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.
Tuesday, April 1st, 2025
Workshop: Andrea Ferrari
Time: 9:30 AM - 10:30 AM
Location: SCGP 102
Title: Quasi-lisse hypertoric VOAs, free fields, (and holography)
Speaker: Andrea Ferrari
Abstract: An early example of VOAs defined on symplectic singularities are the hypertoric VOAs introduced by Kuwabara. These VOAs are not quasi-lisse, however; their associated varieties are in general bigger than the hypertoric varieties they are defined on, and may have infinitely many symplectic leaves. In this talk I will review a closely related family of VOAs, coming from A-twisted 3d N=4 abelian gauge theories, whose associated varieties are conjecturally hypertoric varieties. I will discuss in examples the relation to those obtained by Kuwbara, as well as free field realisations and their relation to Coulomb branch geometries. If time will permit, I will then conclude with some preliminary applications of these constructions to minimial tension holography.
Title: Quasi-lisse hypertoric VOAs, free fields, (and holography)
Speaker: Andrea Ferrari
Abstract: An early example of VOAs defined on symplectic singularities are the hypertoric VOAs introduced by Kuwabara. These VOAs are not quasi-lisse, however; their associated varieties are in general bigger than the hypertoric varieties they are defined on, and may have infinitely many symplectic leaves. In this talk I will review a closely related family of VOAs, coming from A-twisted 3d N=4 abelian gauge theories, whose associated varieties are conjecturally hypertoric varieties. I will discuss in examples the relation to those obtained by Kuwbara, as well as free field realisations and their relation to Coulomb branch geometries. If time will permit, I will then conclude with some preliminary applications of these constructions to minimial tension holography.
Workshop: Gabi Zafrir
Time: 11:00 AM - 12:00 PM
Location:
Title: Generalized symmetries and the dimensional reduction of 6d so SCFTs
Speaker: Gabi Zafrir
Abstract: Dimensional reduction is a useful tool to study quantum field theory at strong coupling. An interesting question here is the mapping of symmetries between the higher and lower dimensional theories. This can become quite intricate in the presence of higher form and higher group symmetries. In this talk I will discuss the torus reduction of a certain class of 6d SCFTs that UV complete 6d so(N) gauge theories with vector matter. These have an intricate structure of higher form and higher group symmetries and we shall discuss the implication and manifestation of this structure in the lower dimensional theory.
Title: Generalized symmetries and the dimensional reduction of 6d so SCFTs
Speaker: Gabi Zafrir
Abstract: Dimensional reduction is a useful tool to study quantum field theory at strong coupling. An interesting question here is the mapping of symmetries between the higher and lower dimensional theories. This can become quite intricate in the presence of higher form and higher group symmetries. In this talk I will discuss the torus reduction of a certain class of 6d SCFTs that UV complete 6d so(N) gauge theories with vector matter. These have an intricate structure of higher form and higher group symmetries and we shall discuss the implication and manifestation of this structure in the lower dimensional theory.
Workshop: Sven Möller
Time: 2:30 PM - 3:30 PM
Location: SCGP 102
Title: Chiral Quantisation of Symplectic Resolutions: The Quiver Case
Speaker: Sven Möller
Abstract: Vertex algebras can be viewed as chiral quantisation of their associated affine Poisson varieties. The latter are sometimes symplectic singularities, in particular when the vertex algebra is obtained as a twist of a 3d or 4d superconformal field theory, in which case the symplectic singularity is conjectured to be the Higgs branch of that theory. When the symplectic singularity (and its resolution) is a quiver variety, there is a procedure to construct a sheaf of vertex algebras over this quiver variety by quantum Hamiltonian reduction. With the right "anomaly cancellation" (by adding free fermions), the expectation is to recover the quiver variety as the associated variety of the global sections of this sheaf. In this talk, I will report on some recent results together with Tomoyuki Arakawa and Toshiro Kuwabara in the case of the punctual Hilbert scheme of the plane, and on some work in progress on further examples.
