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Chris Scaduto: Lectures
June 6, 2022 TITLE: Computing \nu-invariants of Joyce’s G_2-manifolds ABSTRACT: Crowley and Nordström introduced the \nu-invariant of a G_2-structure on a 7-manifold, taking values in the integers modulo 48. This invariant, and its spectral refinement due to Crowley, Goette and Nordström, has been important in understanding the connected components of G_2 metric moduli spaces. In […]
Diarmuid Crowley: Lectures
June 10, 2022 TITLE: A prolegomena to finding higher homotopy in G_2-moduli spaces ABSTRACT: I will begin this talk by reviewing topological approach to studying the connected components of G_2-moduli spaces via the \nu-invariant. Then I will look at the possibility of detecting higher homotopy groups in G_2-moduli spaces. The idea is to define higher-dimensional […]
Hongyi Liu: Lectures
June 7, 2022 TITLE: A compactness theorem for hyperkahler 4 manifolds with boundary ABSTRACT: A hyperkahler triple on a 4-manifold with boundary is a triple of symplectic 2-forms that are pointwise orthonormal with respect to the wedge product, so its restriction to the boundary 3-manifold is a closed framing. Motivated by previous work of Bryant, […]
Ethan Torres: Lectures
06/08/2022: Getting High on Gluing Orbifolds June 8, 2022 TITLE: Getting High on Gluing Orbifolds ABSTRACT: Quantum field theories (QFTs) engineered from M-theory on singular non-compact manifolds often enjoy a rich dictionary between physical data and geometric quantities. For instance, when real codimension-4 ADE orbifold singularities extend out to the asymptotic boundary, the local operators […]
Jeffrey Streets: Lectures
13/01/23: The generalized Kahler Calabi-Yau problem 14/01/22: Singular sets of generalized Einstein metrics January 13, 2023 TITLE: The generalized Kahler Calabi-Yau problem ABSTRACT: In recent years generalized Kahler geometry has emerged as a natural extension of Kahler geometry with applications to complex, Poisson, and symplectic geometry, as well as mathematical physics. In this talk I […]
Jihwan Oh: Lectures
January 12, 2022 TITLE: G2 instantons in twisted M-theory ABSTRACT: I will discuss a string theory way to study G2 instanton moduli space and explain how to compute the instanton partition function for a certain G2 manifold. An important insight comes from the twisted M-theory on the G2 manifold. Building on the example, I will […]
Hiraku Nakajima: Lectures
January 10, 2022 TITLE: Symmetric bow varieties ABSTRACT: In my joint work with Takayama, I showed that Coulomb branches of quiver gauge theories of affine type A, as defined in earlier joint work with Braverman and Finkelberg, are isomorphic to Cherkis’ bow varieties. For quiver gauge theories of affine type D, or more generally of […]
Francis Kirwan: Lectures
January 10, 2022 TITLE: Hyperkahler implosion ABSTRACT: The hyperkahler quotient construction, which allows us to construct new hyperkahler spaces from suitable group actions on hyperkahler manifolds, is an analogue of symplectic reduction (introduced by Marsden and Weinstein in the 1970s), and both are closely related to the quotient construction for complex reductive group actions in […]
Cyril Closset: Lectures
January 11, 2022 TITLE: On SCFTs at canonical singularities ABSTRACT: Canonical threefold singularities are used in string theory to ‘geometrically engineer’ superconformal field theories (SCFTs) in 4d and 5d. I will discuss various aspects of that intriguing relationship between physics and geometry, providing an overview of recent results, conjectures and open questions. Slides of Lecture
Mathew Bullimore: Lectures
January 11, 2022 TITLE: Moduli Stacks and Global Categorical Symmetry ABSTRACT: I will discuss aspects of moduli spaces in supersymmetric gauge theories that take the form of conical symplectic singularities or resolutions thereof. They often admit Hamiltonian group actions arising from continuous global symmetries and feature prominently in geometric representation theory. I will argue that it is […]
