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Guofang Wei: Lectures
April 9, 2018 TITLE: Manifolds with integral curvature bounds ABSTRACT: We begin with a review of early joint work with P. Petersen on the Laplacian and volume comparison for manifolds with only integral Ricci curvature bounds. We then present recent joint work with X. Dai and Z. Zhang producing a local Sobolev constant estimate for […]
Xiaochun Rong: Lectures
April 11, 2018 TITLE: Collapsed manifolds with Ricci local bounded covering geometry ABSTRACT: Collapsed manifolds with local bounded covering geometry (i.e., sectional curvature bounded in absolute value) has been well-studied; the basic discovery by Cheeger-Fukaya-Gromov is the existence of a compatible local nilpotent symmetry structures whose orbits point to all collapsed directions. In this talk, […]
Xenia de la Ossa: Lectures
January 8, 2018 TITLE: The geometry and moduli of heterotic G2 structures ABSTRACT: A heterotic system is a quadrupole , where is a seven dimensional manifold with an integrable structure and is the corresponding associative three form, is a bundle on with an instanton connection , and is an instanton connection on the tangent bundle […]
Xuemiao Chen: Lectures
09/14/21: Compactness for Ω-Yang-Mills connections 01/12/18: Singularities of Hermitian Yang Mills connections and the Harder-Narasimhan-Seshadri filtration September 14, 2021 TITLE: Compactness for Ω-Yang-Mills connections ABSTRACT: We will study the gauge theoretic aspects of stable bundles defined via multipolarizations. The latter turns out to be stable bundles over complex manifolds with balanced metrics of Hodge-Riemann type. […]
Siqi He: Lectures
09/14/2021: The branched deformations of special Lagrangian submanifolds 01/10/2020: A compactness result for the Hitchin-Simpson equations 01/11/2018: The extended Bogomolny equations and generalized Nahm pole solutions September 14, 2021 TITLE: The branched deformations of special Lagrangian submanifolds ABSTRACT: Special Lagrangian submanifolds are a distinguished class of real minimal submanifolds defined in a Calabi-Yau manifold, which […]
Sergey Cherkis: Lectures
January 11, 2018 TITLE: Octonionic Monopoles and another look at the Twistor Transform ABSTRACT: An octonionic monopole is a solution of an octonionic generalization of the Bogomolny equation. Conjecturally, it is dual to a solution of the Haydys-Witten equation and plays central role in using seven-dimentional gauge theory to provide invariants of knot and coassociative […]
Richard Thomas: Lectures
01/10/2023: CY4 quiver representations 01/13/2022: Higher rank DT theory from rank 1 01/06/2020: Borisov-Joyce in algebraic geometry 01/08/2018 and 01/09/2018: Introduction to coherent sheaves January 10, 2023 TITLE: CY4 quiver representations ABSTRACT: Borisov-Joyce found a way to define a count of sheaves on Calabi-Yau 4-folds, using real derived differential geometry. I will talk about joint […]
Matei Toma: Lectures
January 10, 2018 TITLE: Moduli spaces of semistable sheaves with respect to Kähler polarizations ABSTRACT: For a compact Kähler manifold () the Kobayashi-Hitchin correspondence gives homeomorphisms between moduli spaces of irreducible Hermite-Einstein connections and moduli spaces of stable vector bundles on . Whereas gauge theoretical compactifications for these spaces are known to exist by work […]
Hartmut Weiß: Lectures
January 11, 2018 TITLE: On the asymptotic geometry of the Hitchin metric ABSTRACT: I will report on recent joint work with Rafe Mazzeo, Jan Swoboda and Frederik Witt on the asymptotic geometry of the Hitchin metric. This is the natural metric on the moduli space of Higgs bundles. We describe the difference to a more […]
Benjamin Sibley: Lectures
January 8, 2018 TITLE: A complex analytic structure on the compactification of Hermitian-Yang-Mills moduli space ABSTRACT: A key aspect of gauge theory is finding a suitable compactification for the moduli space instantons. For instantons on higher dimensional manifolds, a rough compactification has been defined by Tian, analogous to Uhlenbeck’s compactification of the moduli space of […]
