If there are several versions of a talk, the
later version is usually the more 'complete' (ie, correct) version.
 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://Mathyoutu.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
 Pascal's triangle modulo 2:
https://youtu.be/_vkGakVt1RA
 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.
40 minute version: Michigan Math Club (10/1/21):
pdf
(video:
https://youtu.be/tuL0K1XtGBE)
 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)
Penn State, October 29, 2020
pdf (video: https://youtu.be/1N2IhpifwAk).
 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 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: QuebecVermont
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
MASON VI, March 17, 2023.
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)
 How Low Can We Go?
Understanding Zeros of LFunctions Near The Central Point, New York
Number Theory Seminar, February 18, 2021.
pdf
 The KatzSarnak
Density Conjecture and Bounding Central Point Vanishing of LFunctions,
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 KatzSarnak
Density Conjecture and Bounding Central Point Vanishing of LFunctions
(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 LFunction Coefficients and
Applications to LowLying Zeros, Special Session in Number Theory in
Celebration of the 70th Birthday of Ram Murty, CMS Summer Meeting, 4 June
2023.
pdf
(video: )
 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
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
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 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
 Biases in Second Moments of Elliptic Curves (Aditya Jambhale and Akash
L. Narayanan), MaineQuebec Number Theory Conference, September 30, 2023.
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
 Applications of Moments of Dirichlet Coefficients in Elliptic Curve
Families,
Murmurations in Arithmetic, ICERM, July 7, 2023:
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
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)
NOTE: At some point my pages will be migrating to
https://sites.williams.edu/sjm1/