I’m a senior researcher (postdoc) at Institute for Basic Science (IBS), Center for Geometry and Physics (CGP) (Pohang, South Korea) link
I finished my Ph.D. at University of Notre Dame under the supervision of Michael Gekhtman in 2022.
My current research interests lie in the field of cluster algebras and Poisson geometry (in particular, the Gekhtman-Shapiro-Vainshtein conjecture). I’m also interested in related problems in mathematical physics, integrable systems, representation theory, quantum groups etc.
e-mail: dvoloshy at ibs.re.kr
other names: Dmytro Voloshyn, Dima Voloshyn
This is a 2 hour long talk given at KIAS, Geometry, Algebra and Physics Seminar, May 2024.
It’s an overview of the current state of Poisson geometry on simple complex algebraic groups and the associated cluster structures.
This note contains some additional information on the subject for which we didn’t have enough space in the actual paper. Moreover, it contains some explicitly computed examples of generalized cluster structures on $(\mathrm{SL},\pi_{\mathbf{\Gamma}}^{\dagger})$ for various Belavin-Drinfeld triples $\mathbf{\Gamma}$.