**2024년 05월 QSMS Monthly Seminar**

**Date:**May 24th (Fri) 14:00 ~ 17:00**Place:**27-220**Contents:**

**Speaker: **유화종 (오후2시)

**Title: **Cuspidal subgroups and rational torsion subgroups

**Abstract**: We introduce the cuspidal subgroups of the modular Jacobian varieties and their roles in the study of the rational torsion subgroups of the modular Jacobian varieties.

**Speaker: **김종명 (오후4시)

**Title: **Free subgroups generated by Dehn twists and its categorification

**Abstract**: Dehn twists along simple closed curves in a surface are elementary building blocks of the mapping class group. It is known that Dehn twists along curves generate a free subgroup if the curves do not bound a contractible region and every pair of curves intersects more than once. On the other hand, Seidel and Thomas introduced the notion of spherical twists (of a triangulated category) as a categorical analogue of that of Dehn twists. In this talk, I will explain an ongoing project attempting to find a condition which guarantees the freeness of the subgroup generated by spherical twists.