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RSI/SPUR Lecture Series

Aaron Pixton Lecturing 2018

Aaron Pixton's talk in the 2018 RSI/SPUR Lecture Series

This lecture series is organized by SPUR/RSI faculty advisors Davesh Maulik and Ankur Moitra. These summer lectures are aimed at our RSI and SPUR students.

  • June 26, Anette (Peko) Hosoi

    Luck and the Law: Quantifying the Role of Chance in Fantasy Sports and Other Activities

    Fantasy sports have experienced a surge in popularity in the past decade. One of the consequences of this recent rapid growth is increased scrutiny surrounding the legal aspects of the games, which typically hinge on the relative roles of skill and chance in the outcome of a competition. While there are many ethical and legal arguments that enter into the debate, the answer to the skill versus chance question is grounded in mathematics. In this talk I will analyze data from daily fantasy competitions and propose a new metric to quantify the relative roles of skill and chance in games and other activities. This metric is applied to FanDuel data and to simulated seasons that are generated using Monte Carlo methods; results from real and simulated data are compared to an analytic approximation which estimates the impact of skill in contests in which players participate in a large number of games. We then apply this metric to professional sports, fantasy sports, cyclocross racing, coin flipping, and mutual fund data to determine the relative placement of all of these activities on a skill-luck spectrum.

  • July 3, Tristan Collins

    The Ricci Flow and Applications

    I will introduce the Ricci flow on a Riemannian manifold, which is an approach to "simplifying" or "uniformizing" the geometry of a manifold modeled on the classical heat equation. I will discuss some applications, including the Geometrization conjecture (after Perelman), and connections to algebraic geometry through the minimal model program.

  • July 10, Tanya Khovanova

    How to Write and Not to Write a Math Paper

    As a head mentor for RSI and PRIMES for several years, I reviewed and commented on more than 200 math papers. I have a huge collection of mistakes and misunderstandings on how to write a math paper. I will share the most important and common mistakes with you. I will also give tips on how to write a good math paper.

  • July 17, Andrew Lawrie

    Soliton Collisions in Geometric Wave Equations

    Free waves propagating in a vacuum disperse, spreading out and decaying as time evolves. More complicated dynamical behavior can emerge if there are nonlinear effects, as is the case in many natural systems. For example, classical scalar field theories such as the sine-Gordon equation and the phi-4 model admit soliton solutions. Solitons are coherent solitary waves — their profile is independent of time. In this talk we will discuss the dynamics of solutions that behave in one time direction like a sum of dynamically decoupling solitons. We will then examine the flow of these nonlinear waves in the opposite time direction, where the solitons move towards each other and collide.

  • July 24, David Jerison

    What can we say about the shapes of eigenfunctions and the distribution of eigenvalues?

    We will introduce Schrödinger operators and the Schrödinger evolution equation. Then we will describe the Anderson model, introduced by Philip Anderson in the 1950s, in which the Schrödinger operators are certain finite dimensional matrices. Anderson discovered that sometimes the corresponding eigenvectors are highly localized. This turns out to be crucial to the way that semiconductors work and is very important to the design of LEDs. We will discuss famous unsolved problems in pure mathematics and physics associated with Anderson localization and the adjacent problem of predicting the shapes of the eigenvectors and the distribution of eigenvalues.