Title: Chiral Quantisation of Symplectic Resolutions: The Quiver Case
Speaker: Sven Möller
Abstract: Vertex algebras can be viewed as chiral quantisation of their associated affine Poisson varieties. The latter are sometimes symplectic singularities, in particular when the vertex algebra is obtained as a twist of a 3d or 4d superconformal field theory, in which case the symplectic singularity is conjectured to be the Higgs branch of that theory. When the symplectic singularity (and its resolution) is a quiver variety, there is a procedure to construct a sheaf of vertex algebras over this quiver variety by quantum Hamiltonian reduction. With the right "anomaly cancellation" (by adding free fermions), the expectation is to recover the quiver variety as the associated variety of the global sections of this sheaf. In this talk, I will report on some recent results together with Tomoyuki Arakawa and Toshiro Kuwabara in the case of the punctual Hilbert scheme of the plane, and on some work in progress on further examples.
Workshop: Dražen Adamović
Time: 4:00 PM - 5:00 PM
Location: SCGP 102
Title: On the representation theory of affine VOAs and W-algebras via inverse QHR
Speaker: Dražen Adamovic
Abstract: We review recent progress in understanding the representation theory of affine vertex algebras and W-algebras using the new type of realization motivated by finding the inverse of Quantum Hamiltonian reduction. We shall demonstrate how these realizations can be used for construction of logarithmic and weight modules for affine VOAs. Some applications on vertex algebras appearing in LCFT and 4D/2D duality will also be discussed. This talk is partially based on joint papers with Babichenko, Creutzig, Ridout, Genra and Kawasetsu.
Title: On the representation theory of affine VOAs and W-algebras via inverse QHR
Speaker: Dražen Adamovic
Abstract: We review recent progress in understanding the representation theory of affine vertex algebras and W-algebras using the new type of realization motivated by finding the inverse of Quantum Hamiltonian reduction. We shall demonstrate how these realizations can be used for construction of logarithmic and weight modules for affine VOAs. Some applications on vertex algebras appearing in LCFT and 4D/2D duality will also be discussed. This talk is partially based on joint papers with Babichenko, Creutzig, Ridout, Genra and Kawasetsu.
Math Event: Geometry/Topology Seminar: Gorapada Bera - Dirac operators twisted by ramified Euclidean line bundles
Time: 4:00 PM - 5:15 PM
Location: P-131
Title: Dirac operators twisted by ramified Euclidean line bundles
Speaker: Gorapada Bera [Stony Brook University]
Abstract: This talk explores Dirac operators twisted by ramified Euclidean line bundles, where the branching locus is a closed codimension-two submanifold. These operators appear in various contexts in gauge theory and calibrated geometry due to their connection with harmonic Z/2Z spinors. However, they are generally not Fredholm, leading to questions about their closed Fredholm extensions. A characterization of these extensions is given in terms of the Gelfand–Robbin quotient and its geometric realization. Additionally, aspects of their L^2 regularity theory will be discussed. This is a joint work with Thomas Walpuski. View Details
Title: Dirac operators twisted by ramified Euclidean line bundles
Speaker: Gorapada Bera [Stony Brook University]
Abstract: This talk explores Dirac operators twisted by ramified Euclidean line bundles, where the branching locus is a closed codimension-two submanifold. These operators appear in various contexts in gauge theory and calibrated geometry due to their connection with harmonic Z/2Z spinors. However, they are generally not Fredholm, leading to questions about their closed Fredholm extensions. A characterization of these extensions is given in terms of the Gelfand–Robbin quotient and its geometric realization. Additionally, aspects of their L^2 regularity theory will be discussed. This is a joint work with Thomas Walpuski. View Details
Wednesday, April 2nd, 2025
Workshop: Kevin Costello
Time: 9:30 AM - 10:30 AM
Location:
Title: From vertex algebras to scattering amplitudes
Speaker: Kevin Costello
Abstract: I’ll explain how vertex algebras (of exactly the type studied in this program) can be used to compute certain loop-level scattering amplitudes in four-dimensional gauge theories. This approach yields new results on two-loop scattering amplitudes, which have been successfully cross-checked with results derived using standard techniques at four points. This is based on joint works with Natalie Paquette, Roland Bittleston, and Keyou Zeng.
