Lu Wang, University of Wisconsin-Madison
We show that each end of a properly embedded self-shrinker in 3-Euclidean space of finite topology is smoothly asymptotic to a regular cone or a round cylinder.
MC 5403
Yoav Len, Department of Combinatorics & Optimization, University of Waterloo
Eric Woolgar, University of Alberta
Xinliang An, University of Toronto
Ákos Nagy, University of Waterloo and The Fields Institute
By exploring a duality between planar Abelian vortices and SO(3) invariant SU(2) instantons in 4 dimensions, we construct new finite energy, irreducible solutions to the self-duality equations on the Euclidean Schwarzschild manifold. These solutions are not invariant under the action of the full isometry group, in particular they are not static. Thus, they provide counterexamples to a conjecture of Tekin on a possible, non-Abelian extension of Birkhoff's theorem in general relativity.
Dustin Cartwright, University of Tennessee
While the topology of smooth complex projective varieties has been well-studied from a variety of perspectives, analogous questions about topology over non-Archimedean fields are only recently being investigated. I will talk about what the relevant topology is, as well as the way they can be studied via degenerations and their dual complexes. Then I will explain some results about the topology of dual complexes of degenerations and their relation to the geometry of algebraic varieties.
MC 5479
Michael Bailey, Department of Pure Mathematics, University of Waterloo
Certain local structure results in generalized complex geometry may be seen as a (work-in- progress) much-more-general Newlander-Nirenberg theorem for stacks (or higher stacks/derived geometry).
MC 5403
Eli Shamovich, Department of Pure Mathematics, University of Waterloo
Ali Aleyasin, Department of Pure Mathematics, University of Waterloo
Sebastien Picard, Columbia University