If there are several versions of a talk, the
later version is usually the more 'complete' (ie, correct) version.
Random Matrix Theory and \(L\)Functions
Random Matrix Theory and
Elliptic Curves
Elliptic Curves
Random Matrix
Ensembles
Analysis
&
Probability (especially Benford's Law)
Computers and Mathematics
Education
Colloquium Talks
Baseball (Sabermetrics)
Joint
Meetings (Boston 2012, introductory talks)
 Coronavirus Lectures (see also my math riddles
page:
https://mathriddles.williams.edu/)
 From Pythagoras to Pi: Part I:
https://youtu.be/JHvmP1KXYc (slides here).
Given to 7th grade son who is in Algebra I. 41 minutes
 From Pythagoras to Pi: Part II:
https://youtu.be/ISo8kXDP6U (slides here).
Given to 7th grade son who is in Algebra I. 27 minutes
 What do you MEAN?
https://youtu.be/jBKZaCxpgSE (word file here,
pdf here) (3/19/2020): Comfort with
Algebra sufficient: 40 minutes
 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
 Monovariants:
https://youtu.be/PbZhVLXyatY (powerpoint
here,
pdf here) (3/23/2020): Grade 5 and up:
28 minutes
 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
 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
 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
 Games: Tic Tac Toe, Chocolate Bar, Coins, Devil:
https://youtu.be/4KvxJHBvs0
(slides here)
(3/27/2020): Much of it can be done with K, 2nd and higher to be safe: 38
minutes
 Induction and Sums: Part I: Induction
https://youtu.be/3orVsQECaag (powerpoint
here,
pdf here)
(3/30/2020): Assuming Algebra I: 32 minutes
 Induction and Sums: Part II: Geometric Series Formula
https://youtu.be/CJjglF65x6g (powerpoint
here,
pdf here): (3/31/2020): Assuming
Algebra I: 25 minutes
 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
 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
 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
 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
 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
 Polynomials and Applications: Part 2: Lecture 2: Introduction to Quadratics:
Plotting, Simple Examples and Roots:
https://youtu.be/bkIWsNcwbU (powerpoint
here,
pdf here) (4/13/2020):
Aimed at 7th grade and up: 17 minutes
 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.
 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.
 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.
 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
 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
 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
 Introduction to Probability: Part 1: The Factorial Function:
https://youtu.be/Un3tWIXkDY (powerpoint
here,
pdf here) (4/27/2020):
Aimed at 7th grade and up: 13 minutes
 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
 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
 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
 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 (rerecorded; no TAs)
 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
 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
 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
 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
 Additive Number Theory:
 Applied Mathematics:
 Calculus Lectures
 Cryptography:
VCTAL Lectures Burlington 2019: Introduction to
cryptography, error detection / correction.
 Education
 From M&Ms to Mathematics, or, How I learned to answer questions and love
math.
https://www.youtube.com/watch?v=0lVSEmgeOsI (slides
here)
 Why Cookies And M&Ms Are Good For You (Mathematically).
http://youtu.be/tr6Hb3DGooU
(slides here)
 Why more is better: The power of multiple proofs.
http://youtu.be/XwnzWOc3_0 (slides
here, homework
and research problems here).
 Extending the Pythagorean Formula: http://youtu.be/idIHcgapMG4 (slides
here)
 Secrets of the Tax System with Steve Miller: Keep More of Your MOOLA:
ADD VIDEO LATER (9/19/16: slides
here)
 Advanced Math Course Sharing: Proof of Concept: LACOL 2017 Consortium
Workshop: June 16, 2017:
http://lacol.net/sharedmath/
 LaTeX tutorial:
http://www.youtube.com/watch?v=dKUtJpG4Rt0 (webpage with templates
here)
 Mathematica tutorial:
https://www.youtube.com/watch?v=g1oj7CIqGM8 (webpage with templates
here)

