Kaehler constant scalar curvature metrics on blow ups and resolutions of singularities

Claudio Arezzo
International Centre for Theoretical Physics, Trieste
March 4, 2019

Abstract: After recalling the gluing construction for Kaehler constant scalar curvature and extremal (`a la Calabi) metrics
starting from a compact or ALE orbifolds with isolated singularities, I will show how to compute the Futaki invariant
of the adiabatic classes in this setting, extending previous work by Stoppa, Szekelyhidi and Odaka. Besides giving
new existence and non-existence results, the connection with the Tian-Yau-Donaldson Conjecture and the K-stability

Gysin sequences and cohomology ring of symplectic fillings

Zhengyi Zhou
Member, School of Mathematics
March 4, 2019

It is conjectured that contact manifolds admitting flexible fillings have unique exact fillings. In this talk, I will show that exact fillings (with vanishing first Chern class) of a flexibly fillable contact (2n-1)-manifold share the same product structure on cohomology if one of the multipliers is of even degree smaller than n-1. The main argument uses Gysin sequences from symplectic cohomology twisted by sphere bundles.

Local and global expansion of graphs

Yuval Peled
New York University
March 4, 2019

The emerging theory of High-Dimensional Expansion suggests a number of inherently different notions to quantify expansion of simplicial complexes. We will talk about the notion of local spectral expansion, that plays a key role in recent advances in PCP theory, coding theory and counting complexity. Our focus is on bounded-degree complexes, where the problems can be stated in a graph-theoretic language: 

Global well-posedness and scattering for the radially symmetric cubic wave equation with a critical Sobolev norm

Benjamin Dodson
Johns Hopkins University; von Neumann Fellow, School of Mathematics
February 28, 2019

In this talk we discuss the cubic wave equation in three dimensions. In three dimensions the critical Sobolev exponent is 1/2. There is no known conserved quantity that controls this norm. We prove unconditional global well-posedness for radial initial data in the critical Sobolev space.

Geodesic nets: examples and open problems.

Alexander Nabutovsky
University of Toronto; Member, School of Mathematics
February 26, 2019

Geodesic nets on Riemannian manifolds is a natural generalization of geodesics. Yet almost nothing is known about their classification or general properties even when the ambient Riemannian manifold is the Euclidean plane or the round 2-sphere. 

In this talk I am going to survey some results and open questions (old
and new) about geodesic nets on Riemannian manifolds. Many of these