The Ruth Moufang Lectures is a yearly distinguished lecture series addressing a broad mathematical audience in honour of Ruth Moufang, one of the major figures at Goethe University Frankfurt and a pioneer among women in mathematics. Each year, we will invite a major, established or up-and-coming international figure working in the area of Arithmetic Algebraic Geometry.
This year’s speaker of 2026 will be Mingjia Zhang.
Mingjia Zhang is a professor at Princeton University, USA. She completed her PhD at Bonn University in 2023 under the supervision of Peter Scholze, and previously was a von Neumann Fellow at the Institute for Advanced Study and Princeton University.
Zhang’s research spans a wide range of topics from the Langlands programme to p-adic Hodge theory. Her work on the geometry and cohomology of Shimura varieties, especially on Igusa stacks, has already had far-reaching applications. In recent work with Bhargav Bhatt, she is moreover making ground-breaking advances on the p-adic Simpson correspondence.
Mingjia Zhang received the 2026 Maryam Mirzakhani News Frontiers Prize of the Breakthrough Prize Foundation.
Mingjia Zhang – Colloquium
“Shimura varieties and the Langlands program”
Abstract: The Langlands program originated from Eichler and Shimura’s work on the cohomology of modular curves. They discovered the celebrated Eichler-Shimura congruence relations between Hecke operators and Frobenii, which inspired Langlands to search for a more systematic relation between automorphic forms and Galois representations. Since then, Shimura varieties, as higher dimensional generalizations of the modular curve, have been central geometric objects in the Langlands program. I will review the classical story and survey some recent developments on Shimura varieties and their cohomology.
Mingjia Zhang – Seminar talks
“Intersection cohomology of Shimura varieties”
Abstract: The L2–cohomology of locally symmetric spaces are closely related to automorphic forms and hence plays an important role in the Langlands program. In the case of Shimura varieties, it is related to the algebraic intersection cohomology, due to the work of Looiyenga, Saper–Stern. Arthur and Kottwitz made precise conjectures about how such cohomology groups can be described in terms of automorphic representations and their associated Galois representations/Arthur–Langlands parameters. I will discuss how one can study the intersection cohomology of Shimura varieties and their relation to Galois representations in the framework of categorical local Langlands correspondence, by constructing inter section complexes on the Igusa stack. This is joint work with Ana Caraiani and Linus Hamann.
“p-adic Hodge theory and integral model of Shimura varieties”
Abstract: The development of integral p-adic Hodge theory, especially the introduction of p-adic shtukas and prismatic F-gauges, has enabled new breakthroughs in the theory of canonical integral models of Shimura varieties, including the works of Pappas-Rapoport, Imai-Kato-Youcis, Madapusi-Youcis, Lee-Madapusi. I will explain the basic ideas and survey results in this direction.
| CEST | Room | Thursday, July 02, 2026 | Friday, July 03, 2026 |
| 11:00-12:00 | S2|14 | Mingjia Zhang – Seminar talks “Intersection cohomology of Shimura varieties” |
|
| 14:00-15:00 | S2|14 | Mingjia Zhang – Seminar talks “p-adic Hodge theory and integral model of Shimura varieties” |
|
| 17:00-18:00 | S2|14 | Mingjia Zhang – Colloquium “Shimura varieties and the Langlands program” |