Seminars and Colloquia Schedule

Thesis Defense: James Wenk

Series
Dissertation Defense
Time
Tuesday, July 5, 2022 - 11:00 for 2 hours
Location
Skiles 005
Speaker
James Wenk

I will be defending my thesis on the shortest closed curve to inspect a sphere.<br />
<br />
Time: 11am EST<br />
Location: Skiles 005, also on Zoom at https://gatech.zoom.us/j/97708515339<br />
<br />
Committee:<br />
<br />
Dr. Mohammad Ghomi, Advisor<br />
School of Mathematics<br />
Georgia Institute of Technology<br />
<br />
Dr. Igor Belegradek<br />
School of Mathematics<br />
Georgia Institute of Technology<br />
<br />
Dr. Jason Cantarella<br />
Department of Mathematics<br />
University of Georgia<br />
<br />
Dr. Rob Kusner<br />
Department of Mathematics<br />
University of Massachusetts<br />
<br />
Dr. Galyna Livshyts<br />
School of Mathematics<br />
Georgia Institute of Technology<br />
<br />
Dr. Michael Loss<br />
School of Mathematics<br />
Georgia Institute of Technology<br />
<br />

Factorization theorems and canonical representations for generating functions of special sums

Series
Dissertation Defense
Time
Wednesday, July 6, 2022 - 15:00 for 1 hour (actually 50 minutes)
Location
Hybrid - Skiles 006 and Zoom
Speaker
Maxie Dion SchmidtGeorgia Tech
ABSTRACT: This manuscript explores many convolution (restricted summation) type sequences via certain types of matrix based factorizations that can be used to express their generating functions. These results are a main focus of the author's publications from 2017-2021. The last primary (non-appendix) section of the thesis explores the topic of how to best rigorously define a so-termed "canonically best" matrix based factorization for a given class of convolution sum sequences. The notion of a canonical factorization for the generating function of such sequences needs to match the qualitative properties we find in the factorization theorems for Lambert series generating functions (LGFs). The expected qualitatively most expressive expansion we find in the LGF case results naturally from algebraic constructions of the underlying LGF series type. We propose a precise quantitative requirement to generalize this notion in terms of optimal cross-correlation statistics for certain sequences that define the matrix based factorizations of the generating function expansions we study. We finally pose a few conjectures on the types of matrix factorizations we expect to find when we are able to attain the maximal (respectively minimal) correlation statistic for a given sum type. COMMITTEE:
  • Dr. Josephine Yu, Georgia Tech
  • Dr. Matthew Baker, Georgia Tech
  • Dr. Rafael de la Llave, Georgia Tech
  • Dr. Jayadev Athreya, University of Washington
  • Dr. Bruce Berndt, University of Illinois at Urbana-Champaign
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