Miguel Jack Miller), Quebec-Maine Number Theory Conference, October 15, 2022.  pdf ( video here: https://youtu.be/d_FOSmou9mk )
• Generalized harmonic estimates for the n-level density of L-functions (given by Annika Mauro and Jack Miller), Young Mathematicians Conference August 13, 2022.   pdf
• Extending the support of 1- and 2-level densities for cusp form L-functions under square-root cancellation hypotheses (Annika Mauro and Jack Miller), Quebec-Maine Number Theory Conference, October 15, 2022.  pdf  (video here: https://youtu.be/CDwHaLM7umE )
• MSTD
• Binomial Sets Under Z-Linear Forms (Ryan Jeong), Young Mathematicians Conference, August 16, 2023.
• Sum and Difference Sets in Semidirect Products of Groups (given by Matthew Phang and Andrew Keisling), Young Mathematicians Conference August 13, 2022.  pdf
• Sum and Difference Sets in Generalized Dihedral Groups (given by Ruben Ascoli), Midwest Conference on Combinatorics and Combinatorial Computing, October 22, 2022.   pdf  CANT 2023  pdf
• On the Relative Sizes of Complements of Generalized Sumsets (given by Ryan Jeong), The 21st International Conference on Random Structures and Algorithms, June 16, 2023.   pdf
• Polymath Jr REU
• Avoiding 3-term Geometric Progressions in Non-Commutative Settings (Polymath Ramsey Group), Polymath REU Conference, August 13, 2022. pdf
• Linear Recurrences of Order at Most Two in Nontrivial Divisors (given by Liyang Shen), CANT 2023, May 23, 2023.  pdf
• On Some Observations about a prime factorization sequence called F-palindromes (given by Chris Bispels and Garam Choi), AMS Special Session on Polymath Jr: Mentoring and Learning, Joint Math Meetings, Jan 7, 2023. pdf
•  A Characterization of Prime $v$-palindromes (given by Muhammet Boran and Daniel Tsai), CANT 2023, May 26, 2023.   pdf
• SMALL / POLYMATH / OTHER 2023

• Benford's Law (SMALL)

• Generalized stick fragmentation and Benford's Law (Xinyu Fang and Maxwell Sun), Young Mathematicians Conference, August 16, 2023.  pdf

• Diophantine Equations and Number Theory (Polymath Jr)

• On a pair of Diophantine Equations (S. U. , H. V. Chu, J. Liu, G. Luan, R. Marasinghe and S. J. Miller), Polymath Jr Conference, August 13, 2023.  pdf  Joint Math Meetings, AMS Special Session on Polymath Jr, January 6, 2024.  pdf   Combinatorial and Additive Number Theory: May 22, 2024: pFIXdf

• Power Sums of Primes in Arithmetic Progression (Muhammet Boran, Yildiz, John Byun, Zhangze Li, Steven Joel Miller and Stephanie Reyes), Joint Math Meetings, AMS Special Session on Polymath Jr, January 6, 2024.  pdf

• Sum of Consecutive Terms of Pell and Related Sequences (Alexander Gong), Young Mathematicians Conference: August 2023.

• Fibonacci Numbers

• Fixed Points in the Fibonacci Sequence (given by Amanda Verga), Poster Session, Joint Mathematics Meetings, San Francisco, January 2024. pdf
• Dynamics of the Fibonacci Order of Appearance Map (given by Amanda Verga), Contributed Talk, Joint Mathematics Meetings, San Francisco, January 2024. pdf

• L-Functions (SMALL)

• Biases in Second Moments of Elliptic Curves (Zoe Batterman and Aditya Jambhale), Young Mathematicians Conference, August 16, 2023.   pdf

• Biases in Second Moments of Elliptic Curves (Aditya Jambhale and Akash L. Narayanan), Maine-Quebec Number Theory Conference, September 30, 2023.   pdf

• Modeling the Vanishing of L-functions at the Central Point (Zoe Batterman and Akash L. Narayanan), Young Mathematicians Conference, August 16, 2023.

• Modeling the Vanishing of L-functions at the Central Point (Zoe Batterman and Chris Yao), Maine-Quebec Number Theory Conference, October 1, 2023.   pdf

• MSTD (SMALL)

• Limiting Behavior in Missing Sums of Sumsets (poster: Aditya Jambhale, Rauan Kaldybayev, Chris Yao), Williams College Science Poster Session: August 4, 2023: pdf

• Limiting Behavior in Missing Sums of Sumsets (Rauan Kaldybayev), Young Mathematicians Conference: August 16, 2023: pdf  Combinatorial and Additive Number Theory: May 22, 2024: pdf

RESEARCH INTERESTS:  Analytic Number Theory, Random Matrix Theory, Probability (zeros and n-level statistics for families of $$L$$-functions, especially families of elliptic curves with rank over Q(T), classical random matrix theory, random graphs, computational number theory, Benford's Law, cryptography, linear programming, sabermetrics, ...).

COURSES:    Possible thesis / colloquium projects   Green Chicken contest    Takeaways (all classes)     Advice

RECENT CONFERENCES:  Undergrad Research Panel (Boston 2012)      Undergrad Research Session (HC 2011 and BC 2013)

NOTE: At some point my pages will be migrating to https://sites.williams.edu/sjm1/