Welcome to the seminar page for the Vanderbilt number theory group. We have a vibrant group, currently consisting of Larry Rolen, Andreas Mono, Michael Griffin, and Eleanor McSpirit.
During the pandemic, many previous talks were held on zoom, and many recordings of previous talks can be found on the seminar Youtube page: https://www.youtube.com/@vanderbiltnumbertheory6986/videos
Info on talks from prior semesters can be found on the tabs above.
In addition, many talks of a conference on mock theta functions in 2021 can be found on that YouTube page. The group also hosted a large conference in Spring 2024: https://my.vanderbilt.edu/shanksseries/
If you would like to be added to the seminar email list, let Larry Rolen know by emailing larry.rolen@vanderbilt.edu
| Upcoming Talks Fall 2024:
Date: October 18, 2024, 12:10 PM Central time (Stevenson 1310) Speaker: Walter Bridges (University of North Texas) Title: Zero attractors and sign changes in partition polynomials
Abstract: I will discuss new methods in the asymptotic theory of integer partitions with applications to the following two problems.
The first problem concerns secondary terms in asymptotic equidistribution. For example, if $p(a,b,n)$ denotes the number of partitions of $n$ with parts congruent to $a$ modulo $b$, then it is easy to show that $p(a_1,b,n) \sim p(a_2,b,n)$ as $n \to \infty$ for all $0\leq a_1,a_2 < b$. On the other hand, the difference $p(a_1,b,n)-p(a_2,b,n)$ oscillates as $n \to \infty$ for any $a_1 \neq a_2$. A new technique allows us to predict the oscillation for this and similar problems. The second problem concerns zero attractors for sequences of partition polynomials. If the coefficients of the polynomial $P_n(\zeta)$ count the number of partitions of $n$ into $m$ parts, then R. Stanley asked to identify the zero attractor of the sequence $P_n(\zeta)$ as $n \to \infty$ – that is, the set of limit points of the zero sets of the $P_n(\zeta)$. It was shown by Boyer and Goh that the zero attractor of $P_n(\zeta)$ is a “Pac-Man” shaped curve in the unit disk. We prove a zero attractor for partition polynomials that count hook lengths; somewhat surprisingly, the zero attractor features isolated points. This is joint work with W. Craig, A. Folsom, J. Franke, T. Garnowski, J. Males and L. Rolen. Date: October 21, 12 PM Central time (Buttrick- Room 206) Speaker: Hui Xue (Clemson University) Title:
Subspaces spanned by eigenforms with nonzero central L-values
Abstract:
In this talk, we discuss explicit spanning sets for two vector spaces. One is the subspace generated by integral-weight Hecke eigenforms with nonzero central L- values. The other is a subspace generated by half-integral weight Hecke eigenforms with nonvanishing first Fourier coefficients. We also show that these two spaces are isomorphic via the Shimura lift.
Date: November 5 Speaker: Eleanor McSpirit (Vanderbilt University) Title/Abstract: TBA Date: November 21 Speaker: Gene Kopp (LSU) Date: |