Guest Lectures

The regular program activities are supplemented by diverse weekly lectures by faculty preceptors, Mentors, and guests of the program. These lectures introduce participants to related scientific fields and include discussions of career development and the ethics and philosophy of science; relationship between pure and applied science; and career options.

Guest Lectures in 2021

July 16 Edray Goins Pomona College A Survey of Diophantine Equations
July 23 Philip Engel University of Georgia Tilings and Counting
July 30 Michael Young Carnegie Mellon University Problems on Rainbow 3-term Arithmetic Progressions
August 6 Aditya Karnataki Beijing International Center for Mathematical Research What does a Circle Know about Primes? 


Guest Lectures in 2020

July 10 Diana Davis (Swarthmore College) Billiards on Regular Polygons 
July 16 Agnes Beaudry  (University of Colorado in Boulder)     Ants on Pants
July 17 Matthew Baker (Georgia Institute of Technology)     How Quadratic Reciprocity is Like Dealing Cards
July 24 Vicky Neale (Balliol College at the University of Oxford) Waring's Problem
July 31 Helen Grundman (Bryn Mawr College & Brown University) Joy & Happiness in Mathematics
August 7 Steven J Miller  (Williams College) The German Tank Problem: Math/Stats at War


Guest Lectures 2019

July 9 Keith Conrad (University of Connecticut) The Biggest Known Prime
July 16 Jeremy Booher (University of Arizona) Brussels Sprouts and the Euler Characteristic
July 26 Ila Varma (UC San Diego/University of Toronto) Binary Quadratic Forms and the Conjectures of Gauss 
July 27 Julia Mundy (Harvard University) Designing New Quantum Materials at the Atomic-scale
July 27 David Jao (University of Waterloo) How to Turn Pure Math into Applied Math: My Quest for the Perfect Application
July 27 David R.H. Miller (Google) Natural Language Understanding, Deep Learning, and the BERT Revolution
July 28 Alex Lee (Northwestern University) Perspectives on Law and Mathematics
July 29 Glen Whitney (Harvard) Towers of Life
August 2 Ryan McDermott  (Cornell University) An Introduction to Bernoulli Percolation

 Julia Mundy's talk at the 30th Anniversary July 26-28, 2019
Julia Mundy's talk at the PROMYS 30th Anniversary Celebration July 26-28, 2019

Guest Lectures 2018

July 6 Paul Gunnells (University of Massachusetts Amherst) Generalized Catalan Numbers
July 25 Philip Engel (Harvard/University of Georgia) Tilings and Counting
August 1 Lila Greco (Cornell University) Paradoxes in Probability
August 5 Joshua Greene (Weiss Asset Management) Checker Stacks and Related Musings

Phil Engel delivering guest lecture
Phil Engel delivering a guest lecture at PROMYS 2018

 Lila Greco delivering guest lecture
Lila Greco delivering a guest lecture in 2018

Guest Lectures 2017

July 5 Daniel Jerison (Cornell University) How many times to shuffle a deck of cards?
July 26 Erick Knight (University of Toronto) The Emperor and his Money
August 5 Jonathan Hanke (Goldman Sachs) What's so special about eight dimensions anyway?

Erick Knight guest lecture
Erick Knight giving his guest lecture

Jonathan Hanke's guest lecture
Jonathan Hanke's guest lecture

Erick Knight guest lecture
Students asking Erick Knight questions after his guest lecture

Guest Lectures 2016

July 6 Keith Conrad (University of Connecticut) Impossibility by modular arithmetic

July 14 Tadashi Tokieda (Stanford University/University of Cambridge) Applying physics to mathematics

July 25

August 2

Rob Gross

Ila Varma

(Boston College)

(Harvard and Columbia Universities) 

Summing It Up:  Amazon Rank 20,948

Hasse’s local-global principle  

August 6 Lionel Levine (Cornell University) The future of prediction

Ila Varma giving a guest lecture
Ila Varma giving her guest lecture at PROMYS 2016

Tadashi Tokieda speaking with students and counselors
Tadashi Tokieda speaking with students and counselors after giving his talk on applying physics to mathematics

Lionel Levine after giving his guest lecture at PROMYS 2016
Lionel Levine speaks with participants and alumni after giving his guest lecture in August 2016

Guest Lectures 2015

July 8 Keith Conrad (University of Connecticut) Continued Fractions
July 29 Moon Duchin (Tufts University) Can you hear the shape of a drum?
August 2 Melody Chan (Brown University) Triangles


Guest Lectures 2014

July 3 Dierk Schleicher  (Jacobs University, Bremen)  On useful and useless mathematics: the Mandelbrot set and Newton’s root-finding method
July11 Keith Conrad (University of Connecticut) Decimal Expansions and Number Theory
July 23 David R. H. Miller (Google, Inc.) The Mathematics of Google Search
July 25 Po-Shen Loh (Carnegie Mellon University) IMO meets research
July 30 Margaret Beck (Boston University) Understanding solutions of equations that we can’t actually solve

August 2

Solomon Hsiang (University of California, Berkeley) Quantifying the Influence of Climate on Human Conflict


Guest Lectures 2013
(Lectures on July 5-7 were part of the PROMYS 25th Summer Celebration)

July 5

Dustin Clausen (MIT) Stereographic projection and number theory
July 5  David Speyer (University of Michigan) Seeing (yes, visually!) why we can't solve degree five equations
July 5  Bryden Cais (University of Arizona) Cohen--Lenstra heuristics for class groups of quadratic fields
July 6 Keith Conrad (University of Connecticut) Number Theory and Music
July 6  Lionel Levine (Cornell University) How to make the most of a shared meal: plan the last bite first
July 6  David Frohard-Lane   Predictive Modeling in Sportsbetting
July 6  Jenny Hoffman (Harvard University) Topology: the newest revolution in materials physics
July 7 Li-Mei Lim (Brown University) Circle Inversion and Steiner's Porism
July 12 Robyn Allen (Arcmetra, Inc.) Your life is a startup: Entrepreneurship as preparation for academia, industry and other pursuits 
July 22 David Conlon (Oxford University) Binomial coefficients, the prime number
theorem and Bertrand's postulate
July 26 Ben Elias (MIT) Categorification
August 2 Farshid Hajir (University of Massachusetts Amherst) What are error-correcting codes?