Title: From vertex algebras to scattering amplitudes
Speaker: Kevin Costello
Abstract: I’ll explain how vertex algebras (of exactly the type studied in this program) can be used to compute certain loop-level scattering amplitudes in four-dimensional gauge theories. This approach yields new results on two-loop scattering amplitudes, which have been successfully cross-checked with results derived using standard techniques at four points. This is based on joint works with Natalie Paquette, Roland Bittleston, and Keyou Zeng.
Workshop: Sergei Gukov
Time: 11:00 AM - 12:00 PM
Location: SCGP 102
Title: Geometry of log-VOAs and braiding of Verma modules for U_q (sl_N)
Speaker: Sergei Gukov
Title: Geometry of log-VOAs and braiding of Verma modules for U_q (sl_N)
Speaker: Sergei Gukov
Math Event: Algebraic Geometry Seminar: Eyal Markman - Cycles on abelian 2n-folds of Weil type from secant sheaves on abelian n-folds
Time: 4:00 PM - 5:00 PM
Location:
Title: Cycles on abelian 2n-folds of Weil type from secant sheaves on abelian n-folds
Speaker: Eyal Markman [U. Mass. Amherst]
Abstract: In 1977 Weil identified a 2-dimensional space of rational classes of Hodge type (n,n) in the middle cohomology of every 2n-dimensional abelian variety with a suitable complex multiplication by an imaginary quadratic number field. These abelian varieties are said to be of Weil type and these Hodge classes are known as Weil classes. We prove that the Weil classes are algebraic for all abelian sixfold of Weil type of discriminant -1, for all imaginary quadratic number fields. The algebraicity of the Weil classes follows for all abelian fourfolds of Weil type (for all discriminants and all imaginary quadratic number fields), by a degeneration argument of C. Schoen. The Hodge conjecture for abelian fourfolds is known to follow from the above result. View Details
Title: Cycles on abelian 2n-folds of Weil type from secant sheaves on abelian n-folds
Speaker: Eyal Markman [U. Mass. Amherst]
Abstract: In 1977 Weil identified a 2-dimensional space of rational classes of Hodge type (n,n) in the middle cohomology of every 2n-dimensional abelian variety with a suitable complex multiplication by an imaginary quadratic number field. These abelian varieties are said to be of Weil type and these Hodge classes are known as Weil classes. We prove that the Weil classes are algebraic for all abelian sixfold of Weil type of discriminant -1, for all imaginary quadratic number fields. The algebraicity of the Weil classes follows for all abelian fourfolds of Weil type (for all discriminants and all imaginary quadratic number fields), by a degeneration argument of C. Schoen. The Hodge conjecture for abelian fourfolds is known to follow from the above result. View Details
Thursday, April 3rd, 2025
Workshop: Amihay Hanany
Time: 9:30 AM - 10:30 AM
Location: SCGP 102
Title: TBD
Speaker: Amihay Hanany
Abstract: TBD
Title: TBD
Speaker: Amihay Hanany
Abstract: TBD
Workshop: Dmytro Matvieievskyi
Time: 11:00 AM - 12:00 PM
Location: SCGP 102
Title: Hikita conjecture for Slodowy slices and nilpotent orbit covers
Speaker: Dmytro Matvieievskyi
Abstract: Let G and G^\vee be Langlands dual complex semisimple groups. Consider a nilpotent coadjoint orbit for G^\vee, and let X^\vee be the corresponding nilpotent Slodowy slice, In a joint work with Ivan Losev and Lucas Mason-Brown we suggested that the symplectic dual to X^'vee should be an affinization X of a certain G-equivariant cover of a nilpotent coadjoint G-orbit. The Hikita conjecture predicts an isomorphism between the cohomology of the symplectic resolution of X^\vee and the algebra of functions of the schematic fixed points of X with respect to the maximal Hamiltonian torus. In this talk I will explain why this conjecture fails as stated, and how we modify it to get a new statement that we expect to be true and can prove in some cases. The talk is based on a joint work with Do Kien Hoang and Vasily Krylov.
