Mathematical Physics

We formulate the holomorphic twists of the 6d N=(0,1) and (0,2) abelian tensor multiplets as moduli spaces in derived geometry, using Deligne cohomology as a key tool. This description allows one to mimic the Beilinson-Drinfeld construction of lattice chiral algebras to quantize these 6d theories…

The moduli space of quasimaps gives a partial compactification of maps from an algebraic curve to a variety. In physics, the cohomology of this moduli space can be viewed as the state space of a (twisted) supersymmetric gauge theory. It is shown by Bullimore-Dimofte-Gaiotto-Hilburn-Kim that when the…

In a joint work with Yalong Cao, Andrei Okounkov, and Zijun Zhou, we introduce stable envelopes in critical cohomology and K-theory for symmetric quiver varieties with potentials and related geometries. Critical stable envelopes are compatible with dimensional reductions, specializations, Hall…

In QFT, there exists a well-known set of relations between the scattering amplitudes of gluons in gauge theory and those of gravitons in gravity, known collectively as the double copy. There are many beautiful ways in which this is manifested, famous examples being the KLT double copy, the double…

By a folk theorem (non-extended) 2-dimensional TFTs valued in the category of vector spaces are equivalent to commutative Frobenius algebras. Upgrading the bordism category to an (infinity, 1)-category whose 2-morphism are diffeomorphisms, one can study 2D TFTs valued in higher categories, leading…

We show that specific exponential integrals serve as generating functions of labeled edge-colored graphs. Based on this, we derive asymptotics for the number of edge-colored graphs with arbitrary weights assigned to different vertex structures. The asymptotic behavior is governed by the critical…

K-theoretical Coulomb branches are expected to have cluster structure. Cautis and Williams categorified this expectation. In particular, they conjecture (and prove in type A) that the category of perverse coherent sheaves on the affine Grassmannian is a cluster monoidal categorification. We discuss…

Recent work by Davide Gaiotto and collaborators introduced a new type of parametric Feynman integrals to compute BRST anomalies in topological and holomorphic quantum field theories. The integrand of these integrals is a certain differential form in Schwinger parameters. In a new article together…

In this talk, I will discuss a birational realization of King's conjecture which is indeed true, and its connections with noncommutative algebraic geometry and mirror symmetry. In particular, I will also establish the A-side analog of this result using constructible sheaves and promote the…

In 2010, Kontsevich and Soibelman defined Cohomological Hall Algebras for quivers and potential as a mathematical construction of the algebra of BPS states. These algebras are modeled on the cohomology of vanishing cycles, which makes these algebras particularly hard to study but often result in…

Vertex operator algebras (VOAs) arise in many corners of supersymmetric quantum field theory. One particularly influential instance is in 4d N=2 superconformal field theories, whereby the VOA is realized as the cohomology of a suitable supercharge. Unitarity of the underlying SCFT imposes strong…