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Joint Moscow-Beijing Mathematical Online Colloquium «Beijing-Moscow Mathematics Colloquium»

11:00 (GMT+3)
Maxim Grigoriev Institute for Theoretical and Mathematical Physics, MSU

Bio: Maxim Grigoriev is the deputy director of Institute for Theoretical and Mathematical Physics, Lomonosov Moscow State University. Maxim Grigoriev's scientific interests include mathematical methods for describing gauge systems (dynamical constraints and symmetry, Batalin-Vilkovisky quantization), higher spin gauge theories, holography, sigma models in superstring theory, and noncommutative theories. He proposed the so-called parent formulation of gauge theories, which systematically combines the Batalin-Vilkovisky and Hamiltonian BRST approaches into a single formalism having the structure of the Aleksandrov-Kontsevich-Schwartz-Zaboronsky (AKSZ) (generalized) sigma model.

Presymplectic gauge PDEs and Batalin-Vilkovisky formalism.

Gauge PDE is a geometrical object underlying what physicists call a local gauge field theory defined in terms of BV-BRST formalism. Although gauge PDE can be defined as a PDE equipped with extra structures, the generalization is not entirely straightforward as, for instance, two gauge PDEs can be equivalent even if the underlying PDEs are not. As far as Lagrangian gauge systems are concerned the powerful framework is provided by the Batalin-Vilkovisky (BV) formalism on jet-bundles. However, just like in the case of usual PDEs it is difficult to encode the BV extension of the Lagrangian in terms of the intrinsic geometry of the equation manifold while working on jet-bundles is often very restrictive, especially in analyzing boundary behavior, e.g., in the context of AdS/CFT correspondence. We show that BV Lagrangian (or its weaker analogs) can be encoded in the compatible graded presymplectic structure on the gauge PDE. In the case of genuine Lagrangian systems this presymplectic structure is related to a certain completion of the canonical BV symplectic structure. A presymplectic gauge PDE gives rise to the BV formulation through an appropriate generalization of the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) sigma-model construction followed by taking the symplectic quotient. The construction is illustrated on the standard examples of gauge theories with particular emphasis on the Einstein gravity, where this naturally leads to an elegant presymplectic AKSZ representation of the BV formulation for the Cartan-Weyl Lagrangian.

12:00 (GMT+3)
Yi Xie  

Bio: Yi Xie is an assistant professor at Beijing International Center for Mathematical Research, Peking University. His research focuses on mathematical gauge theory and its application in low-dimensional topology.

Khovanov skein homology for links in the thickened torus.

Khovanov homology is a powerful combinatorial invariant for links in the 3-sphere. Asaeda, Przytycki and Sikora defined a generalization of Khovanov homology for links in thickened compact surfaces. In this talk we will review their definition and show that the Asaeda-Przytycki-Sikora homology detects the unlink and torus links in the thickened torus. This is joint work with Boyu Zhang.

 The meeting will be held in the form of a webinar on the Zoom platform.

Pre-registration for the event is not required.

To join Zoom meeting(You can join in the meeting without a phone number):

Meeting ID : 841 7985 0467