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

- Generalized cluster structures on $\mathrm{SL}_n^{\dagger}$ (with M. Gekhtman) arXiv:2312.04859
- Starfish lemma via birational quasi-isomorphisms arXiv:2311.00404

# Papers

- 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

### Supplementary note to Generalized cluster structures on $\mathrm{SL}_n^{\dagger}$ arXiv:2312.04859

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 2024

- IBS Postdoc lectures series (April 2024) link
*Paris algebra seminar* (April 2024) link
- Gone Fishing 2024 at Northwestern university (April 2024) link
- University of Notre Dame,
*Algebraic geometry and Commutative algebra seminar* (April 2024) link
- Korea Institute for Advanced Studies (KIAS),
*Geometry, Algebra and Physics Seminar* (May 2024) link

# Other links

Google scholar

Github