Online Junior Number Theory Seminar

- Motivation -

A few years ago, a rather naive idea came to my mind: As graduate students, we spend a lot of time working on mini-projects, Master’s and PhD theses, or simply following our noses and exploring whatever catches our interest – so why not share these with each other?

Motivated by this, I started a small and somewhat irregular colloquium with friends, where we took turns talking about what we had been thinking about. It turned out to be a surpisingly nice and efficient way to get exposed to exciting bits of mathematics.

In this sense, the present seminar is a continuation of those earlier, informal activities. As I’ve grown (hopefully) and changed over time, the focus of the seminar has naturally shifted along with me. Now, the idea is to invite junior researchers in number theory and arithmetic geometry to introduce their research projects. There is absolutely no need to present new results – the goal is simply to keep things clear, accessible, and enjoyable.

More than anything, it is a chance for us to get together, chat a bit, and enjoy some mathematics.

Logistics

  • Time: Fridays 9am EST, 2pm GMT, 3pm CET, and 9pm CST
  • Zoom id: 949 924 7490

We are quite flexible when it comes to scheduling, and speakers are free to design their talks as they wish :)


- Upcoming Talks -


Mumford–Tate Conjecture for Hyper-Kähler Varieties

01 May 2026, Haitao Zou (Bielefeld)

Abstract: The Mumford–Tate conjecture serves as a bridge between the analytic world of Hodge theory and the arithmetic world of Galois representations. While the conjecture is difficult even for abelian varieties, hyper-Kähler varieties offer a promising testing ground due to their similarity to K3 surfaces.

In this talk, I will introduce the Mumford–Tate conjecture and the geometry of hyper-Kähler varieties. I will then present recent results (joint with Zhichao Tang) showing that the conjecture holds after taking semisimplification. This generalizes previous results known only for specific deformation types.


TBD

24 April 2026, Moqing Chen (Strasbourg)

Abstract: TBA


- Past Talks -


Some Recent Progress of the Arithmetic Inner Product Formula

17 April 2026, Zhuoni Chi (Zhejiang University)

Abstract: This talk briefly introduces the arithmetic inner product formula for unitary groups and explains how it connects theta lifting, automorphic L-functions, and arithmetic cycles on Shimura varieties. After reviewing the classical picture and method, I will focus on the new difficulties that arise at ramified places with local root number -1.


Previous Edition

  • Minhua Cheng (Utah), Introduction to p-adic Hodge theory
  • Zipei Nie (Huawei - Centre de recherche Lagrange), Card Guessing Game with Partial Feedback
  • Huatao Gui (ETH Zürich), An introduction to right-angled Artin groups
  • Markus Schwagenscheidt (ETH Zürich), From generating functions to modular forms
  • Matthias Gröbner (ETH Zürich), The Riemann zeta function from an adelic perspective
  • Raphael Appenzeller (ETH Zürich), Generalized metric spaces and the Lean theorem prover
  • Francesco Naccarato (Scuola Normale Superiore Pisa), Tunnell’s Theorem and the analytic rank of elliptic curves
  • Linpu Gao (Tsinghua) Kac’s theorem and quiver representations over finite fields
  • Feusi Jeremy (ETH Zürich), Galois groups and fundamental groups, interesting properties and similarities
  • Yixuan Li (UC Berkeley), Geometric representation theory
  • Jiahao Niu (UCAS/Stanford University), Six functor formalism
  • Cunyuan Zhao (ETH Zürich), Bounded cohomology and actions on the circle
  • Zhongkai Tao (UC Berkeley), An introduction to Selberg trace formula
  • Xiangyu Pan (Peking University), Introduction to étale cohomology