Basic Notions Seminar
Spring 2014
All talks are from 3:454:45 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 05Overview of some Problems from Numerical Analysis/Applied Math Sania Garcia

Apr 30A Combinatorial Model for HallLittlewood Polynomials Andy Wills Virginia Tech
View Abstract
We introduce a combinatorial model for HallLittlewood polynomials, a class of symmetric polynomials in N variables, using objects called abacustournaments. Each individual abacustournament is given a signed weight and summing the signed weights of all the abacustournaments gives the HallLittlewood polynomial. Combinatorial proofs of identities for HallLittlewood polynomials, in place of the traditional algebraic methods, can be simple, elegant, and often give insight into the basic structure of the polynomials. 
Apr 28Preperiodic points, heights, and Northcott's theorem Brian Stout

Apr 21Dynamic 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 (HamiltonJacobi) 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 17Mathematics of "Moby Duck": Amy Bower and the Chesapeake Bay Reza MalekMadani USNA

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

Feb 24A 4th grade approach to padics Peter Andre USNA

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