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Ling Lin: Lectures
3/14/2023: K3s at the intersection of Special Holonomy, Generalized Symmetries, and the Swampland 9/13/2022: Gravity, geometry and generalized symmetries March 14, 2023 TITLE: K3s at the intersection of Special Holonomy, Generalized Symmetries, and the Swampland ABSTRACT: K3 surfaces, a prime example of compact special holonomy manifolds, have been a fount of insights for physicists through […]
Greg Parker: Lectures
5/14/2024: A Fredholm framework for singular deformation problems 9/13/2022: Gluing Z2-Harmonic Spinors May 14, 2024 TITLE: A Fredholm framework for singular deformation problems. ABSTRACT: Recent work in several directions has led to singular elliptic operators with infinite-dimensional obstructions, for which the standard Fredholm theory does not apply. In particular, this is the case for singular […]
Gorapada Bera: Lectures
September 13, 2022 TITLE: Deformations and gluing of asymptotically cylindrical associatives ABSTRACT: Given a matching pair of asymptotically cylindrical (Acyl) G_2 manifolds the twisted connected sum construction produces a one parameter family of closed G_2 manifolds. We describe when we can construct closed rigid associatives in these closed G_2 manifolds by gluing suitable pairs of […]
Federico Trinca: Lectures
September 12, 2022 TITLE: T^2-invariant associatives in G_2 manifolds with cohomogeneity-two symmetry ABSTRACT: A classical way to construct calibrated submanifolds is via symmetry reduction. In this talk, we will consider G_2 manifolds with a T^2\times SU(2) structure-preserving action of cohomogeneity-two. For each of these manifolds, we describe the geometry of the T^2-invariant associative submanifolds using […]
Izar Alonso: Lectures
September 12, 2022 TITLE: Heterotic systems, balanced SU(3)-structures and coclosed G_2-structures in cohomogeneity one manifolds ABSTRACT: When considering compactifications of heterotic string theory down to 4D, the Hull–Strominger system arises over a six-dimensional manifold endowed with an invariant nowhere-vanishing holomorphic (3,0)-form. When compactifying down to 3D, we get the heterotic G_2 system over a manifold […]
Henry Liu: Lectures
September 12, 2022 TITLE: Multiplicative vertex algebras and wall-crossing in equivariant K-theory ABSTRACT: K-theory is an interesting multiplicative refinement of cohomology, and many cohomological objects arising in enumerative geometry have K-theoretic analogues — modular forms become Jacobi forms, Yangians become quantum affine algebras, etc. I will explain how this sort of refinement goes for vertex […]
Aaron Kennon: Lectures
September 11, 2022 TITLE: Geometric Flows of 3-Sasakian Structures ABSTRACT: Geometric flows of G_2-Structures are expected to be valuable tools for determining when a G_2-Structure with torsion may be deformed to one which is torsion-free. Several flows of G_2-Structures have been proposed to provide insight into this question, including the Laplacian flow and the Laplacian […]
Daniel Baldwin: Lectures
09/12/2023: On nearby special Lagrangians 09/11/2022: Coulomb and Higgs phases of G_2 manifolds September 12, 2023 TITLE: Coulomb and Higgs phases of G_2 manifolds ABSTRACT: We will discuss the physics of M-theory compactifications onto G_2-orbifolds of the type that can be resolved via the method of Joyce and Karigiannis i.e. orbifolds where one has a […]
Ilyas Khan: Lectures
06/07/2022: Uniqueness of Asymptotically Conical Gradient Shrinking Solitons in G2-Laplacian Flow June 7, 2020 (Jointly with Alec Payne) TITLE: Uniqueness of Asymptotically Conical Gradient Shrinking Solitons in G2-Laplacian Flow ABSTRACT: The Laplacian flow is a natural geometric flow which deforms closed G2-structures on 7-manifolds. This flow could be a major avenue to insight into manifolds […]
Alec Payne: Lectures
09/10/2023: Closed G2-Structures with Negatively Pinched Ricci Curvature 06/07/2022: Uniqueness of Asymptotically Conical Gradient Shrinking Solitons in G2-Laplacian Flow September 10, 2023 TITLE: Closed G2-Structures with Negatively Pinched Ricci Curvature ABSTRACT: The Goldberg conjecture is a well-known question about whether compact almost Kähler, Einstein manifolds must be Kähler. The analogue of the Goldberg conjecture for […]
