Opening Room: Valhalla room The start of our fun event

Pavel Suprun "Hardships of non--abelian 2--forms and their prevoznemoganie" Room: Valhalla room I continue the series of my not-so-regular talks devoted to problems of non-abelian integration over surfaces. I will start with a broad-brush introduction to the subject, covering in particular Eckmann-Hilton argument, a sort of no-go theorem essentially forbidding two-dimensional non-abelian constructions relying on associative multiplication. We will hopefully see how this argument affects a version of non-abelian 2-form fields relying on the crossed module theory, essentially bounding their 3-curvatures to abelian sector. After that I will try and explain my own work on the subject, which uses contraction of three-index tensors instead of associative multiplication as a base operation. The basic example I hope to understand completely soon enough is the restoration of (infinitely-indexed) multiplication tensor from structure constants in Lie algebras, given by continuous-limit BCH formula. One of the key understanding checks for non-abelian surface integration theory would be giving a loop-space differential equation-based derivation for this formula. The prevoznemoganie techniques introduced and developed by Profs. Zaigraev and Kolganov are essential in this process, but the fast-working methods have been surprisingly fruitless so far.

Nikita Kolganov Room: Valhalla room TBA

Julia Zernina Room: Valhalla room TBA

Hasib Sifat "Matrix Models in Wess-Zumino-Witten Theories" Room: Valhalla room Regardless of Prof. Zaigarev’s determined criticism, matrix models continue to appear as a universal tool in modern theoretical physics. In this talk, I will explain how a particular type of matrix model arises in the holomorphic correlators of the affine sl(2)_k and sl(3)_k Wess–Zumino–Witten (WZW) models. I will then discuss how these solutions satisfy the Knizhnik–Zamolodchikov (KZ) equation and how one can obtain their hypergeometric form. Finally, I will make a few comments on higher-rank WZW models, as well as on the matrix-model structure of their holomorphic correlators and the corresponding KZ solution spaces.

Solving second-order matrix differential equations

• Yaroslav Drachov (MIPT)

Room: Valhalla room Matrix models field has gone wild in terms of average equation size. On the example of Gaussian model I'll show the perspective, where everything simplifies, compactifies, familiar concepts become more apparent and integrals even become convergent. Infinite amount of Virasoro constraints becomes one matrix Ward identity. Generating function of Gaussian model correlators becomes multivariate Hermite polynomial. W-representation becomes standard differential operator representation of this Hermite polynomial and Rodrigues' type formulas complement this representation. Equivalence of 2d quantum and topological gravities seems to have something in common with the known fact that asymptotic of Hermite functions as n→∞ is Airy function. The β-deformation of this picture is also rather straightforward.

Dmitriy Lezhnev "Relational quantum dynamics crash course and pathetic progress in the Schwinger-Keldysh relational technique" Room: Valhalla room В современной квантовой гравитации и космологии центральной проблемой остается «проблема времени», возникающая из-за репараметризационной инвариантности теории, что приводит к «замороженному формализму», где гамильтониан является ограничением. В данной работе предлагается расширение формализма Швингера-Келдыша на полное релятивистское фазовое пространство, что позволяет вычислять корреляционные функции в реальном времени в отсутствие внешнего временного параметра. В рамках доклада демонстрируется, как реляционные подходы позволяют извлечь динамику путем выбора внутренних степеней свободы в качестве часов и эквивалентность различных методов. Мы представляем формулировку SK в классическом пределе (линейный порядок по квантовому полю) и основу для дальнейшего развития квантового случая.

Radomir Stepanov Room: Valhalla room TBA

Nika Gribova Room: Valhalla room TBA

Dmitrii Trunin (online) Room: Valhalla room TBA

Matthew Fedin (online) Room: Valhalla room TBA