Title: Hikita conjecture for Slodowy slices and nilpotent orbit covers
Speaker: Dmytro Matvieievskyi
Abstract: Let G and G^\vee be Langlands dual complex semisimple groups. Consider a nilpotent coadjoint orbit for G^\vee, and let X^\vee be the corresponding nilpotent Slodowy slice, In a joint work with Ivan Losev and Lucas Mason-Brown we suggested that the symplectic dual to X^'vee should be an affinization X of a certain G-equivariant cover of a nilpotent coadjoint G-orbit. The Hikita conjecture predicts an isomorphism between the cohomology of the symplectic resolution of X^\vee and the algebra of functions of the schematic fixed points of X with respect to the maximal Hamiltonian torus. In this talk I will explain why this conjecture fails as stated, and how we modify it to get a new statement that we expect to be true and can prove in some cases. The talk is based on a joint work with Do Kien Hoang and Vasily Krylov.
YITP Event: YITP Seminar Speaker: Eric Putney (Rutgers)
Time: 11:00 AM - 12:00 PM
Location: YITP Common Room 6-125
Title: Machine Learning for Galactic Dynamics - model-free analyses of Gaia: mapping the local potential, dust, and dark matter
Abstract: The massive Gaia survey coupled with novel techniques in machine learning has ushered in new era of astrometry - the study of the motions of stars - allowing particle physicists to study the influence of dark matter on stars in our galactic neighborhood. In particular, I am interested in using normalizing flows to accurately model the complex six-dimensional phase space of local stars, allowing us to solve the equilibrium collisionless Boltzmann equation in full generality. I will present a brief timeline of flow-based solutions to the Boltzmann equation, demonstrating its success in toy systems and the road to the analysis of the real Gaia DR3 six-dimensional dataset. Finally, I will present our map of the local gravitational potential, the local dark matter density, and the outlook for and challenges of this novel analysis.
Title: Machine Learning for Galactic Dynamics - model-free analyses of Gaia: mapping the local potential, dust, and dark matter
Abstract: The massive Gaia survey coupled with novel techniques in machine learning has ushered in new era of astrometry - the study of the motions of stars - allowing particle physicists to study the influence of dark matter on stars in our galactic neighborhood. In particular, I am interested in using normalizing flows to accurately model the complex six-dimensional phase space of local stars, allowing us to solve the equilibrium collisionless Boltzmann equation in full generality. I will present a brief timeline of flow-based solutions to the Boltzmann equation, demonstrating its success in toy systems and the road to the analysis of the real Gaia DR3 six-dimensional dataset. Finally, I will present our map of the local gravitational potential, the local dark matter density, and the outlook for and challenges of this novel analysis.
Physics Seminar: Csaba Csaki
Time: 2:00 PM - 3:00 PM
Location: 313
Title: Lessons from the Seiberg-Witten axion
Abstract: The photon-axion coupling is our main experimental tool for axion searches. Since it is generated by the anomaly, it is usually expected to be quantized and its magnitude to be well constrained. However some of these arguments seem to be invalidated by the presence of magnetic monopoles charged under the PQ symmetries. We try to clarify these issues by examining a toy example based on the SU(2) Seiberg-Witten theory where all of these ingredients appear automatically. We determine the effect of the magnetic monopole (or equivalently those of strongly coupled instantons) on the axion coupling and comment on the duality of the Maxwell equations for axion electrodynamics.
Title: Lessons from the Seiberg-Witten axion
Abstract: The photon-axion coupling is our main experimental tool for axion searches. Since it is generated by the anomaly, it is usually expected to be quantized and its magnitude to be well constrained. However some of these arguments seem to be invalidated by the presence of magnetic monopoles charged under the PQ symmetries. We try to clarify these issues by examining a toy example based on the SU(2) Seiberg-Witten theory where all of these ingredients appear automatically. We determine the effect of the magnetic monopole (or equivalently those of strongly coupled instantons) on the axion coupling and comment on the duality of the Maxwell equations for axion electrodynamics.
