Abstract: In the recent papers by Braverman-Finkelberg-Nakajima a mathematical construction of the Coulomb branches of 3d N=4 quiver gauge theories was proposed, whose quantization is conjecturally described via the so-called shifted Yangians and shifted quantum affine algebras. The goal of this talk is to explain how both of these shifted algebras provide a new insight towards integrable systems via the … Read More

The nonabelian Hodge correspondence gives a diffeomorphism between the moduli of flat connections and the moduli of higgs bundles on a smooth Riemann surface. The two moduli, however, are completely different as algebraic varieties. Thus natural structures on one side of the correspondence, such as Hitchin’s integrable system, become rather mysterious on the other side. I will discuss joint work … Read More

In the first part of the talk, I will analyze two dimensional Jackiw Teitelboim gravity with positive cosmological constant. I will study the Hartle-Hawking wavefunction of the universe and comment on non perturbative effects. In the second part, I will explain the relevance of this analysis to higher dimensions.

Abstract: In this talk I will present some of the results and recent developments in 1811.10592, where a technique for constructing Bridgeland stability conditions on Fukaya categories associated to marked surfaces. I will introduce the results of that paper and give examples; time allowing I will also mention some recent developments.

Abstract: Lifshitz scaling is an anisotropic scaling where time and space scale differently. Quantum field theories that exhibit Lifshitz scale symmetry provide a framework for studying low energy systems with an emergent dynamic scaling such as quantum critical points. Introducing supersymmetry to the Lifshitz algebra leads to a rich structure that is less constrained compared to that of relativistic supersymmetry. … Read More

We discuss a class of vertex operator algebras $\mathcal{W}_{m|n\times \infty}$ generated by a super-matrix of fields for each integral spin $1,2,3,\dots$. The algebras admit a large family of truncations that are in correspondence with holomorphic functions on the Calabi-Yau singularity given by solutions to $xy=z^mw^n$. We propose a free-field realization of such truncations generalizing the Miura transformation for $\mathcal{W}_N$ algebras. … Read More

Contact geometry is the overarching geometric setting for the study of dynamical systems because contact manifolds are odd-dimensional and may be viewed as “phase-spacetime’’. Contact geometry is therefore particularly suited to quantization independent of the choice of time. Applying BRST quantization to dynamics on a contact manifold leads to a new formulation of quantum mechanics where quantum dynamics becomes parallel … Read More

Recently, Costello proposed how to systematically apply Omega deformation on string theory and M-theory. Upon the deformation, one can discuss the exact topological holography of both M2 and M5 branes. The goal of the talk is to review Costello’s formalism and to discuss a combined system of the M2 and M5 branes, which is the joint work with D. Gaiotto. … Read More