Geometry and topology of wild character varieties

Abstract: Wild character varieties parametrize monodromy representations of flat meromorphic connections on compact Riemann surfaces. They are classical objects with remarkable geometric and topological properties.

I will recall how intrinsic geometric structures resolve singularities of wild character varieties and will show that their algebraic symplectic structures extend naturally to the resolutions. This is based on a new universal method for producing symplectic structures which is a joint work with Arinkin and Toen. I will also describe recent joint works with Chuang, Diaconescu, Donagi, and Nawata in which we use string dualities to extract cohomological invariants of twisted wild character varieties from BPS counts on Calabi-Yau threefolds and refined Chern-Simons invariants of torus knots.

differential geometrymetric geometry

Audience: researchers in the discipline

Western Hemisphere colloquium on geometry and physics

Series comments: Description: Biweekly colloquium of geometers and physicists

This weekly online colloquium features geometers and physicists presenting current research on a wide range of topics in the interface of the two fields. The talks are aimed at a broad audience. They will take place via Zoom on alternate Mondays at 3pm Eastern, noon Pacific, 4pm BRT. Each session features a 60 minute talk, followed by 15 minutes for questions and discussion. You may join the meeting 15 minutes in advance. Questions and comments may be submitted to the moderator via the chat interface during the talk, or presented in person during the Q&A session. These colloquia will be recorded and will be available (linked from the website) asap after the event.