Introduction

The Tsukuba Workshop for Young Mathematicians (TWYM) has been held annually in Tsukuba since 2008.

The purpose of this workshop is for students studying mathematics at Asian universities to interact, and for young mathematicians to give research presentations.

We sincerely appreciate guest speakers attending our workshop during COVID-19 situation.

Guest Speakers

Speaker : Lutian Zhao

Title : Moduli of Parabolic Higgs Bundles and Langlands Duality

Abstract : We investigate the geometry of moduli spaces of parabolic Higgs bundles and Langlands duality. We begin by revisiting Hitchin's framework for Higgs bundles, extended by parabolic structures that handle singularities at marked points on a Riemann surface. By imposing stability conditions and constructing the Hitchin fibration, we show that the fibers, which are Prym varieties, form an integrable system mirroring the duality between moduli spaces of \(SL_2\) and \(PGL_2\) bundles. This correspondence applies to a broader setting in the geometric Langlands program, where dual abelian varieties arise from gauge theory and S-duality. We aim to unify these perspectives by establishing an equality of (stringy) Hodge numbers for mirror-symmetric moduli spaces of general reductive groups with fixed orbits.

Link of YouTube : https://youtu.be/3XJ3lpUBwHg

Details

Dates

February 6(Thursday) - 20(Thursday) , 2025

Venue

This workshop will be held online, available on Youtube. The videos can be viewed during the dates above.

Organizers

・Umino Tetsuya (海野 哲也 , t.umino_at_math.tsukuba.ac.jp)

・Yanaka Masaya (谷中 勝哉 , yanakama_at_math.tsukuba.ac.jp)