String Math Seminar: Jae Hee Lee (MIT) “Quantum Steenrod operations of symplectic resolutions”
We study the quantum connection in positive characteristic for conical symplectic resolutions. We conjecture the equivalence of the p-curvature of such connections with (equivariant generalizations of) quantum Steenrod operations of Fukaya and Wilkins. The conjecture is verified in a wide range of examples, including the Springer resolution, thereby providing a geometric interpretation of the p-curvature and a full computation of … Read More
String Math Seminar: Niklas Garner (University of Washington) “Ravioli and Holomorphic-Topological QFT”
Abstract: Two-dimensional chiral/holomorphic quantum field theories serve as an arena where exact algebraic techniques offer a great deal of control over the spectrum of the theory. The underlying algebraic structure, known as a vertex algebra or vertex operator algebra, has seen countless applications ranging from superstring theory and pure mathematics to statistical and condensed matter physics. In this talk I … Read More
String Math Seminar: Shaoyun Bai (Simons Center)”Landau-Ginzburg models, fixed point Floer cohomology, and Fukaya categories”
Abstract: Fixed point Floer cohomology of a symplectic automorphism categorifies the Lefschetz trace formula. On the categorical side, twisted Hochschild homology of an automorphism on an A infinity category can be understood as a categorical trace. I will explain how the twisted open-closed maps are used to relate these two invariants in the setting of Fukaya categories of Landau-Ginzburg models. … Read More
String Math Seminar: Nathan Haouzi (IAS) “Ramification in the Langlands Program, and a new realization of quantum algebras in Gauge Theory”
ABSTRACT: In its simplest incarnation, the geometric Langlands program was defined by Beilinson and Drinfeld in the 90’s as relating, on one side, a flat connection on a Riemann surface, and on the other side, a more sophisticated structure known as a D-module. A recent generalization of the correspondence, due to Aganagic-Frenkel-Okounkov, establishes an isomorphism between q-deformed versions of conformal … Read More
String Math Seminar: Gleb Aminov (Stony Brook University) “What languages do black holes speak?”
Abstract: Like many physical objects, under smallperturbations, black holes possess the property of vibrating at discretecharacteristic frequencies (known as QNM frequencies). They are complex anddepend on the type of black hole and the boundary conditions imposed on theperturbation. As we anticipate “hearing” these frequenciesthrough new experiments more distinctly, it becomes essential to understandtheir mathematical structure better or, in other words, … Read More
String Math Seminar: Harold Williams (USC) ” Differential operators on the base affine space and quantized Coulomb branches “
Abstract: We discuss joint work with Tom Gannon, showing that the algebra $D(SL_n/U)$ of differential operators on the base affine space of $SL_n$ is the quantized Coulomb branch of a certain 3d $\mathcal{N} = 4$ quiver gauge theory. In the semiclassical limit this confirms a conjecture of Dancer-Hanany-Kirwan on the universal hyperk\”ahler implosion of $SL_n$. In fact, we prove a … Read More
String Math Seminar: Tommaso Botta (ETH Zurich) “Bow varieties, stable envelopes, and their 3d mirror symmetry”
Abstract: Mirror symmetry for 3d N=4 SUSY QFTs has recently received much attention in geometry and representation theory. Theories within this class give rise to interesting moduli spaces of vacua, whose most relevant components are called the Higgs and Coulomb branches. Nakajima initiated the mathematical study of Higgs branches in the 90s; since then, their geometry has been pivotal in … Read More
String Math Seminar: Mykola Dedushenko (Simons Center for Geometry and Physics) “A new look at the SCFT/VOA correspondence”
Abstract: “We link several constructions of vertex operator algebras (VOA) in supersymmetric QFT. One is the SCFT/VOA correspondence of Beem et al, identifying VOA inside the protected sector of a 4d N=2 SCFT. Using the Omega-background approach to the SCFT/VOA, and compactifying the 4d theory on the infinite cigar geometry, we relate this to the construction of boundary VOAs in … Read More
String Math: Alexei Oblomkov (UMass Amherst) “Kapustin-Rozanksy-Witten (KRS) theory path to knot homology”
Abstract: My talk is based on the joint project with Lev Rozansky. I will explain how we rigorously construct 3D TQFT, which is a KRS theory with targets Hilbert scheme of points on a plane. Defects in the last theory encode a knot in the three-space and we rediscover the HOMFLY-PT homology of a link as a part of the … Read More
Spencer Tamagni (UCB) “Quasimaps with monopoles and nonabelian shift operators”
Abstract: We revisit supersymmetric localization with monopole operators in 3D N=4 gauge theories, arriving at a new point of view on their quantized Coulomb branch algebras. Our construction agrees with and recovers the existing mathematical definition. We apply the machinery to define a nonabelian analog of shift operators in enumerative theory of quasimaps, and illustrate the construction in detail for … Read More