Geometric Analysis Learning Seminar

from Thursday
June 01, 2017 to Sunday
December 31, 2017
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Instructions for subscribing to Stony Brook Math Department Calendars

Friday
September 08, 2017

4:00 PM - 6:00 PM
P-131 Math Tower
Christina Sormani, Stony Brook University
Introduction to Gromov-Hausdorff Convergence


Friday
September 15, 2017

4:00 PM - 6:00 PM
P-131 Math Tower
Christina Sormani, Stony Brook University
Intrinsic Flat Convergence: Definition, Examples, and Theorems


Friday
September 22, 2017

4:00 PM - 6:00 PM
P-131 Math Tower
Yuanqi Wang, Stony Brook University
Stable reflexive sheaves on projective spaces

We will discuss a rank 2 reflexive sheaf on P3,
and the construction of rank 2 stable bundles on P2 with
c_{1}=0, c_{2}=2.


Friday
September 29, 2017

4:00 PM - 6:00 PM
P-131 Math Tower
Jean-François Arbour, Stony Brook University
Relative index formula for elliptic operators on manifolds with cylindrical ends

This is the first of two talks on R. Lockhart and R. McOwen's 1984 paper "Elliptic Differential Operators on Noncompact Manifolds". The paper is concerned with elliptic operators acting on weighted Sobolev spaces on manifolds with cylindrical ends. The main result is that there is a discrete set of "critical weights" outside of which the acting operator is Fredholm. Moreover, a formula is given describing the jump in Fredholm index when a critical weight is crossed. Their results found many important applications later on for gluing problems arising in geometry.


Friday
October 06, 2017

4:00 PM - 6:00 PM
P-131 Math Tower
Jean-François Arbour, Stony Brook University
Relative index formula for elliptic operators on manifolds with cylindrical ends

This is the second of two talks on R. Lockhart and R. McOwen's 1984 paper "Elliptic Differential Operators on Noncompact Manifolds". The paper is concerned with elliptic operators acting on weighted Sobolev spaces on manifolds with cylindrical ends. In this talk, I will discuss the proof of the formula describing the jump in Fredholm index when a critical weight is crossed. Following the authors, I will then show how to use this formula to understand whether or not certain L2 harmonic forms on manifolds with isolated conical singularities are also closed and co-closed.


Friday
October 13, 2017

4:00 PM - 6:00 PM
P-131 Math Tower
Demetre Kazaras, Stony Brook University
Positive Scalar Curvature and Minimal Hypersurfaces

A celebrated result of Schoen and Yau from ’79 states that any stable minimal hypersurface in a manifold of positive scalar curvature (psc) is Yamabe positive (i.e. there is a psc metric in the same conformal class as the restriction metric). When used alongside regularity results from geometric measure theory, this observation is a major tool used to study psc metrics on manifolds of dimension 8 and below (above dimension 8, the regularity results fail dramatically). In this talk, I will describe the ’79 paper and discuss a recent preprint of Schoen and Yau where a method is produced which applies to all dimensions.


Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars