Speaker: Dr. Weifeng Sun (Stanford University)

Time: 14:00-15:00  January 9, 2024 (Tuesday)

Place: N913

Title: The Bogomolny equations with a knot singularity

Abstract: The regular solutions of the Bogomolny equations on R^3 are well studied in the last century. There are at least two different famous approaches: The twistor method by Hitchin, Donaldson etc. and the pure analytical method by Taubes. In this talk, I will give a brief introduction on these approaches. Then I will use Taubes' approach to study the Bogomolny equations with a knot singularity. I hope these solutions will be useful in knot theory in the future.

Speaker: Prof. Jinbang Yang (USTC)

Time: 14:00-15:00  January 11, 2024 (Thursday)

Place: MCM110

Title: Motivic local systems and motivic Higgs bundles

Abstract: Families of smooth varieties give rise to numerous invariants, among which are the notable Betti-local systems and the Kodaira-Spencer maps—graded Higgs bundles. Direct summands of these local systems and graded Higgs bundles are called motivic. Our understanding of motivic local systems is currently limited, with only a few known cases. In this talk, I will present a method for determining the motivicity of a local system or a Higgs bundle of a specific type. As a consequence, we obtain infinitely many algebraic solutions to the Painleve VI equation. This is a joint work with Kang Zuo.