Inrtoduwtion to Erorr Dwtetcion and Czorrectmon,
TCNJ Math Camp, July 14, 2019. MathFest, August 1, 2019.
pdf
(video: https://youtu.be/RPWMAqPhv6w)
UNFORTUNATELY the video did not advance the slides (talk about errors to
correct, though the audience saw the slides advance). I tried to record the
audio with the slides advancing at home, but it garbled the audio! So, here's
how you correct the error. Play the video from https://youtu.be/RPWMAqPhv6w
but ONLY play it for the audio, ignore the video! Start that at 40 seconds.
Now play the video from
https://youtu.be/P6I0Z9CFPcQ BUT start that at 20 seconds and have that on
mute! Thus you listen to the audio from the first to the video of the second.
 Solving the Rubik's cube (thanks Alan Chang and Umang Varma!):
 Calculus Continuing Education Lectures:
Wellesley High School
 Part 1: October 13, 2017
 Review of differentiation, exponential function, need for proofs,
Russell's paradox, inverse funcctions:
https://youtu.be/8jmrccy5_Xc
 Inverse trig functions, trigonometry in a minute, trig differentiation,
birthday problem:
https://youtu.be/jckjVogsSKs
 Big No's in math, 0 * oo = 1, Babylonian multiplication, Horner's
algorithm, Newton's method, Divide and conquer:
https://youtu.be/piUHHHCW3lw
 Stacking dominoes, harmonic series, integral test, egg drop problem:
https://youtu.be/75AtD14hlA4
 Part 2: December 15, 2017
 Sequences and series: Convergence, Geometric series, Term by term
differentiation, Differentiating Identities, IVT, MVT, Fund Thm Calculus:
https://youtu.be/sQhZdfFL_Zk
 First order Taylor theorem, Taylor with remainder, Streaming Video,
Fibonacci Numbers:
https://youtu.be/H5BdJGfOkRc
 Fibonacci and recurrence relations, Binet's formula: divine inspiration
and generating functions, Applications, Zeckendorf's theorem, Matrix
formulations:
https://youtu.be/GCNmLKIrLk
 Riemann zeta function, Infinitude of primes, Local to global principle;
more generating functions, 3x+1, Look and say:
https://youtu.be/Cbvj5nN4nZ0
 Part 3: January 29, 2017
 Zombie Mathematics, Monovariants, TicTacToe, Sperner Games, Nash
Equilibria, Fixed Point Theorems:
https://youtu.be/AAyAiW36Ok
 Zeckendorf games and monovariants, Method of Least Squares:
https://youtu.be/St_455zfb8
 Drowning Swimmer Problem, the AMGM, Farmer Fencing Optimization:
https://youtu.be/GRIsFMUmB8
 Fundamental Theorems, Stirling's Formula, Central Limit Theorem:
https://youtu.be/7IzrTTBLh8
 LFunctions and Random Matrix Theory:
 Number Theory and Probability
 Teachers as Scholars Lectures 2020: March 18th,
April 1st and April 2nd (two different classes)
 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
Teachers as Scholars:
https://youtu.be/RaajCJ8Zfv0 (3/18/2020)

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):
TAS: https://youtu.be/_qTVbzpkPM
(3/18/2020)

Inrtoduwtion to Erorr Dwtetcion and Czorrectmon, slides
here: pdf TAS:
https://youtu.be/BxHXUBxzOJs (3/18/2020)

Introduction to Cryptography: Alphabet codes
https://youtu.be/KF_zRLNcmHQ,
Vigenere, Primes, and RSA definition
https://youtu.be/7NG66oHUxnA
(slides pdf) (4/1/2020)

Introduction to Cryptography: Fermat's little
Theorem https://youtu.be/U5GSLF7wlPc,
Horner's Algorithm and Fast Multiplication
https://youtu.be/p2GdoKELCJk,
Euclidean Algorithm and implementing RSA
https://youtu.be/ckjwHS8qMeY
(slides
pdf) (4/1/2020)
 Monovariants and Zombies:
https://youtu.be/O9bYbPhTFEM (powerpoint
here,
pdf here): Grade 5 and up
(4/2/2020)
 What do you MEAN?
https://youtu.be/nuRzXNz9LQ (word file
here,
pdf here): Comfort with
Algebra sufficient
(4/2/2020)
 Extending Pythagoras
https://youtu.be/W1gN9YI84TE
(slides:
pdf) (4/2/2020)
 I Love Rectangles Game:
https://youtu.be/W4L5rjrq2Ns (powerpoint
here,
pdf here): Aimed for K,
should be good for all ages.
(4/2/2020)
 Games: Tic Tac Toe
https://youtu.be/27_w9cQDzQ, Chocolate Bar
https://youtu.be/pKsPPo75xNc,
Triangle game and Chomp
https://youtu.be/yJ_GZnM6QQ
(slides here): Much of it can be done with K, 2nd and higher to be safe
(4/2/2020)
 Bonus Talks
 From M&Ms to Mathematics, or, How I learned to answer questions and love
math.
https://www.youtube.com/watch?v=0lVSEmgeOsI (slides
here)
 Why more is better: The power of multiple proofs.
http://youtu.be/XwnzWOc3_0 (slides
here, homework
and research problems here).

