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.