# Programme

### Presentations:

**Monday**

**Monday**

Mikhail Bershtein, Twisted representations of toroidal algebra from DAHA

Alexey Litvinov, Affine Yangians and integrable structures in conformal field theories

Andrey Mudrov, Generalized parabolic categories over quantum conjugacy classes of finite order

Dimitri Gurevich, Quantum doubles and q-cut-and-join formula

Georgy Sharygin, Operations on universal enveloping algebra and the "argument shift" method}

Olga Postnova, Tensor powers of vector representation of $u_q(sl_2)$ at even root of unity}

**Tuesday**

**Tuesday**

Oleg Zaboronski, Hecke algebra and duality

Anton Nazarov, Skew Howe duality and limit shape of Young diagrams

Anastasiia Trofimova, Current statistics in Asymmetric Avalanche Process

Daria Shabetnik, $T\bar{T}$- and long-range deformations of lattice models

Khaydar Nurligareev, Watermelon correlation functions near the boundary in the Spanning Trees Model

Nikolai Kuchumov, A variational principle for domino tilings of multiply-connected domains

**Wednesday**

**Wednesday**

Anton Shchechkin, Folding transformations for q-Painlevé equations

Vladimir Roubtsov, Monodromies of confluent Painlevé systems, Their quantization, and Calabi-Yau 3-algebras

Vitaly Tarasov, (gl_k,gl_n) duality for integrable models. Grassmann case.

Dmitry Talalaev, Weighted graphs and discrete geometry

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**Th**

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Sergei Lukyanov, Generalized affine sl(2) Gaudin model

Andrei Zotov, Manakov triple for double elliptic integrable system

Vsevolod Adler, Painlevé type reductions in the non-Abelian Toda lattice

Alexander Mikhailov, Quantisation of Nonabelian Dynamical Systems. Quantisation Ideals

Evgeny Sobko, $SU(N)$ Principal Chiral Model at Large N and the glimpse of a new String Theory

Mikhail Alfimov, Normal form of beta-function for $D=2$ sigma-models

Vadim Prokofev, Integrable hierarchies of nonlinear differential equations and many-body systems

Mikhail Vasilyev, Quantum-Classical dualities for Gaudin magnets with diagonal boundary conditions

Irina Bobrova, On matrix Painlevé-4 equations

Margarita Preobrazhenskaia, Group extensions and the parametric Yang-Baxter equation

**Friday**

**Friday**

Michael Gekhtman, Generalized cluster structures and periodic difference operators

Michael Shapiro, Noncommutative cluster integrability

Sergei Lando, Combinatorics of real normalized differentials

Alexey Basalaev, Integrable hierarchies associated to infinite families of Frobenius manifolds

Alexander Shapiro, Cluster realization of spherical DAHA

Čestmír Burdík, Nested Bethe Ansatz and trace formula for RTT–algebra of sp(4) type

Ivan Sechin, Quadratic algebras based on SL(NM) elliptic quantum R-matrices