Seminars and Colloquia by Series

TBA

Series
Mathematical Biology Seminar
Time
Friday, November 6, 2020 - 15:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Peter HinowUniversity of Wisconsin-Milwaukee

TBA

TBA by Ruth Luo

Series
Graph Theory Seminar
Time
Tuesday, November 3, 2020 - 15:45 for 1 hour (actually 50 minutes)
Location
https://us04web.zoom.us/j/77238664391. For password, please email Anton Bernshteyn (bahtoh ~at~ gatech.edu)
Speaker
Ruth LuoUniversity of California, San Diego

TBA

Counting integer partitions with the method of maximum entropy

Series
Combinatorics Seminar
Time
Friday, October 30, 2020 - 15:05 for 1 hour (actually 50 minutes)
Location
Bluejeans link: https://bluejeans.com/751242993/PASSWORD (To receive the password, please email Lutz Warnke)
Speaker
Gwen McKinleyUniversity of California, San Diego, CA

We give an asymptotic formula for the number of partitions of an integer n where the sums of the kth powers of the parts are also fixed, for some collection of values k. To obtain this result, we reframe the counting problem as an optimization problem, and find the probability distribution on the set of all integer partitions with maximum entropy among those that satisfy our restrictions in expectation (in essence, this is an application of Jaynes' principle of maximum entropy). This approach leads to an approximate version of our formula as the solution to a relatively straightforward optimization problem over real-valued functions. To establish more precise asymptotics, we prove a local central limit theorem using an equidistribution result of Green and Tao.

A large portion of the talk will be devoted to outlining how our method can be used to re-derive a classical result of Hardy and Ramanujan, with an emphasis on the intuitions behind the method, and limited technical detail. This is joint work with Marcus Michelen and Will Perkins.

An Introduction to Gabor Analysis

Series
School of Mathematics Colloquium
Time
Thursday, October 29, 2020 - 11:00 for 1 hour (actually 50 minutes)
Location
Online (link to be announced)
Speaker
Kasso OkoudjouTufts University

In 1946, Dennis Gabor claimed that any Lebesgue square-integrable function can be written as an infinite linear combination of time and frequency shifts of the standard Gaussian.  Since then, decomposition methods for larger classes of functions or distributions in terms of various elementary building blocks have lead to an impressive body of work in harmonic analysis. For example, Gabor analysis, which originated from Gabor's claim, is concerned with both the theory and the applications of the approximation properties of sets of time and frequency shifts of a given function. It re-emerged with the advent of wavelets at the end of the last century and is now at the intersection of many fields of mathematics, applied mathematics, engineering, and science. In this talk, I will introduce the fundamentals of the theory highlighting some applications and open problems.

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