Events Archive
Principal component analysis for topologists
GAUGE-TOPOLOGY-SYMPLECTIC
September 27, 2019 3:30 pmAbstract: Geometrically, PCA finds the k-dimensional subspace nearest a point cloud in m-dimensional Euclidean space. Numerically, PCA also specifies a basis for this subspace, the principal directions of the data....
Read more
Thurston norm minimizing Seifert surfaces
GAUGE-TOPOLOGY-SYMPLECTIC
September 20, 2019 3:30 pmAbstract: Let K be a null-homologous knot in a closed 3-manifold Y, and F be a Seifert surface. One can cap off the boundary of F with a disk in...
Read more
Floer-theoretic heaviness and Lagrangian skeleta
GAUGE-TOPOLOGY-SYMPLECTIC
September 13, 2019 3:30 pmAbstract: I will talk on what I have learned from Umut Varolgunes, and on our work in preparation. In 2007, Entov and Polterovich introduced the notion of heavy and superheavy...
Read more
Heegaard Floer and homology cobordism
GAUGE-TOPOLOGY-SYMPLECTIC
April 26, 2019 3:30 pmAbstract: We show that the three-dimensional homology cobordism group admits an infinite-rank summand. It was previously known that the homology cobordism group contains an infinite-rank subgroup and a Z-summand. The...
Read more
Exotic Structures, Homology Cobordisms and Chern-Simons Functional
GAUGE-TOPOLOGY-SYMPLECTIC
April 19, 2019 3:30 pmAbstract: An exotic structure on a smooth manifold X is another smooth manifold which is homeomorphic but not diffeomorphic to X. There are many closed 4-manifolds which admit exotic smooth...
Read more
Feral pseudoholomorphic curves and minimal sets
GAUGE-TOPOLOGY-SYMPLECTIC
April 12, 2019 3:30 pmAbstract: I will discuss some recent joint work with Helmut Hofer, in which we define and establish properties of a new class of pseudoholomorhic curves (feral J-curves) to study certain...
Read more
The Yang-Mills Equations over Klein Surfaces
GAUGE-TOPOLOGY-SYMPLECTIC
April 5, 2019 3:30 pmAbstract: In "The Yang-Mills equations over Riemann surfaces", Atiyah and Bott studied Yang-Mills functional over a Riemann surface from the point of view of Morse theory, and derived results on...
Read more
Instantons and lattices of smooth 4-manifolds with boundary
GAUGE-TOPOLOGY-SYMPLECTIC
March 29, 2019 3:30 pmAbstract: Given a 3-manifold Y, what are the possible definite intersection forms of smooth 4-manifolds with boundary Y? Donaldson's theorem says that if Y is the 3-sphere, then all such...
Read more
Inductively collapsing Fukaya categories and flexibility
GAUGE-TOPOLOGY-SYMPLECTIC
March 15, 2019 3:30 pmAbstract: A Weinstein manifold is a symplectic manifold which admits a Lagrangian skeleton, and associated to any Weinstein manifold is its wrapped Fukaya category, a powerful algebraic invariant. One important...
Read more