Basic Notions Spring 2014
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.
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May05
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Overview of some Problems from Numerical Analysis/Applied MathSania GarciaTime: 12:00 PM
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Apr30
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A Combinatorial Model for Hall-Littlewood PolynomialsAndy WillsVirginia TechTime: 03:45 PM
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.
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Apr28
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Preperiodic points, heights, and Northcott's theoremBrian StoutTime: 03:45 PM
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Apr21
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Dynamic programming and the jungleSommer GentryUSNATime: 03:45 PM
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.
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Apr17
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Mathematics of "Moby Duck": Amy Bower and the Chesapeake BayReza Malek-MadaniUSNATime: 03:45 PM
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Apr02
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Image restoration using equations from fluid dynamicsEvelyn LunasinUSNATime: 03:45 PM
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Feb24
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A 4th grade approach to p-adicsPeter AndreUSNATime: 03:45 PM
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Feb05
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Sums of generalized harmonic series (NOT multiple zeta values)Mike HoffmanUSNATime: 03:45 PM