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)
 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  Québec
Number Theory Conference (10/3/09):
pdf
Rutgers University (expanded version, 3/2/10):
pdf
 The nlevel density of zeros of quadratic Dirichlet \(L\)functions (presented by Jake Levinson), Young Mathematicians Conference, August 19, 2011. pdf
 Lowlying zeros of cuspidal Maass forms (presented by Oleg Lazarev and Liyang Zhang), Young Mathematicians Conference, August 20, 2011. pdf MaineQuebec Number Theory Conference, October 2, 2011. pdf
 Determinantal Expansions in Random Matrix Theory and Number Theory (with
Nicholas Triantafillou), MaineQuebec Number Theory Conference,
September 29, 2012.
pdf
(trimmed
pdf)
 Lowlying zeros of cuspidal Maass forms (blackboard talk given by Levent
Alpoge), MaineQuebec Number Theory Conference,
September 29, 2012.
 Lowlying zeros of GL(2) \(L\)functions, University
of Michigan, October 22, 2012.
part 1
part 2
 Lowlying 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: QuébecVermont
Number Theory Seminar, Concordia University, March 21, 2013.
pdf
 Newman's Conjecture for Automorphic and Function Field \(L\)functions
(presented by Alan Chang), MaineQuebec 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 MinhTam Trinh), MaineQuebec Number Theory
Conference (10/5/13).
pdf
 Problems in the
theory of lowlying zeros, Simons Symposium on Families of
Automorphic Forms and the Trace Formula, Puerto Rico, January 27, 2014.
pdf
Results in the theory of lowlying 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 Lfunction Zeros (with Kevin Yang),
MaineQuebec Number Theory Conference, October 3, 2015.
pdf
 Biases in Moments of
Satake Parameters and in Zeros near the Central Point in Families of
LFunctions,
Computational Aspects of Lfunctions, ICERM, Providence, RI (11/10/15).
pdf
 Gaps Between Zeros of
GL(2) Lfunctions,
Southern New England Conference on Quadratic Forms and Modular Forms, June
2, 2016.
pdf
 Extending Agreement in the
KatzSarnak Density Conjecture (joint with Peter Cohen and Roger Van Peski),
QuebecMaine Number Theory Conference, October 8, 2016.
pdf
 Onelevel density for
holomorphic cusp forms of arbitrary level, 31^{st} 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), MaineQu\'ebec Number
Theory Conference, October 14, 2017.
pdf
 Variance of Gaussian
Primes Across Sectors and The Hecke LFunction Ratios Conjecture (with Yujin
Kim and Shannon Sweitzer), MaineQu\'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
nLevel Densities and Applications to Central Point Vanishing (with Charles
Devlin VI), MaineQu\'ebec Number Theory Conference, October 5, 2019.
pdf
(video:
https://youtu.be/I4j374CQgfg)
 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, Montréal,
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
dvi. Another 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
 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 SwinnertonDyer 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
 Closedform moments in elliptic curve families and lowlying zeros,
Simons Symposium on Families of Automorphic Forms and the Trace Formula,
Puerto Rico, January 31, 2014.
pdf
 From SatoTate Distributions to LowLying 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 Lfunctions: 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) LFunctions (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 oneparameter
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
 Elliptic Curves
 Ranks of OneParameter 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 1Parameter 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 SwinnertonDyer
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,
QuebecMaine 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
 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 mCirculant 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 mCirculant Ensembles
(presented with Murat Kologlu), AMS Special Session
on Random Processes, Worcester, MA (4/9/11):
pdf
 Painleve VI and TracyWidom 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!),
Crossdomain Conference on Benford's Law
application, Stresa, Italy, July 10, 2019.
pdf
PIMS Distinguished Lecture, UNBC, November 14, 2019.
pdf
Vassar College
pdf
(video:
https://youtu.be/fm3sxjcnAE)
 See also some of the talks in the Additive Number Theory section and
the colloquium section.

