Day 5: July 03, 2026
10:00 - 11:00 Jen-Chieh Hsiao
11:20 - 12:20 Sungwook Jang
14:30 - 15:30 Minzhe Zhu
16:00 - 17:00 Yen-An Chen
Speakers
Jen-Chieh Hsiao (National Cheng Kung University)
Title: The Motivic Monodromy Conjecture in the Toric Setting
Abstract: Igusa's p-adic monodromy conjecture predicts a deep connection between the poles of zeta functions and the eigenvalues of Milnor monodromy. Motivated by this, Denef and Loeser formulated a corresponding conjecture in the framework of motivic integration. In this talk, we study the motivic monodromy conjecture for toric varieties. We prove that the conjecture holds for torus invariant ideals on smooth toric varieties, while exhibiting counterexamples in the singular case. The proof combines a combinatorial description of toric motivic zeta functions with the theory of Bernstein--Sato polynomials for toric varieties.
Sungwook Jang (IBS-CCG)
Title: Minimal model program for the anticanonical divisor
Abstract: Roughly speaking, the minimal model program is a sequence of birational maps which makes the canonical divisor closer to a nef divisor. In this talk, we study the analogue of this program for the anticanonical divisor. We want to construct a sequence of birational maps which makes the anticanonical divisor closer to a nef divisor. However, several obstructions arise when we replace the canonical divisor. We will explain these obstructions and show that we can run an anticanonical minimal model program with scaling if the variety satisfies pklt condition. This is based on the joint work with Sung Rak Choi, Donghyeon Kim, Dae-Won Lee.
Minzhe Zhu (KIAS)
Title: MMP for klt adjoint foliated surfaces
Abstract: The minimal model program for foliations on surfaces was developed through the work of Brunella, McQuillan, Spicer, and Svaldi. In this talk, I will introduce adjoint foliated surfaces, where the relevant divisor is an adjoint combination of the canonical divisor of the foliation and the canonical divisor of the underlying surface, and explain the proof of the MMP for klt adjoint foliated surfaces. More precisely, I will discuss the cone theorem, the construction of divisorial and fiber type contractions, and the termination of the MMP in this setting. I will also explain the existence of good minimal models and log canonical models. This is based on the joint work with Yen-An Chen.
Yen-An Chen (KIAS)
Title: On slope unstable Fano varieties
Abstract: In the recent year, significant progress for Fano varieties has been made recently in the study of K-stability, while the understanding of the weaker but more algebraic concept of (-K_X)-slope stability remains intricate. In this talk, we present a method that aims to characterize the geometry of (-K_X)-slope unstable Fano variety. This approach utilizes modern advancements in the foliated minimal model program. In dimension two, our approach leads to a complete classification of (-K_X)-slope unstable weak del Pezzo surfaces with canonical singularities. This is the joint work with Ching-Jui Lai.