Math Event: Colloquium: Daniel Pomerleano - Cohomological splittings in algebraic and symplectic geometry
Time: 2:15 PM - 3:15 PM
Location:
Title: Cohomological splittings in algebraic and symplectic geometry
Speaker: Daniel Pomerleano [UMass Boston]
Abstract: In the 1980s, Atiyah, Bott, and Kirwan established fundamental results on the rational cohomology of a compact symplectic manifold X with a Hamiltonian action of a connected, compact group G. I will review these classical results and then discuss recent integral and even stable homotopical refinements, drawing on ideas from chromatic homotopy theory and Gromov-Witten theory. This talk is based on joint work with Shaoyun Bai, Guangbo Xu, and Constantin Teleman. View Details
Title: Cohomological splittings in algebraic and symplectic geometry
Speaker: Daniel Pomerleano [UMass Boston]
Abstract: In the 1980s, Atiyah, Bott, and Kirwan established fundamental results on the rational cohomology of a compact symplectic manifold X with a Hamiltonian action of a connected, compact group G. I will review these classical results and then discuss recent integral and even stable homotopical refinements, drawing on ideas from chromatic homotopy theory and Gromov-Witten theory. This talk is based on joint work with Shaoyun Bai, Guangbo Xu, and Constantin Teleman. View Details
Workshop: Shlomo Razamat
Time: 2:30 PM - 3:30 PM
Location: SCGP 102
Title: Generalized lattices, conformal manifolds, and symmetries
Speaker: Shlomo Razamat
Title: Generalized lattices, conformal manifolds, and symmetries
Speaker: Shlomo Razamat
Workshop: Alexander Braverman
Time: 4:00 PM - 5:00 PM
Location: SCGP 102
Title: Koszul duality in Relative Langlands duality/S-duality.
Speaker: Alexander Braverman
Abstract: Ben-Zvi, Sakellaridis and Venkatesh conjectured that X is a smooth affine spherical variety over a reductive group G (the definition will be recalled at the talk) then to that one can explicitly attached certain Poisson variety Y^{\vee} over the Langlands dual group G^{\vee} of G (over it is equal to cotangent bundle of some (also spherical) G^{\vee}-variety X^{\vee}), so that the (derived) category of G[[t]]-equivariant sheaves on X((t)) which are also equivariant with respect to the loop rotation is equivalent to the category of G^{\vee} over the quantization of Y (viewed as a dg-algebra with certain grading). This can be thought of some special case of S-duality for boundary conditions in 4d gauge theory. This has been checked in many case (some examples will be discussed at the talk). I will talk about a conjecture of Finkelberg, Ginzburg and Travkin which says that the category of B-equivariant sheaves on X should be Koszul dual to a close relative of the category B^{\vee}-equivariant modules over the quantization of Y^{\vee} (more precisely, the word "equivariant" must be replaced with "monodromic with unipotent monodromy"). In the case when X=G considered as a space with GxG-action, one recovers a well-known work of Beilinson, Ginzburg and Soergel. The purpose of the talk will be: 1) Give a review of cases when the Ben-Zvi-Sakellaridis-Venktatesh conjecture is known 2) Explain a framework for proving this conjecture in a slightly weaker form (instead of Koszul duality we shall prove an equivalence of the corresponding Z_2-graded categories). The latter part is a joint work with M.Finkelberg and R.Travkin.
Title: Koszul duality in Relative Langlands duality/S-duality.
Speaker: Alexander Braverman
Abstract: Ben-Zvi, Sakellaridis and Venkatesh conjectured that X is a smooth affine spherical variety over a reductive group G (the definition will be recalled at the talk) then to that one can explicitly attached certain Poisson variety Y^{\vee} over the Langlands dual group G^{\vee} of G (over it is equal to cotangent bundle of some (also spherical) G^{\vee}-variety X^{\vee}), so that the (derived) category of G[[t]]-equivariant sheaves on X((t)) which are also equivariant with respect to the loop rotation is equivalent to the category of G^{\vee} over the quantization of Y (viewed as a dg-algebra with certain grading). This can be thought of some special case of S-duality for boundary conditions in 4d gauge theory. This has been checked in many case (some examples will be discussed at the talk). I will talk about a conjecture of Finkelberg, Ginzburg and Travkin which says that the category of B-equivariant sheaves on X should be Koszul dual to a close relative of the category B^{\vee}-equivariant modules over the quantization of Y^{\vee} (more precisely, the word "equivariant" must be replaced with "monodromic with unipotent monodromy"). In the case when X=G considered as a space with GxG-action, one recovers a well-known work of Beilinson, Ginzburg and Soergel. The purpose of the talk will be: 1) Give a review of cases when the Ben-Zvi-Sakellaridis-Venktatesh conjecture is known 2) Explain a framework for proving this conjecture in a slightly weaker form (instead of Koszul duality we shall prove an equivalence of the corresponding Z_2-graded categories). The latter part is a joint work with M.Finkelberg and R.Travkin.
