**2023년 3월 QSMS Monthly Seminar**

**Date:**3월 24일 금 오후 2시 ~ 5시**Place:**27동 220호**Contents:**

**Speaker : **유화종 (오후 2시)

**Title : **Rational points on abelian varieties

**Abstract** :

In this talk, we first introduce some well-known results about the rational points on algebraic curves over the rationals, especially on elliptic curves. Then we specialize our interest to those of finite order, called the rational torsion points, and discuss Mazur's theorem.

If time permits, we introduce a natural generalization of Mazur's result.

**Speaker : **배한울 (오후 4시)

**Title : **Duality in Rabinowitz Fukaya category

**Abstact** :

Rabinowitz Floer cohomology is a Floer theoretic invariant associated to the contact boundary of a Liouville domain X, which measures the failure for the continuation map from the symplectic homology of X to the symplectic cohomology of X to be an isomorphism. This is a Floer theoretic analogue of the fact that the cohomology of the boundary Y of a manifold X measures the failure for the natural map from the relative cohomology of the pair (X,Y) to the cohomology of X to be an isomorphism. In this talk, I will first briefly introduce Rabinowitz Floer homology associated with a pair of Lagrangians and then introduce its categorification, called Rabinowitz Fukaya category. Finally, I will explain that, under certain conditions, Rabinowitz Fukaya category admits a certain duality, which is a Floer theoretic analogue of Poincare duality. This is based on joint work with Wonbo Jeong and Jongmyeong Kim.