Additive Number Theory (especially More Sum Than Difference
Sets and Zeckendorf Decompositions) (images for Zeckendorf / gaps)
 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
 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
 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
 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
 Gaps between summands in generalized Zeckendorf decompositions (presented by Olivia Beckwith), Young Mathematicians Conference, August 19, 2011. pdf
 Constructing Generalized SumDominant Sets (presented by Geoff Iyer and Liyang Zhang), Young Mathematicians Conference, August 19, 2011. pdf; MaineQuebec 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
 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
 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
 Distribution of summands in generalized Zeckendorf decompositions,
AMS Session on Number Theory, I, Joint Meetings San
Diego, January 9, 2013.
pdf
 When Almost All Sets Are Difference Dominated,
Number Theory Seminar, University of Illinois, March
25, 2013.
pdf
 When Almost All Generalized Sumsets Are DifferenceDominated (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
 Mind the Gap: Distribution of Gaps in Generalized Zeckendorf
Decompositions, CANT, May 21, 2013.
pdf
Williams Math/Stats Faculty
Seminar (9/12/13),
Maine  Québec 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
Confernece, 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
 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), QuébecMaine
Number Theory Conference, Sept 28, 2014
pdf AMS Special Session on Continued
Fractions, JMM 2015, January 12, 2015.
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
 MSTD Subsets and Properties of Divots in the Distribution of Missing
Sums (with Victor Xu and Xiaorong Zhang), 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
 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
 Classification of Crescent Configurations
on Four and Five Points (given by Chi Huynh),
Integers Conference,
University of West Georgia, October 7, 2016.
pdf
AMSMAASIAM Special Session on Research in Mathematics by
Undergraduates and Students in PostBaccalaureate Programs, III, Joint
Math Meetings, Atlanta, January 2017 (given
by Becky Durst, Chi Huynh, Max Hlavacek)
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
 Ramsey Theory over Number Fields,
Finite Fields and Quaternions, CANT, May 26, 2017.
pdf
 Generalizations of Zeckendorf's Theorem
to TwoDimensional 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.
 Withinperfect & nearperfect numbers (with Kevin Kwan),
CANT May 22, 2018
pdf
 Monovariants to
Zeckendorf Decompositions and Games, The Eighteenth International
Conference on Fibonacci Numbers and Their Applications, Dalhousie
University, July 2, 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 squarefree walks (with Joshua
Ackerman, Tudor Popescu, Zimu Xiang), CANT May
23, 2019
 Crescent Configurations
In NonEuclidean Norms, given by Dylan King and Cathy Wahlenmayer,
MaineQu\'ebec Number Theory Conference, October 5, 2019.
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 WonLoss 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.
MaineQuebec Number Theory Conference, October 3, 2015.
pdf
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,
AMSMAA Special Session on Innovative Ideas in Enhancing Success in
Mathematics Classes, Joint Meetings of the AMSMAA, 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/sharedmath/)
 YouTube University: Shared upper level math courses across schools,
AMSMAA Special Session: Novel Methods of Enhancing
Success in Mathematics Classes, Joint Mathematics Meeting, San Diego,
January 2018.
pdf

Where's the Remote? UpperLevel 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 SatoTate Conjecture in Arithmetic Progressions,
QuebecMaine Number Theory Conference, October 7,
2018.
pdf
 Summer Data Science (online): By and for the liberal arts,
panelist in discussion on an online class coteaching,
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)
 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)
 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 GreavesTunnell, 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, cRamanujan).
 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 LatkeHamantaschen Debate: The Primacy of Three,
Williams College, March 19, 2014.
pptx
pdf
(YouTube clip:
http://www.youtube.com/watch?v=tt4_4YajqRM)

Fractals:
From Khan to Frozen,
Williams College, March 20, 2014 (supplemental
lecture for multivariable calculus).

Some Results on LowLying Zeros of LFunctions, 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 (8316).
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

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.