Friday, April 4th, 2025
Workshop: Heluani Reimundo
Time: 9:30 AM - 10:30 AM
Location: SCGP 102
Title: The (lack of) progress on chiral homology and extensions of vertex algebra modules
Speaker: Heluani Reimundo
Abstract: We will describe the connection between the degree 1 chiral homology of the projective line with coefficients in two vertex algebra modules, and the extension group between these modules. We then will report on the (lack of) progress towards extending this to higher degrees. This is a report of joint work with T. Cardoso, J. V. Ekeren, and J. Guzmán
Title: The (lack of) progress on chiral homology and extensions of vertex algebra modules
Speaker: Heluani Reimundo
Abstract: We will describe the connection between the degree 1 chiral homology of the projective line with coefficients in two vertex algebra modules, and the extension group between these modules. We then will report on the (lack of) progress towards extending this to higher degrees. This is a report of joint work with T. Cardoso, J. V. Ekeren, and J. Guzmán
Workshop: Mitch Weaver
Time: 11:00 AM - 12:00 PM
Location: SCGP 102
Title: Higher Products of the Vertex Operator Algebra of 4d N = 2 SCFTs
Speaker: Mitch Weaver
Abstract: Every 4d N=2 superconformal field theory contains a BPS protected sub- algebra of local operators that has the structure of a vertex operator algebra (VOA). This VOA is identified by passing to the cohomology of a nilpotent supercharge, T, whose local operator cohomology is represented by twist-translations of Schur operators within a Euclidean two-plane. When working in 4d Minkowski space, this cohomology admits extended operators — so-called descent operators — that are constructed from Schur operators, have worldvolumes extending in the transverse Lorentzian two-plane (so they are point-like w.r.t. the plane supporting the VOA), and subsequently behave like chiral operators supported in the VOA plane. The result is the extended vertex algebra (EVA): a universal extension of the VOA that naturally has the structure of a quasi-VOA, i.e. a vertex algebra (VA) with no conformal vector but which still possesses a representation of sl(2). In Minkowski space, the T-cohomology theory also admits a set of higher products that act on the space of Schur operators and represent higher dimensional versions of mode operators for the fields of a 2d Euclidean chiral algebra. I will describe the construction and basic properties of these higher products along with their relation to the descent operators that give rise to the EVA. These results suggest the VOA of Schur operators in Minkowski space can be equipped with (novel) structures that are commonly found in the higher dimensional chiral algebras describing the minimal twist of 3d N =2 and 4d N =1 theories. This talk is based on 2211.04410 and forthcoming work.
Title: Higher Products of the Vertex Operator Algebra of 4d N = 2 SCFTs
Speaker: Mitch Weaver
Abstract: Every 4d N=2 superconformal field theory contains a BPS protected sub- algebra of local operators that has the structure of a vertex operator algebra (VOA). This VOA is identified by passing to the cohomology of a nilpotent supercharge, T, whose local operator cohomology is represented by twist-translations of Schur operators within a Euclidean two-plane. When working in 4d Minkowski space, this cohomology admits extended operators — so-called descent operators — that are constructed from Schur operators, have worldvolumes extending in the transverse Lorentzian two-plane (so they are point-like w.r.t. the plane supporting the VOA), and subsequently behave like chiral operators supported in the VOA plane. The result is the extended vertex algebra (EVA): a universal extension of the VOA that naturally has the structure of a quasi-VOA, i.e. a vertex algebra (VA) with no conformal vector but which still possesses a representation of sl(2). In Minkowski space, the T-cohomology theory also admits a set of higher products that act on the space of Schur operators and represent higher dimensional versions of mode operators for the fields of a 2d Euclidean chiral algebra. I will describe the construction and basic properties of these higher products along with their relation to the descent operators that give rise to the EVA. These results suggest the VOA of Schur operators in Minkowski space can be equipped with (novel) structures that are commonly found in the higher dimensional chiral algebras describing the minimal twist of 3d N =2 and 4d N =1 theories. This talk is based on 2211.04410 and forthcoming work.