Monday, March 31st, 2025
Workshop: Heeyeon Kim
Time: 9:30 AM - 10:30 AM
Location: SCGP 102
Title: 3d TFTs from 4d N=2 BPS particles
Speaker: Heeyeon Kim
Abstract: I will discuss a general strategy for constructing a 3d topological field theory that admits a boundary condition supporting a vertex operator algebra associated with a 4d N=2 Argyres-Douglas theory. This construction naturally leads to the IR Schur index formula of Cordova-Shao, which gives the vacuum character of the boundary VOA, as well as its generalizations -- new trace formulas that compute various partition functions of 3d TFTs using the data from the Coulomb branch BPS algebra of 4d SCFTs.
Title: 3d TFTs from 4d N=2 BPS particles
Speaker: Heeyeon Kim
Abstract: I will discuss a general strategy for constructing a 3d topological field theory that admits a boundary condition supporting a vertex operator algebra associated with a 4d N=2 Argyres-Douglas theory. This construction naturally leads to the IR Schur index formula of Cordova-Shao, which gives the vacuum character of the boundary VOA, as well as its generalizations -- new trace formulas that compute various partition functions of 3d TFTs using the data from the Coulomb branch BPS algebra of 4d SCFTs.
Workshop: Jaewon Song
Time: 11:00 AM - 12:00 PM
Location: SCGP 102
Title: Families VOAs from BPS Particles
Speaker: Jaewon Song
Abstract: We find that multiple vertex operator algebras (VOAs) can arise from a single 4d N=2 superconformal field theory (SCFT). The connection is given by the BPS monodromy operator M, which is a wall-crossing invariant quantity that captures the BPS spectrum on the Coulomb branch. We find that the trace of the multiple powers of the monodromy operator Tr M^N produces the vacuum characters of a VOA for each N. In particular, we realize unitary VOAs of the Deligne-Cvitanović exceptional series type (A2)_1, (G2)_1, (D4)_1, (F4)_1, (E6)_1 from Argyres-Douglas theories. We also find the modular invariant characters of the `intermediate vertex subalgebra' (E7.5)_1 and (X1)_1. Our analysis allows us to construct 3d N=2 gauge theories that flow to N=4 SCFTs in the IR, which gives rise to the topological field theories realizing the VOAs with these characters.
Title: Families VOAs from BPS Particles
Speaker: Jaewon Song
Abstract: We find that multiple vertex operator algebras (VOAs) can arise from a single 4d N=2 superconformal field theory (SCFT). The connection is given by the BPS monodromy operator M, which is a wall-crossing invariant quantity that captures the BPS spectrum on the Coulomb branch. We find that the trace of the multiple powers of the monodromy operator Tr M^N produces the vacuum characters of a VOA for each N. In particular, we realize unitary VOAs of the Deligne-Cvitanović exceptional series type (A2)_1, (G2)_1, (D4)_1, (F4)_1, (E6)_1 from Argyres-Douglas theories. We also find the modular invariant characters of the `intermediate vertex subalgebra' (E7.5)_1 and (X1)_1. Our analysis allows us to construct 3d N=2 gauge theories that flow to N=4 SCFTs in the IR, which gives rise to the topological field theories realizing the VOAs with these characters.
Math Event: Symplectic Geometry, Gauge Theory, and Low-Dimensional Topology Seminar: Mike Miller Eismeier - ASD Connections & Cosmetic Surgery
Time: 12:30 PM - 1:55 PM
Location: Math P-131
Title: ASD Connections & Cosmetic Surgery
Speaker: Mike Miller Eismeier [University of Vermont]
Abstract: The cosmetic surgery conjecture predicts that, given a knot K in a 3-manifold, the oriented diffeomorphism type of surgery on K determines the surgery slope (up to oriented diffeomorphism). For knots in the 3-sphere, a sequence of restrictions coming from Heegaard Floer homology implies that if the cosmetic surgery is false for K, then r-surgery on K is not oriented diffeomorphic to (-r)-surgery, for some r in {2, 1, 1/2, 1/3, …}, but Heegaard Floer homology techniques reach a limit here. I will discuss how a quantitative enhancement of instanton homology rules out the cases r = 1/n, leaving only the possibility of 2-surgery. I will discuss limitations of this approach as well as possible future developments. View Details
Title: ASD Connections & Cosmetic Surgery
Speaker: Mike Miller Eismeier [University of Vermont]
Abstract: The cosmetic surgery conjecture predicts that, given a knot K in a 3-manifold, the oriented diffeomorphism type of surgery on K determines the surgery slope (up to oriented diffeomorphism). For knots in the 3-sphere, a sequence of restrictions coming from Heegaard Floer homology implies that if the cosmetic surgery is false for K, then r-surgery on K is not oriented diffeomorphic to (-r)-surgery, for some r in {2, 1, 1/2, 1/3, …}, but Heegaard Floer homology techniques reach a limit here. I will discuss how a quantitative enhancement of instanton homology rules out the cases r = 1/n, leaving only the possibility of 2-surgery. I will discuss limitations of this approach as well as possible future developments. View Details
Workshop: Ben Webster
Time: 2:30 PM - 3:30 PM
Location: SCGP 102
Title: Geometry of Coulomb Branches
Speaker: Ben Webster
Abstract: I’ll report recent progress on understanding the geometry of Coulomb branches of 3d N=4 supersymmetric gauge theories, in particular on results relating Coulomb branches with different gauge groups.
Title: Geometry of Coulomb Branches
Speaker: Ben Webster
Abstract: I’ll report recent progress on understanding the geometry of Coulomb branches of 3d N=4 supersymmetric gauge theories, in particular on results relating Coulomb branches with different gauge groups.
Workshop: Gwyn Bellamy
Time: 4:00 PM - 5:00 PM
Location: SCGP 102
Title: Minimal degenerations for quiver varieties
Speaker: Gwyn Bellamy
Abstract: For any symplectic singularity, one can consider the minimal degenerations between symplectic leaves - these are the relative singularities of a pair of adjacent leaves in the closure relation. I will describe a complete classification of these minimal degenerations for Nakajima quiver varieties. It provides an effective algorithm for computing the associated Hesse diagrams. In the physics literature, it is known that this Hasse diagram can be computed using quiver subtraction. Our results appear to recover this process. I will explain applications of our results to the question of normality of leaf closures in quiver varieties. The talk is based on joint work in progress with Travis Schedler.
Title: Minimal degenerations for quiver varieties
Speaker: Gwyn Bellamy
Abstract: For any symplectic singularity, one can consider the minimal degenerations between symplectic leaves - these are the relative singularities of a pair of adjacent leaves in the closure relation. I will describe a complete classification of these minimal degenerations for Nakajima quiver varieties. It provides an effective algorithm for computing the associated Hesse diagrams. In the physics literature, it is known that this Hasse diagram can be computed using quiver subtraction. Our results appear to recover this process. I will explain applications of our results to the question of normality of leaf closures in quiver varieties. The talk is based on joint work in progress with Travis Schedler.