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

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

From the Manhattan Project to Number Theory: How Nuclear Physics Helps Us
Understand Primes, Yale University, October 8, 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)

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

VCTAL CRYPTOGRAPHY LECTURES: June 1920, 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
 Baseball / Sabermetrics Talks
 The Pythagorean WonLoss 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
 Pythagoras on the Ice: Hockey Conference, Babson
(10/1/16): pdf
 See also talks on Computers and Mathematics Education.
 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 2729, 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
TurnageButterbaugh, 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) Lfunctions (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 QuebecMaine 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 LFunctions Associated to GL(2) Cusp Forms
(given by David Burt & Blaine Talbut), MaineQuebec Number Theory
Conference, October 3, 2015.
pdf
 A Ramsey Theoretic Approach to Finite Fields and Quaternions (given by
Sarah Manski), MaineQuebec Number Theory Conference, October 3, 2015.
pdf
 Biases in Moments of Satake Parameters and Models for $L$function Zeros
(with Kevin Yang), MaineQuebec 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), MaineQuebec
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 NonNegative
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 1921, 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 KatzSarnak
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: Nearperfect, withinperfect, and orderaabundant
numbers: Adam Lott and Chung Hang Kwan
 SMALL 2017
 Variance of Gaussian Primes Across
Sectors and the Hecke LFunction Ratios Conjecture (given by Jared
Lichtman and Shannon Sweitzer), Young Mathematicians Conference, Ohio State,
August 2017.
 Limiting Distributions in Generalized
bbin Zeckendorf Decompositions (given by Shannon Sweitzer and Jianing
Yang), Young Mathematicians Conference, Ohio State, August 2017. (poster
here)
 Bounds for High Vanishing in Families
of LFunctions (given by Eric Winsor and Ryan Chen), Young
Mathematicians Conference, Ohio State, August 2017.
 Spectral Statistics of NonHermitian
Random Matrix Ensembles (given by Ryan Chen and Eric Winsor), Young
Mathematicians Conference, Ohio State, August 2017.
 Lower order biases in Fourier
coefficients of elliptic curve and cuspidal newform families (given by
Jianing Yang and Jared Lichtman), Young Mathematicians Conference, Ohio
State, August 2017.
 Slow Decay and Missing Term
Distributions in Generalized Sum and Difference Sets (poster given by
Eric Winsor), Young Mathematicians Conference, Ohio State, August 2017.
 SMALL 2018 (plus CMU)

Distribution of Primes in Number Fields
(Maria
R Ross and Casimir M Kothari),
Young Mathematicians Conference, Columbus, Ohio, August 10, 2018.
pdf

Playing Ball with the
Largest Prime Factor
(Madeleine
L Farris),
Young Mathematicians Conference, Columbus, Ohio, August 10, 2018.
pdf

Linear Recurrence
Relations with Nonconstant Coefficients and Benford's Law
(Mengxi
Wang and Lily Shao),
Young Mathematicians Conference, Columbus, Ohio, August 10, 2018.
pdf

GraphRestricted
Decompositions: A Further Generalization of Zeckendorf's Theorem
(Noah
Luntzlara and Hunter Wieman),
Young Mathematicians Conference, Columbus, Ohio, August 11, 2018.
pdf

Rank and Bias in
Families of Hyperelliptic Curves via Nagao's Conjecture
(Ben
C Logsdon and Trajan A Hammonds),
Young Mathematicians Conference, Columbus, Ohio, August 11, 2018.
pdf

Phase transitions in the
distribution of missing sums
(Hung
Viet Chu and Lily Shao), Young
Mathematicians Conference, Columbus, Ohio, August 11, 2018.
pdf

Gaussian Behavior in Zeckendorf Decompositions Arising
From Lattices
(Joshua Siktar), Young Mathematicians Conference, Columbus, Ohio, August 12,
2018.
pdf

Eigenvalue Distribution
of Kronecker Products of Random Matrices
(poster;
Mengxi Wang and Noah Luntzlara),
Young Mathematicians Conference, Columbus, Ohio, August, 2018.
pdf

SatoTate in Arithmetic
Progressions and Lehmer's Conjecture
(poster;
Trajan A Hammonds and Casimir M Kothari), Young
Mathematicians Conference, Columbus, Ohio, August, 2018.
pdf

