There are no events at the Simons Center today. Here are the events for this week
Monday, November 18th, 2024
Program Talks: Scott Sheffield
Time: 11:15 AM - 12:15 PM
Location: SCGP 313
Title: Random surfaces and Yang-Mills theory: results and conjectures
Speaker: Scott Sheffield
Title: Random surfaces and Yang-Mills theory: results and conjectures
Speaker: Scott Sheffield
Math Event: Symplectic Geometry, Gauge Theory, and Low-Dimensional Topology Seminar: Søren Galatius - Hopf algebras related to GL_n(Z)
Time: 12:30 PM - 1:55 PM
Location: Math P-131
Title: Hopf algebras related to GL_n(Z)
Speaker: Søren Galatius [University of Copenhagen]
Abstract: The general linear group of the integers acts on the symmetric space GL_n(R)/O(n), and the orbit space X_n can be regarded as a "moduli space of real tori". I will discuss recent joint work with Brown, Chan, and Payne (2405.11528) in which we study the compactly supported cohomology of this orbit space using Hopf algebra structures. A certain Hopf algebra of graphs, a version of the Connes--Kreimer Hopf algebra, will be used to deduce lower bounds. View Details
Title: Hopf algebras related to GL_n(Z)
Speaker: Søren Galatius [University of Copenhagen]
Abstract: The general linear group of the integers acts on the symmetric space GL_n(R)/O(n), and the orbit space X_n can be regarded as a "moduli space of real tori". I will discuss recent joint work with Brown, Chan, and Payne (2405.11528) in which we study the compactly supported cohomology of this orbit space using Hopf algebra structures. A certain Hopf algebra of graphs, a version of the Connes--Kreimer Hopf algebra, will be used to deduce lower bounds. View Details
Tuesday, November 19th, 2024
Program Talks: Scott Sheffield
Time: 11:15 AM - 12:15 PM
Location: SCGP 313
Title: Random surfaces and Yang-Mills theory: results and conjectures
Speaker: Scott Sheffield
Title: Random surfaces and Yang-Mills theory: results and conjectures
Speaker: Scott Sheffield
Math Event: Geometry/Topology Seminar: Semyon Alesker - Intrinsic volumes in Riemannian and Alexandrov geometry
Time: 4:00 PM - 5:15 PM
Location: P-131
Title: Intrinsic volumes in Riemannian and Alexandrov geometry
Speaker: Semyon Alesker [Tel Aviv University]
Abstract: Intrinsic volumes are invariants of compact smooth Riemannian manifolds, possibly with corners.These invariants play a significant role in convex geometry and include the volume, Euler characteristic, and the integral of scalar curvature (the latter for closed manifolds). We discuss several conjectures regarding their behavior under Gromov-Hausdorff convergence, particularly when sectional curvature is bounded from below, and their potential extension to Alexandrov spaces. Although these conjectures remain largely open, we review various known special cases. View Details
Title: Intrinsic volumes in Riemannian and Alexandrov geometry
Speaker: Semyon Alesker [Tel Aviv University]
Abstract: Intrinsic volumes are invariants of compact smooth Riemannian manifolds, possibly with corners.These invariants play a significant role in convex geometry and include the volume, Euler characteristic, and the integral of scalar curvature (the latter for closed manifolds). We discuss several conjectures regarding their behavior under Gromov-Hausdorff convergence, particularly when sectional curvature is bounded from below, and their potential extension to Alexandrov spaces. Although these conjectures remain largely open, we review various known special cases. View Details
Wednesday, November 20th, 2024
Program Talks: Scott Sheffield
Time: 11:15 AM - 12:15 PM
Location: SCGP 102
Title: Random surfaces and Yang-Mills theory: results and conjectures
Speaker: Scott Sheffield
Title: Random surfaces and Yang-Mills theory: results and conjectures
Speaker: Scott Sheffield
Math Event: Algebraic Geometry Seminar: Aaron Betram - Seeking Exceptional Collections for Non-Exceptional Groups
Time: 4:00 PM - 5:00 PM
Location:
Title: Seeking Exceptional Collections for Non-Exceptional Groups
Speaker: Aaron Betram [University of Utah]
Abstract: Castravet and Tevelev found a symmetric exceptional collection of line bundles and \r\ntorsion sheaves on the Losev-Manin space of pointed rational curves, which is naturally the compactificationof the maximal torus in PGL(n+1). With Alicia Lamarche, we have been working on a generalization to the other non-exceptional root systems, where we have found some surprises that I want to share with you. View Details
Title: Seeking Exceptional Collections for Non-Exceptional Groups
Speaker: Aaron Betram [University of Utah]
Abstract: Castravet and Tevelev found a symmetric exceptional collection of line bundles and \r\ntorsion sheaves on the Losev-Manin space of pointed rational curves, which is naturally the compactificationof the maximal torus in PGL(n+1). With Alicia Lamarche, we have been working on a generalization to the other non-exceptional root systems, where we have found some surprises that I want to share with you. View Details
Thursday, November 21st, 2024
Math Event: Colloquium: Semyon Alesker - Monge-Ampere equations: beyond the classical cases.
Time: 3:45 PM - 4:45 PM
Location: P-131
Title: Monge-Ampere equations: beyond the classical cases.
Speaker: Semyon Alesker [Tel Aviv University]
Abstract: Real and complex Monge-Ampère equations are classical, well-studied, and have numerous applications in analysis and geometry. Over the past two decades, several attempts have been made to generalize these equations to new contexts, including calibrated and quaternionic geometries. In this talk, we introduce an octonionic analogue of Kähler metrics on a class of 16-manifolds and present an octonionic version of the Monge-Ampère equation in this setting. We also prove an octonionic Calabi-Yau type theorem for this equation. The new results presented in this talk are joint work with P. Gordon. View Details
Title: Monge-Ampere equations: beyond the classical cases.
Speaker: Semyon Alesker [Tel Aviv University]
Abstract: Real and complex Monge-Ampère equations are classical, well-studied, and have numerous applications in analysis and geometry. Over the past two decades, several attempts have been made to generalize these equations to new contexts, including calibrated and quaternionic geometries. In this talk, we introduce an octonionic analogue of Kähler metrics on a class of 16-manifolds and present an octonionic version of the Monge-Ampère equation in this setting. We also prove an octonionic Calabi-Yau type theorem for this equation. The new results presented in this talk are joint work with P. Gordon. View Details