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.

July 6 | Professor Paul Gunnells | (University of Massachusetts Amherst) | Generalized Catalan Numbers |

July 25 | Dr. 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 |

July 5 | Professor Daniel Jerison | (Cornell University) | How many times to shuffle a deck of cards? |

July 26 | Dr. Erick Knight | (University of Toronto) | The Emperor and his Money |

August 5 | Dr. Jonathan Hanke | (Goldman Sachs) | What's so special about eight dimensions anyway? |

Erick Knight giving his guest lecture

Jonathan Hanke's guest lecture

Students asking Erick Knight questions after his guest lecture

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 her guest lecture at PROMYS 2016

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

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

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 |

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 |

(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? |

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 |
(Bowdoin) (Google) |
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 |

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 |

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 |

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 |

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 |

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 |

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 |

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 |

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 |

August 3 | Keith Conrad | (UC San Diego) | The End of Continued Fractions |

August 5 | Henry Cohn | (Microsoft Research) | Self-reference |

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 |

July 27 | David Jao | (Harvard University) | 41 Primes in a Row |

August 3 | Dev Sinha | (University of Oregon) | Some Knotty Problems |