### TBA by Cosmin Pohoata

- Series
- Graph Theory Seminar
- Time
- Tuesday, October 31, 2023 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Cosmin Pohoata – Emory University – cosmin.pohoata@gmail.com

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- Series
- Graph Theory Seminar
- Time
- Tuesday, October 31, 2023 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Cosmin Pohoata – Emory University – cosmin.pohoata@gmail.com

- Series
- Geometry Topology Seminar
- Time
- Monday, October 30, 2023 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Speaker

- Series
- Algebra Seminar
- Time
- Monday, October 30, 2023 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Cristian Lenart – SUNY Albany – clenart@albany.edu

- Series
- Combinatorics Seminar
- Time
- Friday, October 27, 2023 - 15:15 for 1 hour (actually 50 minutes)
- Location
- Skiles 308
- Speaker
- Sam Mattheus – Vrije Universiteit Brussel – smattheus@ucsd.edu

- Series
- Stochastics Seminar
- Time
- Thursday, October 26, 2023 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Manuel Fernandez – Georgia Tech

- Series
- Athens-Atlanta Number Theory Seminar
- Time
- Tuesday, October 24, 2023 - 17:15 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Vesselin Dimitrov – Georgia Tech – vdimitrov3@gatech.edu

If the formal square root of an abelian surface over Q looks like an elliptic curve, it has to be an elliptic curve."

We discuss what such a proposition might mean, and prove the most straightforward version where the precise condition is simply that the L-function of the abelian surface possesses an entire holomorphic square root. The approach follows the Diophantine principle that algebraic numbers or zeros of L-functions repel each other, and is in some sense similar in spirit to the Gelfond--Linnik--Baker solution of the class number one problem.

We discuss furthermore this latter connection: the problems that it raises under a hypothetical presence of Siegel zeros, and a proven analog over finite fields. The basic remark that underlies and motivates these researches is the well-known principle (which is a consequence of the Deuring--Heilbronn phenomenon, to be taken with suitable automorphic forms $f$ and $g$): an exceptional character $\chi$ would cause the formal $\sqrt{L(s,f)L(s,f \otimes \chi)}L(s,g)L(s, g \otimes \chi)$ to have a holomorphic branch on an abnormally big part of the complex plane, all the while enjoying a Dirichlet series formal expansion with almost-integer coefficients. This leads to the kind of situation oftentimes amenable to arithmetic algebraization methods. The most basic (qualitative) form of our main tool is what we are calling the "integral converse theorem for GL(2)," and it is a refinement of a recent Unbounded Denominators theorem that we proved jointly with Frank Calegari and Yunqing Tang.

- Series
- Athens-Atlanta Number Theory Seminar
- Time
- Tuesday, October 24, 2023 - 16:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Alexandra Florea – University of California Irvine – floreaa@uci.edu

I will talk about negative continuous and discrete moments of the Riemann zeta-function, focusing in both cases on upper bounds and asymptotic formulas. I will explain how to obtain asymptotic formulas for the continuous moments when the shift in the zeta-function in the denominator is large enough, and how to obtain upper bounds for the discrete moments and continuous moments in much wider regions for the shift. Joint work with Hung Bui and with Hung Bui and Micah Milinovich.

- Series
- Graph Theory Seminar
- Time
- Tuesday, October 24, 2023 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Clough Commons room 102
- Speaker
- Yuzhou Wang – Georgia Tech – ywang3694@gatech.edu

- Series
- Geometry Topology Seminar
- Time
- Monday, October 23, 2023 - 14:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Chris Leininger – Rice University

- Series
- Algebra Seminar
- Time
- Monday, October 23, 2023 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Speaker
- Ayah Almousa – University of Minnesota - Twin Cities – almou007@umn.edu