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...
Computing volumes of moduli spaces has significance in many
fields. For instance, Witten's conjecture regarding intersection
numbers on the Deligne–Mumford moduli space of stable Riemann
surfaces has a fascinating connection to the Weil–Petersson...
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...
Abstract: We discuss singularities of Teichmueller harmonic map
flow, which is a geometric flow that changes maps from surfaces
into branched minimal immersions, and explain in particular how
winding singularities of the map component can lead to...
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...
Abstract: Given a class of conformally compact Einstein
manifolds with boundary, we are interested to study the compactness
of the class under some local and non-local boundary constraints. I
will report some joint work with Yuxin Ge and Jie Qing...
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...
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.
