Next Seminar:  June 26, 2026 at TU Wien

Time:  June 26, 13:00 - 18:00

Location: Freihaus TU Wien (Wiedner Hauptstr. 8-10), Turm A, 7th floor, Zeichensaal 3

Schedule:  

13:00-14:00:   Rena Chu

Title: Short character sums evaluated at polynomials 

Abstract: Let p be a prime. Bounding short sums of Dirichlet characters mod p is a classical problem in analytic number theory, and the celebrated work of Burgess provides nontrivial bounds for sums as short as p1/4 + ε for all ε >0. In this talk, we will first survey known bounds in the original and generalized settings. Then we discuss the so-called "Burgess method'' and present a new variation and new results for characters evaluated at polynomials.

14:00-14:30: Tea break

14:30-15:30: Yijie Diao

Title: Square values of odd-degree binary forms 

Abstract: In this talk, I will present a new upper bound for the number of integer pairs for which an odd-degree binary form takes square value. As an application, this improves a recent result of Heath-Brown on sums of three square-full integers. 

15:30-16:30: Break

16:00-17:00:  Julia Stadlmann

Title: tba

Abstract: tba

18:00: Dinner