강연영상 13 페이지 > 서울대학교 수리과학부

(강연자료 다운: Geometric Langlands Theory [A Bridge between Number Theory and Physics] (2022.04.28).pdf )

초록: The Langlands program consists of a tantalizing collection of surprising results and conjectures which relate algebraic geometry, algebraic number theory, harmonic analysis, and representation theory among other things. The geometric Langlands program was discovered as a geometric analogue of the Langlands program. In recent years, it has been discovered that the geometric Langlands program has another unexpected origin in the ideas of quantum field theory, which is the best existing framework of physics in describing our universe on the micro scale. In this talk, we aim to provide a global overview of this giant program and mention some applications of quantum field theory to the geometric Langlands program.

초록: Mirror symmetry has served as a rich source of striking coincidences of various kinds. In this talk we will first review two kinds of mirror symmetry statements, and observe how they are related. Then we will investigate the relation between pairings of two Frobenius algebras which are quantum cohomology and Jacobian ring respectively, via Cardy identity in 2-dimensional open-closed TQFT. As an example we will deal with an elliptic orbifold sphere, and see that the expected equivalence between two pairings gives rise to an identity of modular forms. This is a joint work with Cheol-Hyun Cho and Hyung-Seok Shin.