1. 일 시 : 2025년 10월 31일 (금) 오후 4:00-5:00
2. 장 소 : 아산이학관 526호
3. 연 사 : 이석형 박사님 (KIAS)
4. 제 목 : How to count lattices
5. 초 록 : The problem of counting finite-index sublattices of Z^n has long been studied in connection with counting finite-index subalgebras and ideals of Lie algebras over Z. The associated Dirichlet series exhibits remarkable structure, with local factors given by rational functions satisfying functional equations. We will give a short survey of this problem, together with its application in various areas of algebra and number theory. We also introduce our new framework of counting sublattices Λ⊂Z^n according to their cotypes, i.e. the invariant factors of the quotient Z^n/Λ. This talk is based on joint work with Seungjai Lee (Incheon National University).