SMALL 2019
 Erdos Distance Problem
 Crescent Configurations In NonEuclidean Norms Speakers: Sara Fish,
Dylan King, Catherine Wahlenmayer,
Conference for New England REU. 7/23/19.
pdf
Young Mathematicians Conference,
August 9, 2019
pdf
MaineQu\'ebec Number Theory Conference, October 5,
2019.
pdf
 Convolutions
 Extensions of Autocorrelation Inequalities with Applications to Additive
Combinatorics,
Young Mathematicians Conference,
August 10, 2019
pdf
 Lfunctions
 Zeros of LFunctions 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
MaineQu\'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

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.
pdf
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 ddimensional
Lattices: Neelima Borade and Annie Xu,
Young Mathematicians Conference,
August 10, 2019.
pdf
Random Matrix Theory and \(L\)Functions
Random Matrix Theory and
Elliptic Curves
Elliptic Curves
Random Matrix
Ensembles
Analysis
&
Probability (especially Benford's Law)
Computers and Mathematics
Education
Colloquium Talks
Baseball (Sabermetrics)
Joint
Meetings (Boston 2012, introductory talks)
Thesis
Papers
Talks
Books:
Invitation Modern
Number Theory
Mathematics of Encryption
Benford's Law
Handouts
My
Riddles Page
 RESEARCH INTERESTS:
Analytic Number Theory, Random Matrix Theory,
Probability (zeros and nlevel 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, ...).
Thesis
Papers
Talks
Books:
Invitation Modern
Number Theory
Mathematics of Encryption
Benford's Law
Handouts
My
Riddles Page
 COURSES:
Welcome letter
to Williams Students
Possible
thesis / colloquium projects
Green Chicken contest
Takeaways (all classes)
Advice
 Williams Classes: 20162017: FALL:
Math/Stat 341
(Probability),
Math 377
(Operations Research); SPRING: Number Theory, Problem Solving
 Calculus:
Math 103
(Calculus I), Math 150
(Multivariable Calculus)
 Analysis:
Math 209 (Differential Equations
and Vector Calculus),
Math 372
(Complex Analysis),
Math 389 (Advanced
Analysis)
 Applied Analysis:
Math 317
(Operations Research),
Math 416 (Advanced
Applied Linear Programming)
 Probability and Stats:
Math 317
(Operations Research),
Math/Stat 341
(Probability '15)
 Problem Solving:
Math 331 (The little Questions),
 Number Theory:
Math 10
(cryptography, winter study),
Math 308/406
(Analysis and Number Theory), Math 389
(Advanced Analysis),
Math 406
(Analysis and Number Theory);
 Senior Seminars:
Math 308/406
(Analysis and Number Theory), Math 406
(Analysis and Number Theory),
Math 416 (Advanced
Applied Linear Programming)
 Independent Studies: Putnam
Independent Study (Fall
2010), Math
399 (Sabermetrics)

Winter Studies:
LQWURGXFWLRQ WR FUBSWRJUDSKB (2013 version)
Star Trek and Science
(2013)
Mathematics of Legos
(2014, 2015)
 Smith / Mount Holyoke:
Math 238 (number
theory, Smith 2011),
Math/Stat 342
(Probability, MH 2011),
Math
395 (Linear Programming, MH 2011)
 Brown:
Math
1 (freshman seminar: riddles to modern mathematics), Math 90 (calc
I,
summer calc I),
Math 35
(honors multivariable calculus),
Math
52 (linear algebra),
Math 54
(honors linear algebra),
Math 153 (abstract
algebra),
Math 162
(mathematical statistics), Math 197 (Benford's
law,
sabermetrics)
 Ohio State:
Math 104 (Basic College
Math),
Math 148 (Algebra/Trig),
Math 187/487 (Problem / Advanced
Problem Solving),
Math 683L (Grad
Linear Algebra), Working groups (Euler,
fractals)
 Teachers As Scholars: Cryptography and Benford's Law:
2011,
2012; AHa Moments in Math/Science:
2013,
2014 Math Moments:
2015
LINKS:
photos of Cam
Pictures
Twistie
Art
Arxiv
MathSciNet
Mathlabs (Princeton
, NYU,
OSU,
AIM)
Williams Math
Williams College
Spencer Neighborhood
RECENT CONFERENCES: Undergrad Research Panel (Boston 2012)
Undergrad
Research Session (HC 2011 and
BC 2013)