Dmitriy Voloshyn

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

Preprints

  1. Multiple rational normal forms in Lie theory (2025) arXiv:2506.01530
  2. Starfish lemma via birational quasi-isomorphisms (2023) arXiv:2311.00404
  3. Generalized cluster structures related to Poisson duals of $\mathrm{SL}_n$ (with M. Gekhtman) (2023) arXiv:2312.04859

Papers

  1. Multiple generalized cluster structures on $D(\mathrm{GL}_n)$, Forum of Mathematics, Sigma 11(46) (2023), 1–78. doi:10.1017/fms.2023.44 arXiv:2111.01771

Videos & Notes

Cluster algebras and Poisson geometry

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.

video pdf notes .pptx notes

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 $\mathbf{\Gamma}$.

pdf

Examples of cluster structures on the Drinfeld double of $\mathrm{GL}_n$

pdf

Invited talks in 2025

  1. Poisson geometry and cluster algebras conference, Nankai University (January 2025)
  2. 2025 Algebra camp, Seoul National University (February 2025)
  3. Special session for group actions in algebraic geometry and related topics (SS-05), KMS meeting at KAIST (April 2025)
  4. Geometry seminar, University of Hong Kong (April 2025)
  5. Conference on Integrable Systems and Related Areas, Institute for Basic Science, Center for Geometry and Physics (June 2025)

Invited talks in 2024

  1. IBS Postdoc lectures series (April 2024) link
  2. Paris algebra seminar (April 2024) link
  3. Gone Fishing 2024, Northwestern university (April 2024) link
  4. Algebraic geometry and Commutative algebra seminar, University of Notre Dame (April 2024) link
  5. Geometry, Algebra and Physics Seminar, Korea Institute for Advanced Studies (KIAS) (May 2024) link
  6. Special session for representation theory and related topics (SS-01), KMS meeting at Sungkyunkwan University (October 2025)

Other links

Google scholar

Github