Workshop on Automorphic forms,
Arithmetic, and Geometry
I. Young Researchers in Number Theory

The first Workshop on Automorphic forms, Arithmetic, and Geometry (WAAG-I) will be held at KIAS on March 27, 2026.

WAAG aims to provide presentations on recent developments in number theory and related areas that are accessible to a broad audience and to promote exchange between researchers, especially those in their early careers.

Speakers

• Anand Chitrao (UNIST)

• Héctor del Castillo (Chonnam National University)

• Yong-Gyu Choi (UNIST)

Schedule

• 12:00 - 14:00 Lunch

• 14:00 - 15:00 Chitrao

• 15:00 - 15:30 Coffee break

• 15:30 - 16:30 Castillo

• 16:30 - 17:00 Coffee break

• 17:00 - 18:00 Choi

• 18:00 - Dinner

Abstract

• Anand Chitrao
  Title: Reduction mod p of semi-stable Galois representations.
  Abstract: We describe a new method to compute the reductions mod p of irreducible two-dimensional semi-stable representations of the absolute Galois group \GQp of \Qp. This method uses the compatibility with respect to the reduction mod p between the p-adic Local Langlands Correspondence and the Iwahori theoretic version of the mod p Local Langlands Correspondence. By estimating certain logarithmic functions on \Qp by polynomials on open subsets of \Zp, we compute the reductions mod p completely for weights at most p + 1. This method can be used, in theory, to compute the reductions mod p of semi-stable representations of arbitrarily large weights. At the end, we will discuss the recent progress made towards computing the reductions for weights larger than p + 1.
  This talk is based on joint work with Eknath Ghate.
  For details, please refer to https://arxiv.org/abs/2311.03740

• Héctor del Castillo
  Title: On Smooth Representations.
  Abstract: We introduce the notion of smooth representations, analogous to representations of Lie groups but over non-Archimedean fields. These play a key role in the Langlands program. We then present a result we obtained jointly with Henniart and Lomelí regarding these representations. Finally, if time permits, we will mention an application of this result to automorphic representations.

• Yong-Gyu Choi
  Title: Degeneration of D-shtukas over ramified legs.
  Abstract: Canonical integral models of Shimura varieties associated to reductive groups that are anisotropic modulo center are expected to be proper. However, the analogous statement is known to fail for moduli stacks of shtukas over global function fields. More specifically, let G be a parahoric group scheme over a smooth proper curve X over a finite field, corresponding to a maximal order of a central division algebra D. Lau established a numerical criterion for the properness of the moduli stack of bounded G-shtukas with legs restricted to the split locus of D. Consequently, there are cases where the moduli stack is not proper over the split locus. Building on the work of Arasteh Rad-Hartl and Bieker, we consider moduli stacks of bounded G-shtukas where the legs are allowed to lie in the ramification locus of D. We extend Lau's result to a setting that includes the ramified case. In particular, we demonstrate that a moduli stack of G-shtukas can be proper when legs are restricted to the split locus, yet fail to be proper when the legs extend over the entire curve. This is joint work with Wansu Kim and Junyeong Park.

Organizer

• Heejong Lee (KIAS HCMC)
  email: heejonglee<at>kias.re.kr

With the support of

• Korea Institute for Advanced Study (KIAS)

• June E Huh Center for Mathematical Challenge (HCMC)