Event Category: Berkeley String-Math Seminar

Berkeley String-Math Seminar

–

The Affine Grassmannian is an ind-scheme associated to a reductive group G. It has a cell structure similar to the one in the usual Grassmannian. Transversal slices to these cells give an interesting family of Poisson varieties. Some of them admit a smooth symplectic resolution and have an interesting geometry related to the representation theory of the Langlands dual group. … Read More

–

Abstract: I will give an overview of some new invariants of 3- and 4-manifolds that arise naturally in the study of compactifications of M-theory. I will discuss homological invariants of 3-manifolds and their “decategorifications” that take the form of q-series with integer coefficients, and, if time permits, homotopy-theoretic invariants of 4-manifolds that generalize the more familiar Donaldson and Seiberg-Witten invariants.

–

G2 manifolds constitute a class of Einstein seven-manifolds and are of substantial interest both in Riemannian geometry and theoretical physics. At present a vast number of compact G2 manifolds is known to exist. In this talk I will discuss a gauge-theoretic approach to the construction of invariants of compact G2 manifolds. I will focus on an interplay between gauge theories … Read More

–

In this talk we discuss Koszul duality from a physics perspective, and emphasize its role in coupling quantum field theories to topological line defects. Using this physical translation of Koszul duality as inspiration, we propose a physical definition of Koszul duality for vertex algebras. The appearances of vertex algebras (physically: holomorphic conformal field theories) in physics are legion; one particularly … Read More

–

Abstract: It is well-known that the GIT quotient depends on a choice of an equivariant ample line bundle. Various different quotients are related by birational transformations, and their B-models (D^bCoh) are related by semi-orthogonal decompositions, or derived equivalences. If we apply mirror symmetry, it is natural to ask how the A-models of the mirror of various quotients are related. We … Read More

–

Given a quiver with potential, Kontsevich-Soibelman constructed a Hall algebra on the cohomology of the stack of representations of (Q,W). In particular cases, one recovers the Yangian of a quiver Q as defined by Maulik-Okounkov. However, for general (Q,W), the Hall algebra has nice structure properties, for example Davison-Meinhardt proved a PBW theorem for it using the decomposition theorem. One … Read More

–

Abstract: A vertex algebra is the chiral algebra of a two-dimensional conformal field theory and appears in many exciting problems. W-algebras are the broadest class of these and they are associated to certain data of Lie superalgebras. These W-algebras and their representation categories appear as invariants of 4-dimensional gauge theories and dualities of physics translate into isomorphisms of vertex algebras … Read More

–

Abstract: It has long been known that holomorphic field theories on twistor space lead to “physical” field theories on Minkowski space. In this talk I will discuss a type I (unoriented) version of the topological B model on twistor space. The corresponding theory on Minkowski space is a sigma-model with target the group SO(8). This is a variant of the … Read More

–

Abstract: Abelianization of flat connections is a construction motivated by supersymmetric quantum field theory, which has turned out to be connected to various bits of geometry — in particular, to Donaldson-Thomas theory, cluster algebra, the exact WKB method for analysis of ODEs, and hyperkahler geometry. In some of these subjects it is known that there exists a natural q-deformation which … Read More