**2023년 4월 QSMS Monthly Seminar**

**Date:**April 21 (Fri) 14:00 ~ 17:00**Place:**129-101 (SNU)**Contents:**

**Speaker: **강정수 (오후 2시)

**Title:** Lagrangian submanifolds and their Legendrian lifts

**Abstract**: A symplectic manifold with integral symplectic form serves as the base space of a prequantization bundle, a principal circle bundle with canonical contact structure. I will talk about Lagrangian submanifolds in integral symplectic manifolds that admit Legendrian lifts to prequantization bundles. After giving a gentle introduction to this setting, I will propose a method of studying such Lagrangian submanifolds using the symplectic homology of the corresponding Legendrian lifts.

**Speaker: **이석형 (오후 4시)

**Title: **Counting lattice points and number theoretic objects

**Abstract**: Counting lattice points in a given region seems easy at first, but it can have surprisingly profound connections to many areas of number theory. Bhargava and Shankar's results on counting rings of small ranks having bounded discriminant rely on their new technique of counting lattice points corresponding to integral orbits of GLn-representations. In this talk, we will discuss various problems of counting lattice points starting from elementary examples, and describe the 'averaging' technique of Bhargava-Shankar in the end.