Number Theory Seminar

Upcoming Talks

时间地点	报告人	题目与摘要
5月15日 (周五) 16:00–17:00 光华东主楼1601	杜托平华北电力大学	Title. On the central derivatives of L-functions and modularity of Heegner cycles Abstract. The derivative of cusp forms can be represented by the global height pairing between higher Heegner cycles. This result provides a framework for the Gross–Zagier–Zhang formula and its generalizations. Furthermore, we investigate the modularity of the generating series of Heegner cycles, proving a weak version of the conjecture and reducing the full modularity to a vanishing conjecture.
5月22日 (周五) 16:00–17:00 SCMS 106	杨金榜中国科学技术大学	Title. A Lefschetz Theorem for Crystalline Representations Abstract. As a corollary of nonabelian Hodge theory, Simpson proved a strong Lefschetz theorem for complex polarized variations of Hodge structure. In this talk, I will introduce an arithmetic analog. The primary technique is p-adic nonabelian Hodge theory. This is based on joint work with Raju Krishnamoorthy and Kang Zuo.
5月29日 (周五) 16:00–17:00 光华楼东主楼 1801	杨瑞杰 University of Kansas	Title. strong monodromy conjecture for hyperplane arrangements Abstract. To control the asymptotic of p-adic exponential sums, Igusa proposed the Strong Monodromy Conjecture, which predicts that the p-adic zeta function of an integer coefficient polynomial is governed by the D-module theory over complex numbers. However, there are very few known cases. In this talk, I will explain my recent joint work with Dougal Davis, where we prove this conjecture for any hyperplane arrangement, based on our new theory of multivariate V-filtration and its interaction with the theory of mixed Hodge modules.
6月5日 (周四) 16:00–17:00 SCMS 102	罗渝 University of Wisconsin-Madison	Title. Arithmetic Siegel--Weil formula and Kudla--Rapoport conjecture Abstract. Kudla—Rapoport conjecture predicts a precise identity between the arithmetic intersection number of special cycles on unitary Rapoport-Zink spaces and the derivative of local representation densities of hermitian forms. This result was proven by C. Li and W. Zhang in 2022 at the hyperspecial level. In this talk, I will discuss and motivate the conjecture and its global counterpart. If time permits, I will present a new proof of the conjecture using a global method.

时间地点

报告人

题目与摘要

5月15日 (周五)

16:00–17:00

光华东主楼1601

杜托平
华北电力大学

Title. On the central derivatives of L-functions and modularity of Heegner cycles

Abstract. The derivative of cusp forms can be represented by the global height pairing between higher Heegner cycles. This result provides a framework for the Gross–Zagier–Zhang formula and its generalizations. Furthermore, we investigate the modularity of the generating series of Heegner cycles, proving a weak version of the conjecture and reducing the full modularity to a vanishing conjecture.

5月22日 (周五)

16:00–17:00

SCMS 106

杨金榜
中国科学技术大学

Title. A Lefschetz Theorem for Crystalline Representations

Abstract. As a corollary of nonabelian Hodge theory, Simpson proved a strong Lefschetz theorem for complex polarized variations of Hodge structure. In this talk, I will introduce an arithmetic analog. The primary technique is p-adic nonabelian Hodge theory. This is based on joint work with Raju Krishnamoorthy and Kang Zuo.

5月29日 (周五)

16:00–17:00

光华楼东主楼 1801

杨瑞杰
University of Kansas

Title. strong monodromy conjecture for hyperplane arrangements

Abstract. To control the asymptotic of p-adic exponential sums, Igusa proposed the Strong Monodromy Conjecture, which predicts that the p-adic zeta function of an integer coefficient polynomial is governed by the D-module theory over complex numbers. However, there are very few known cases. In this talk, I will explain my recent joint work with Dougal Davis, where we prove this conjecture for any hyperplane arrangement, based on our new theory of multivariate V-filtration and its interaction with the theory of mixed Hodge modules.

6月5日 (周四)

16:00–17:00

SCMS 102

罗渝
University of Wisconsin-Madison

Title. Arithmetic Siegel--Weil formula and Kudla--Rapoport conjecture

Abstract. Kudla—Rapoport conjecture predicts a precise identity between the arithmetic intersection number of special cycles on unitary Rapoport-Zink spaces and the derivative of local representation densities of hermitian forms. This result was proven by C. Li and W. Zhang in 2022 at the hyperspecial level. In this talk, I will discuss and motivate the conjecture and its global counterpart. If time permits, I will present a new proof of the conjecture using a global method.

数论讨论班

Upcoming Talks

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