Tamely Ramified Geometric Langlands Correspondence

The geometric Langlands correspondence (GLC) is a geometric analogue of the Langlands conjecture in number theory, relating algebraic geometry, representation theory, and many other areas. Since A. Kapustin and E. Witten pointed out the relation between GLC and mirror symmetry, there have been various studies on GLC from a physics perspective as well as a mathematical perspective.

First talk: An introduction to Langlands conjecture for everyone
This is an entirely accessible overview of the Langlands conjecture. Starting from famous topics, such as the Pythagorean theorem and Fermat’s Last Theorem, I will introduce the statement and motivations behind the Langlands conjecture.
No prior background will be assumed, and technical details will often be sketched rather than fully developed, so that anyone with a general mathematical curiosity can follow along.

Second talk: On a certain tamely ramified geometric Langlands correspondence
In this talk, I will present my research. Arinkin’s 2001 result established the geometric Langlands correspondence for the case G = SL2 on the complex projective line P1 with four fixed regular singularities. When one attempts to extend this to five or more singularities, it turns out to be more natural to decompose the correspondence into a Radon transform-type correspondence and a “GLC‑like” correspondence.
I will report on the calculations of cohomology that support the proof of this GLC‑like correspondence in the P1 with five fixed regular singularities case.