Basic Notions Seminar  

Spring 2014

All talks are from 3:45-4:45 p.m. in the Seminar room, unless otherwise specified.

The idea of this seminar is to present a fundamental topic in a way that many faculty can understand.

For questions please contact Max Wakefield.

  • May 05
    Overview of some Problems from Numerical Analysis/Applied Math Sania Garcia

  • Apr 30
    A Combinatorial Model for Hall-Littlewood Polynomials Andy Wills Virginia Tech

    View Abstract

    We introduce a combinatorial model for Hall-Littlewood polynomials, a class of symmetric polynomials in N variables, using objects called abacus-tournaments. Each individual abacus-tournament is given a signed weight and summing the signed weights of all the abacus-tournaments gives the Hall-Littlewood polynomial. Combinatorial proofs of identities for Hall-Littlewood polynomials, in place of the traditional algebraic methods, can be simple, elegant, and often give insight into the basic structure of the polynomials.
  • Apr 28
    Preperiodic points, heights, and Northcott's theorem Brian Stout

  • Apr 21
    Dynamic programming and the jungle Sommer Gentry USNA

    View Abstract

    Stochastic, dynamic optimization problems are incredibly varied and difficult to solve. It's no surprise that different research communities have developed different algorithms, notation, and names for algorithms tuned to different aspects of the "curse of dimensionality". Solution methods go under the names of reinforcement learning, markov decision processes, stochastic programming, approximate dynamic programming, and more. I'll offer a road map through the jungle, starting with the celebrated Bellman (Hamilton-Jacobi) equation that recursively defines the best decision to make at any time point t as a function of the expected value of making optimal decisions from time t+1 forward.
  • Apr 17
    Mathematics of "Moby Duck": Amy Bower and the Chesapeake Bay Reza Malek-Madani USNA

  • Apr 02
    Image restoration using equations from fluid dynamics Evelyn Lunasin USNA

  • Feb 24
    A 4th grade approach to p-adics Peter Andre USNA

  • Feb 05
    Sums of generalized harmonic series (NOT multiple zeta values) Mike Hoffman USNA

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