Guest Lectures 2012

July 13 Ben Harris (Louisiana State University) Distributions on the Unit Circle
July 25 Stephen Wolfram (Wolfram Research) Doing and Discovering Math with Computers

July 27

July 27

Michael King

David Miller



The Laurent Phenomenon

On Integers, Intervals, and the Internet

August 1 Amanda Beeson (University of Rochester) Euler's Pentagonal Number Theorem
August 3 Ila Varma (Princeton) Hasse's Local-Global Principle

Guest Lectures 2011

July 5 David Miller (Google) Statistical Interference and Modeling the Unseen: How Bayesian statistics powers Google's voice search and machine translation technology
July 13 Dan Klain (University of Massachusetts at Lowell) Angle sums for polyhedra
July 27 Michael King (Bowdoin College) Triangulations of the n-gon and Root Systems
July 29 Jonathan Hanke (University of Georgia) Random Numbers and the Zeta Function
August 2 Bryden Cais (University of Arizona) Every integer is the sum of four squares


Guest Lectures 2010

July 2 Keith Conrad (University of Connecticut) Polynomial Roots on a Circle
July 9 Andrew Lo (MIT) Finance Made Difficult: Mathematics, Money, and Financial Crises
July 20 Amanda Beeson (Williams College and University of Rochester) Did Escher Know What an Elliptic Curve Is?
July 23 Henry Cohn (Microsoft Research Institute) How to Break Cryptosystems by Finding Small Solutions of Equations
July 27 Kirsten Wickelgren (Harvard University) Fixed Point Theorems and Solving Equations
July 27 Paul Gunnells (University of Massachusetts, Amherst) Expander Graphs


Guest Lectures 2009

July 7 David Miller (Cambridge Googleplex) The Mathematics of Google Search
July 14 Farshid Hajir (University of Massachusetts Amherst) The ABC Conjecture
July 28 Steven Miller (Williams) Heuristics and Ballpark Estimates
July 30 Keith Conrad (University of Connecticut) Pythagorean Triples


Guest Lectures 2008

July 8 Keith Conrad (University of Connecticut) Applications of Pell’s Equations
July 11 Paul Gunnells (University of Massachusetts Amherst) Configuration Spaces
July 25 Steven J. Miller (Williams) The Pythagorean Won-Loss Formula in Baseball
August 1 Farshid Hajir (University of Massachusetts Amherst) Asymptotically Good Families of Graphs


Guest Lectures 2007

July 6 Jon Hanke (Duke University) Geometry of Affine and Projective Space
July 13 Keith Conrad (University of Connecticut) A Universal Divisibility Test
July 16 Steven Miller (Brown) Benford’s Law: From Number Theory to the IRS
July 27 David Jao (University of Waterloo) Elliptic Curve Cryptography
August 3 Keith Conrad (University of Connecticut) Counting in Z[√d]
August 6 Ander Steele   Carmichael Numbers in Number Rings


Guest Lectures 2006

July 26 Matthew Szudzik (Wolfram Research) Antor's Absurd Question
July 27 Jon Hanke (Duke University) Exact Formulas for Representing Numbers by a Quadratic Form


Guest Lectures 2005

July 15 Matthew Szudzik (Wolfram Research) Who was Laszlo Kalmar and what were his functions?
July 18 Curt Monash (Monash Information Services) The Power of Maybe
July 29 Kiran Kedlaya (MIT) Elliptic Curves
August 2 Cleve Moler (The MathWorks, Inc.) The Evolution of MATLAB
August 4 Keith Conrad (University of Connecticut) Check Digits


Guest Lectures 2004

July 16 Robert Pollack (Boston University) Unique Factorization and Diophantine Equations
July 19 Ira Gessel (Brandeis University) The Chung-Feller theorem
July 21 Matthew Szudzik (Wolfram Research) Exploring Recursively Defined Sequences
August 2 David Jao (Microsoft Research) Codebreaking
August 4 Keith Conrad (University of Connecticut) Quaternions
August 6 Paul Gunnells (UMass Amherst) Diophantine Equations in Polynomials


Guest Lectures 2003

August 3 Keith Conrad (UC San Diego) The End of Continued Fractions
August 5 Henry Cohn (Microsoft Research) Self-reference


Guest Lectures 2002

July 17 David Miller (Aventis Pharmaceuticals) Bioinformatics and Gene Expression Analysis
July 19 Henry Cohn (Microsoft Research) Sphere Packing
July 31 Jonathan Lubin (Brown University) p-adic Numbers
August 2 Paul Gunnells (UMass Amherst) Continued Fractions and Hyperbolic Geometry
August 9 Keith Conrad (UC San Diego) Sums of Three Squares


Guest Lectures 2001

July 27 David Jao (Harvard University) 41 Primes in a Row
August 3 Dev Sinha (University of Oregon) Some Knotty Problems