Dustin Clausen giving a talk at the 25th Summer Celebration

Click** here **for Celebration schedule

**Dustin Clausen**: "*Stereographic projection and number theory"*

**Abstract**: Stereographic projection is a simple geometric operation which relates the sphere and the plane. We'll talk about some of its applications in number theory.

**Bio:** I was a student in 2002, a JC in 2003, and a counselor from 2004-2007. BA from Harvard '08, Ph.D from MIT '13. Will be a post-doc at the University of Copenhagen.

**David Speyer***: "Seeing (yes, visually!) why we can't solve degree five equations"*

**Abstract:** You have probably heard that there is no formula for the roots of a degree five polynomial. I'll explain what this means and how we can prove it be looking at how the roots of such a polynomial change as we vary the coefficients. I am aiming to give a talk which will be understandable for current undergrads and PROMYS students, and for alumni who have been away from math for a few years. Of course, professional mathematicians are welcome too!

**Bio**: I was a counselor at PROMYS 99 and 00 and head counselor 01 and 02. I believe PROMYS is an ideal setting to learn how to study, teach and think about mathematics, and in many ways, about life. I have a Ph. D in math from UC Berkeley and am now an associate professor of mathematics at the University of Michigan, working in algebraic geometry and combinatorics. I am married and have an amazing two year old daughter.

**Bryden Cais**: "*Cohen--Lenstra heuristics for class groups of quadratic fields"*

**Abstract**: In his 1801 treatise "Disquisitiones Arithmeticae," Gauss conjectured that there are infinitely many real quadratic fields with class number one. In the early 1980's, Cohen and Lenstra proposed an amazing refinement of Gauss' conjecture, which predicts, among other things, that about 75% of all real quadratic fields have class number 1. We will discuss these heuristics of Cohen and Lenstra, and explain how they were led to formulate them.

**Bio:** I was a student in 1996 and 1997, and a counselor in 2000 and 2002. BA (Harvard) in 2002, PhD (Michigan) 2007. Postdoc at CRM-ISM in Montreal from 2007--2010 and Van Vleck Assistant Professor at Wisconsin from 2010-11. Currently Assistant Professor at University of Arizona.

**Keith Conrad:*** "Number Theory and Music"*

**Abstract:** The idea that math and music are related to each other goes back to the ancient Greeks, when Pythagoras discovered that two plucked strings sound harmonious together if their lengths are in the ratio of small whole numbers. We will describe how three fundamental aspects of musical performances -- tuning, playing, and listening -- are related not just to mathematics, but more specifically to number theory.

**Bio:** I grew up on Long Island and attended the Ross program as a student and counselor in the late 1980s and early 1990s. After studying mathematics at Princeton and Harvard, I spent 3 years as a postdoc at Ohio State, where again I was involved in the Ross program, and then 3 years as a postdoc at UC San Diego. Since 2003 I've been at UConn, where my colleagues include two former PROMYS counselors.

**Lionel Levine: **"*How to make the most of a shared meal: plan the last bite first"*

**Abstract:** If you are sharing a meal with a companion, how best to make sure you get your favorite mouthfuls? Ethiopian Dinner is a game in which two players take turns eating morsels from a common plate. Each morsel comes with a pair of utility values measuring its tastiness to the two players. Kohler and Chandrasekaharan discovered a good strategy -- a subgame perfect equilibrium, to be exact -- for this game. The players arrive at the equilibrium by figuring out their last move first and working backward. That means it's never too early to start thinking about dessert.

**Bio**: Lionel Levine is an assistant professor at Cornell University. He and fellow PROMYSian Kate Stange came up with the idea for Ethiopian Dinner during a fiercely competitive meal at Asmara restaurant on Mass Ave. in Cambridge.

