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: 

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: 

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

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