**2023년 5월 QSMS Monthly Seminar**

**Date:**May 26 (Fri) 11:00 ~ 16:00**Place:**25-103 (SNU)**Contents:**

**Speaker: **홍한솔 (오전 11시)

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

**Abstract**: Given a Laurent polynomial defined over non-Archimedean field (typically the Novikov ring), I will introduce a tropical method to find possible locations of its critical points.

The main application is to study closed string mirror symmetry for a class of blowups of toric surfaces. The mirror geometry in this case, consists of a Laurent polynomial (or series) called the potential, which can be combinatorially computed by counting broken lines on some scattering diagram.

**Speaker: **최승일 (오후 3시)

**Title: **Symmetric and nonsymmetric Cauchy identities

**Abstract**: The Cauchy identity, which is the decomposition of the symmetric Cauchy kernel into a product of two Schur polynomials, is an important subject in the symmetric function theory and representation theory. Lascoux introduced a generalization of the Cauchy kernel, called nonsymmetric Cauchy kernels, and provided a decomposition into a product of key polynomials (or Demazure characters). In this talk, we will provide an overview of these results and then explore further extended results to other types.