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Zhenhua Liu: Lectures
5/17/2024: General behavior of area-minimizing submanifolds 9/14/2021: Every finite graph arises as the singular set of a compact 3-d calibrated area minimizing submanifold May 17, 2024 TITLE: General behavior of area-minimizing submanifolds ABSTRACT: We will review some recent progress on the general geometric behavior of homologically area-minimizing currents, namely, objects that minimize area with respect […]
Daniel Platt: Lectures
May 15, 2024: New Spin(7)-instantons on compact manifolds September 13, 2023: Approximations of harmonic 1-forms on real loci of Calabi-Yau 3-folds September 11, 2022: Associatives in the generalised Kummer construction September 15, 2021: New estimates for G2-structures on resolutions of orbifolds May 15, 2024 TITLE: New Spin(7)-instantons on compact manifolds ABSTRACT: Slides of Lecture September […]
Nicos Kapouleas: Lectures
May 27, 2021 TITLE: Gluing Eguchi-Hanson Metrics and a Question of Page ABSTRACT: I will discuss a paper of Simon Brendle and myself (Comm. Pure Appl. Math. 70 (2017), no. 7, 1366-1401) motivated by a question Page asked in 1981. Page’s question was based on a physical picture for the Ricci-flat Kähler metrics on the […]
Panagiota Daskalopoulos: Lectures
May 26, 2021 Lecture cancelled TITLE: Ancient compact solutions to Ricci flow and Mean curvature flow ABSTRACT: Some of the most important problems in partial differential equations are related to the understanding of singularities. This usually happens through a blow up procedure near the potential singularity which uses the scaling properties of the equation. In […]
Richard Bamler: Lectures
May 28, 2021 TITLE: U(2)-invariant Ricci flows in dimension 4 and partial regularity theory for Ricci flows ABSTRACT: In this talk I will present work of my former graduate student, Alexander Appleton, on cohomogeneity-1 Ricci flows in dimension 4 that are invariant under an isometric U(2)-action. I will first show that there are certain U(2)-invariant, […]
Dan Knopf: Lectures
May 28, 2021 TITLE: Ricci Solitons, Conical Singularities, and Nonuniqueness ABSTRACT: In dimension n=3, there is a complete and well-posed theory of weak solutions of Ricci flow: existence in the form of “Ricci Flow Spacetimes” was proved by Kleiner and Lott, and uniqueness was proved by Bamler and Kleiner. I will describe joint work with […]
Tristan Ozuch: Lectures
May 27, 2021 TITLE: Noncollapsed degeneration and desingularization of Einstein 4-manifolds ABSTRACT: We study the noncollapsed singularity formation of Einstein 4-manifolds. We prove that any smooth Einstein 4-manifold close to a singular one in a mere Gromov-Hausdorff (GH) sense is the result of a gluing-perturbation procedure that we develop and which handles the presence of […]
Simon Brendle: Lectures
May 26, 2021 TITLE: Ancient solutions to the Ricci flow in dimension 3 ABSTRACT: The Ricci flow is a natural evolution equation for Riemannian metrics on a manifold. The central problem is to understand singularity formation. In other words, what does the geometry look like at points where the curvature is large? In his spectacular […]
Michael Douglas: Lectures
May 24, 2021 TITLE: Numerical Calabi-Yau metrics from holomorphic networks ABSTRACT: We propose machine learning inspired methods for computing numerical Calabi-Yau (Ricci flat Ka ̈hler) metrics. In joint work with Yidi Qi and Subramanian Lakshminarasimhan, we implemented them using Tensorflow/Keras and compared with previous work. We will also discuss ideas for numerical study of other […]
Greg Moore: Lectures
January 13, 2021 Informal Remarks Complementary To, And Preparatory For, Fei Yan’s Talk: ABSTRACT: Slides of Lecture, part 1 Slides of Lecture, part 2
