The Simons Center for Geometry and Physics is pleased to announce the following talks during the week of Monday, November 17th - Saturday, November 22nd

Geometric Flows Program Seminar: Simone Calamai (Università di Firenze), "About Hermitian metrics whose scalar curvature of the Chern connection is constant"

Monday, November 17th at 2:30pm in SCGP 313

Speaker: Simone Calamai (Università di Firenze)

Title: About Hermitian metrics whose scalar curvature of the Chern connection is constant.

Abstract: Given a smooth compact complex manifold, we consider the problem on existence, in a fixed conformal class, of Hermitian metrics whose scalar curvature induced by the Chern connection is constant. In particular, we describe the interesting role in the picture played by the Gauduchon metrics (work in progress with Daniele Angella and Cristiano Spotti).

Geometric Flows Program Seminar: Yuanqi Wang, "Kahler-Ricci Flow with conic singularities"

Wednesday, November 19th at 2:30pm in SCGP 313

Speaker: Yuanqi Wang (UC Santa Barbara)

Title: Kahler-Ricci Flow with conic singularities.

Abstract: Inspired by Donaldson’s program, we introduce the Kahler Ricci flows with conic singularities. The main part of this talk is to show that the conical Kahler Ricci flow exists for short time in a proper space. These existence results are hight related to the heat kernel. We will also discuss the long time existence and convergence of this flow to conic Ricci flat metrics.

Tracking the Cosmos Art Exhibition Closing Reception

Thursday, November 20th at 5:00pm in SCGP Art Gallery and Lobby

Geometric Flows Program Seminar: Kai Zheng, "The long-time behavior of the Calabi flow"

Friday, November 21st at 11:30am in SCGP 313

Speaker: Kai Zheng (Gottfried Wilhelm Leibniz Universität)

Title: The long-time behavior of the Calabi flow

Abstract: We define regularity scales as alternative quantities of $(\max_{M} |Rm| )^{-1}$ to study the behavior of the Calabi flow. Based on estimates of the regularity scales, we obtain convergence theorems of the Calabi flow on extremal K\"ahler surfaces, under the assumption of global existence of the Calabi flow solutions. Our results partially confirm Donaldson's conjectural picture for the Calabi flow in complex dimension 2.

Program Seminar: John Morgan, "A Topologist looks at Sheaf Theory"

Friday, November 21st at 2:45pm in SCGP 313

Title: A Topologist looks at Sheaf Theory

Abstract: Sheaf theory has long been an essential tool in algebraic geometry, algebraic number theory, and complex analysis, but its inspiration comes directly from topology. This lecture course will emphasize these roots, hopefully making sheaf theory seem natural to those with a topological bent. The course will begin by covering the basic topics in sheaf theory describing the objects and the four basic maps of the theory and then will culminate with a discussion of Verdier duality, which generalizes Poincare duality. This theory will then be applied to define a bordism theory, called duality bordism, whose coefficient group agrees with the Grothendieck group of chain complexes satisfying Poincare duality modulo those that sit as the boundary term in an exact sequence satisfying Lefschetz duality. This bordism group is the Pontryjagin dual homology theory to the cohomology theory associated with surgery theory. This means that a surgery problem is completely classified by evaluating surgery obstructions (signatures, and Arf invariants) of its restrictions to all possible duality bordism elements. Direct analysis of this bordism theory allows one to identify it at odd primes with real K-theory and at the prime 2 with ordinary homology.