Seminar Calendar
for events the day of Thursday, April 27, 2017.

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Thursday, April 27, 2017

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, April 27, 2017
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Submitted by sahlgren.
Andrew Sills (Georgia Southern University)
A formula for the partition function that "counts"
Abstract: A partition of an integer n is a representation of n as a sum of positive integers where the order of the summands is considered irrelevant. Thus we see that there are five partitions of the integer 4, namely 4, 3+1, 2+2, 2+1+1, 1+1+1+1. The partition function p(n) denotes the number of partitions of n. Thus p(4) = 5. The first exact formula for p(n) was given by Hardy and Ramanujan in 1918. Twenty years later, Hans Rademacher improved the Hardy-Ramanujan formula to give an infinite series that converges to p(n). The Hardy-Ramanujan-Rademacher series is revered as one of the truly great accomplishments in the field of analytic number theory. In 2011, Ken Ono and Jan Bruinier surprised everyone by announcing a new formula which attains p(n) by summing a finite number of complex numbers which arise in connection with the multiset of algebraic numbers that are the union of Galois orbits for the discriminant -24n + 1 ring class field. Thus the known formulas for p(n) involve deep mathematics, and are by no means "combinatorial" in the sense that they involve summing a finite or infinite number of complex numbers to obtain the correct (positive integer) value. In this talk, I will show a new formula for the partition function as a multisum of positive integers, each term of which actually counts a certain class of partitions, and thus appears to be the first truly combinatorial formula for p(n). The idea behind the formula is due to Yuriy Choliy, and the work was completed in collaboration with him. We will further examine a new way to approximate p(n) using a class of polynomials with rational coefficients, and observe this approximation is very close to that of using the initial term of the Rademacher series. The talk will be accessible to students as well as faculty, and anyone interested is encouraged to attend!

Math-Physics Seminar
12:30 pm   in 464 Loomis Laboratory,  Thursday, April 27, 2017
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Submitted by katz.
Gabriel Wong (Virginia Physics)
To Be Announced

Mathematics Colloquium: Tondeur Lectures in Mathematics
4:00 pm   in 245 Altgeld Hall,  Thursday, April 27, 2017
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Submitted by kapovich.
Ulrike Tillmann (Oxford University)
TBA
Abstract: The Spring 2017 Tondeur Lectures in Mathematics will be held April 25-April 27, 2017. Faculty host: Vesna Stojanoska.