Friday September 08, 2017 4:00 PM  6:00 PM P131 Math Tower
 Christina Sormani, Stony Brook University
Introduction to GromovHausdorff Convergence

Friday September 15, 2017 4:00 PM  6:00 PM P131 Math Tower
 Christina Sormani, Stony Brook University
Intrinsic Flat Convergence: Definition, Examples, and Theorems

Friday September 22, 2017 4:00 PM  6:00 PM P131 Math Tower
 Yuanqi Wang, Stony Brook University
Stable reflexive sheaves on projective spacesWe 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 P131 Math Tower
 JeanFrançois Arbour, Stony Brook University
Relative index formula for elliptic operators on manifolds with cylindrical endsThis 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 P131 Math Tower
 JeanFrançois Arbour, Stony Brook University
Relative index formula for elliptic operators on manifolds with cylindrical endsThis 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 coclosed.

Friday October 13, 2017 4:00 PM  6:00 PM P131 Math Tower
 Demetre Kazaras, Stony Brook University
Positive Scalar Curvature and Minimal HypersurfacesA 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.

