Time & Location: All talks are on Thursdays in TBA at 3:30 pm unless otherwise noted. Refreshments in Gibson 426 after the talk.
Organizer: Tommaso Buvoli and Samuel Punshon-Smith
Thursday, January 16
Title: On the flow of zeros of derivatives of polynomials
Andrei Martinez-Finkelshtein - Baylor University (Host: Ken)
Abstract: Assume we have a sequence of polynomials whose asymptotic zero distribution is known. What can be said about the zeros of their derivatives? Especially if we differentiate each polynomial several times, proportional to its degree? This simple-to-formulate problem has recently attracted the attention of researchers. Both the problem and the methods of its solution have exciting connections with free probability, random matrices, and approximation theory on the complex plane. In this talk, I will explain some known results in this direction and our approach to the problem, which uses only some elementary complex analysis. This is a joint work with E. Rakhmanov from the University of South Florida.
Location: Gibson Hall 126
Time: 3:30
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Special Friday, January 31
Title: Partitions Detect Primes
Speaker: Ken Ono - University of Virginia (Host: Olivia)
Abstract: This talk presents “partition theoretic” analogs of the classical work of Matiyasevich that resolved Hilbert’s Tenth Problem in the negative. The Diophantine equations we consider involve equations of MacMahon’s partition functions and their natural generalizations. Here we explicitly construct infinitely many Diophantine equations in partition functions whose solutions are precisely the prime numbers. To this end, we produce explicit additive bases of all graded weights of quasimodular forms, which is of independent interest with many further applications. This is joint work with Will Craig and Jan-Willem van Ittersum.
Location: Gibson Hall 126 Subject to change
Time: 4:00
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Tuesday, February 25
Title: Dynamical Systems Insights into Map Enumeration
Joceline Lega - University of Arizona - Host: (Ken McLaughlin)
Abstract: This talk will highlight techniques from discrete dynamical systems theory that have led to significant advances in map enumeration. We will start with a brief overview of generating functions for map counts and their relation to solutions of the discrete Painlevé I equation. We will then present computational and analytical results that lead to specific generating functions and, in the case of 4-valent maps, derive explicit expressions for map counts as functions of the number of vertices and the genus of the surface on which the map is embedded. We will conclude with open as well as recently solved questions associated with this research program. This is joint work with Nick Ercolani and Brandon Tippings..
Location: TBA
Time: 4:30
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Thursday, March 13
Title: _______
Theo Drivas - Affiliation: SUNY Stony Brook (Host: Sam)
Abstract: _______
Location: _______
Time: 3:30
