Title: Minimal surfaces - organizational meeting

Abstract: The goal is to give an overview of some of the topics that we hope to cover over the semester, and to find volunteers to give talks.…

Title: Minimal hypersurfaces in compact symmetric spaces

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Title: Some results on stability for toric surfaces

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Title: Analysis in weighted spaces

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Title: Constant scalar curvature Kahler metrics on blow-ups I

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Title: The Yamabe problem, Part II

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Title: The Yamabe problem I

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Title:  The Uniformization Theorem

Abstract: This is a continuation of the earlier talk, on the uniformization theorem for closed surfaces.…

Title: Topological realization and geometric models

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Title: The Uniformization Theorem

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Title: Global Estimates for Abreu's Equation

Abstract: I will try to explain Chen-Li-Sheng's global estimates for Abreu's equation on a toric surface.…

Lecture Title: K-stable toric and Fano reductive varieties

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Title: Interior estimates for Abreu's equation

Abstract: I will continue talking about Donaldson's approach to the interior estimates for Abreu's equation, on a toric surface.…

Title: Abreu's equation, continued

Abstract: I will complete the proof of Donaldon's integration by parts formula, then discuss the one-dimensional case. …

Title: Abreu's equation

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Title: Interior estimates for Abreu's equation

Abstract: I will give an overview of Donaldson's interior estimates for Abreu's equation in the two-dimensional case. …

Title: Abreu's equation on polytopes

Abstract: I will give an introduction to Abreu's equation on convex polytopes. This is a PDE related to finding constant scalar curvature metrics on toric manifolds.…

Title: From the boundary distance function to the Dirichlet to Neumann operator

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Title: Infinitely many solutions to the Yamabe problem on noncompact manifolds

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Title: Diffeomorphism stability and codimension 4

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Title: Ricci Solitons

Abstract: I will talk about some progress on the classification problem for four dimensional shrinking Ricci solitons. This study is useful for understanding the singularity analysis of the Ricci flow on four dimensional manifolds.…

Title: L² Hodge Theory on Negatively Curved Manifolds

Abstract: In this talk, we will discuss the L² vanishing theorem of harmonic forms on negatively curved manifolds. In particular, I will give a proof of Gromov's results on L²-Hodge theory on Kahler hyperbolic manifolds.…

Title: Holomorphic sections on Kahler-Einstein manifolds

Abstract: I will explain Donaldson-Sun's construction of holomorphic sections of line bundles on Kahler-Einstein manifolds, combining the L2 estimate for the dbar operator with Cheeger-Colding's structure theory.…

Title: Anderson's rigidity and compactness result

Abstract: I will give some details of the proof of Anderson's result about the existence of "good" coordinates on balls with Ricci curvature bounds and volume close to the Euclidean value (more precisely, Theorem 3.2 in Anderson's 1990 Inventiones paper).…

Title: Cheeger-Colding Theory

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Title: Hormander's L^2 estimate

Astract: I will discuss the classical L^2 estimate for constructing holomorphic functions, due to H\"ormander. In subsequent talks we will explore related recent developments.…

Title: Function Theory on Negatively Curved Manifolds

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Title:  Volume bounds on the nodal sets of solutions to elliptic PDEs

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Title: Kahler metrics with conical singularities

Abstract: I will give an introduction to Kahler metrics with conical singularities, and the analysis of the Laplacian for such metrics.…

Title: Monotonicity formula functions

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