# Melting crystals and cluster integrable systems

### APA

Semenyakin, M. (2023). Melting crystals and cluster integrable systems. Perimeter Institute. https://pirsa.org/23010102

### MLA

Semenyakin, Mykola. Melting crystals and cluster integrable systems. Perimeter Institute, Jan. 17, 2023, https://pirsa.org/23010102

### BibTex

@misc{ pirsa_23010102, doi = {10.48660/23010102}, url = {https://pirsa.org/23010102}, author = {Semenyakin, Mykola}, keywords = {Quantum Fields and Strings}, language = {en}, title = {Melting crystals and cluster integrable systems}, publisher = {Perimeter Institute}, year = {2023}, month = {jan}, note = {PIRSA:23010102 see, \url{https://pirsa.org}} }

Mykola Semenyakin Perimeter Institute for Theoretical Physics

## Abstract

The language of integrable systems is widely applicable to string theory. One context where it is useful is the Seiberg-Witten theory, describing low-energy dynamics of confined 4d N=2 supersymmetric gauge theories: the families of complex curves with differentials, playing a central role in this description, appeared to be spectral curves, solving the integrable systems of interacting particles. Moreover, the spectrum of stable BPS particles appears from the consideration of hyperkahler structures on the phase spaces of integrable systems. And the full partition functions of instantons, regularized by Omega-background, solve deuatonomized systems of particles.

In my talk, I will explain correspondence unifying to some extent two latter ones. It relates discrete dynamics of so-called cluster integrable systems and partition functions of 5d N=1 supersymmetric gauge theories, or more generally of topological stings on corresponding local Calabi-Yau manifolds. Based on the simplest non-trivial example, I will show how both "equations" and "solutions" sides of correspondence naturally appear in the simple statistical models of dimers and "melting crystals" made out of them.

Zoom link: https://pitp.zoom.us/j/91449709915?pwd=eUVDeDdHVGI2ZVRwQ0hneXFpQk1wQT09