**David Frohardt-Lane: "***Predictive Modeling in Sportsbetting"*

**Abstract:** In this talk, I will talk about the process of building a prediction model. The model in question will be designed predict the outcomes of NFL games, using only box score statistics in previous games, and built with the intention of identifying profitable wagering opportunities. The focus of the talk will be on how to extract as much information as possible from a limited data set. This should be easy to follow; I won't be assuming prior familiarity with statistics or football.

**Bio: **I spent two years at PROMYS, in '94 and '95. After PROMYS, I went to Carleton College where I majored in math and then onto get a MS in stats from U-Chicago. In 2004, I ended up at a proprietary trading company called GETCO, and spent the next 8 years there, working out of their Chicago, NY and Singapore offices and trading a wide variety of financial products. As of July 1, I have started a new job with 3Red, a small trading firm in Chicago. I have always been interested in sports analytics and for a period of time (2003), I was making the majority of my income from betting on baseball. While I no longer gamble (the legal situation has changed since then) I continue to dabble with sports prediction models as a hobby. Recently I've started consulting with an MLB team to help them project high school and college players for the amateur draft. A common theme across these endeavors is building quantitative models to make predictions.

**Jenny Hoffman:*** "Topology: the newest revolution in materials physics"*

**Abstract:** Once or twice per decade, the discovery of a new class of materials takes the world by storm, turning the attention of scientists everywhere, generating thousands of publications per year, and bringing broad hopes for practical applications. Most of these discoveries are lucky accidents, with experiments leading as theory struggles to keep up. But the latest revolutionary class of materials, the so-called "topological materials", are unusual in that they have all along been predicted and driven by theoretical ideas, with experimentalists racing to achieve the configurations suggested by theorists.

Topological materials are typically bulk insulators hosting topologically protected metallic surface states whose strongly coupled spin and momentum degrees of freedom have prompted numerous proposals for nanoscale devices. I will give a 10-minute crash course in solid state physics, and a short introduction to topological materials. I will then describe efforts in my own laboratory to measure their properties via low temperature scanning tunneling microscopy. In the topological semimetal antimony (Sb), we observe Landau quantization of electron states in an applied magnetic field. We further observe quasiparticle interference – standing waves produced by the interference of incoming & outgoing quantum mechanical waves. These phenomena allow us to quantify parameters relevant to spintronics applications.

**Bio:** (CV)

* Promys 1993

* BA from Harvard in 1999

* PhD in Physics from U. California, Berkeley in 2003

* postdoc at Stanford in 2004

* currently Associate Professor of Physics at Harvard

* scientific awards: Mathcounts 2nd place in 1992, Hertz Graduate Fellowship, Presidential Early Career Award in Science & Engineering,

National Science Foundation CAREER, Sloan Fellowship, Radcliffe Fellowship

* teaching awards: winner of 3 different teaching awards at Harvard (Spark Award, Roslyn Abramson Award, Fannie Cox Prize)

* ultrarunner (= long distance runner), US national team qualifier in 2006 (by running 126 miles in 24 hours)

* the most important "achievement" (blessing) is 3 beloved children, ages 6, 4, and 11 months

**Li-Mei Lim:** "*Circle Inversion and Steiner's Porism"*

**Abstract:** In an effort to branch out of number theory for a time, we will discuss a remarkable fact in geometry, Steiner's Porism. This theorem states that given two circles, one inside the other, that if you can make a ring of circles tangent to each other and to the original two circles, then you can do so in infinitely many ways. (I promise that this will make more sense with pictures, of which there will be many.) The proof of this fact uses circle inversion, a useful idea for many areas of math.

**Bio:** Li-Mei grew up in Lexington, MA, where she was a student of Tanya Finkelstein at Diamond Middle School. She attended PROMYS all four years of high school, first as a student, then as a JC. As an undergrad at MIT, she majored in mathematics and returned to PROMYS as a counselor. Li-Mei graduated with her PhD in mathematics from Brown this May and studies analytic number theory and automorphic forms. Starting in the fall, she will be Visiting Assistant Professor at Boston College.

**Click here for Celebration schedule**