Talk_id  Date  Speaker  Title 
18593

Thursday 8/29 2:00 PM

Chris Gerig, Harvard University

Probing 4manifolds with nearsymplectic forms
 Chris Gerig, Harvard University
 Probing 4manifolds with nearsymplectic forms
 08/29/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
Most closed 4manifolds do not admit symplectic forms, but most admit "nearsymplectic forms", certain closed 2forms which are symplectic outside of a collection of circles. This provides a gateway from the symplectic world to the nonsymplectic world. I will first briefly sketch a geometric interpretation of the SeibergWitten invariants in terms of Jholomorphic curves that are compatible with the nearsymplectic form. Although the SeibergWitten invariants don't apply to (potentially exotic) 4spheres, nor do these spheres admit nearsymplectic forms, there is still a way to bring in nearsymplectic techniques.

19602

Thursday 9/5 2:00 PM

Alex Waldron, Michigan State University

$G_2$instantons on the 7sphere
 Alex Waldron, Michigan State University
 $G_2$instantons on the 7sphere
 09/05/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
I'll discuss a forthcoming paper studying families of $G_2$instantons on $S^7$, focusing on those which are obtained by pulling back asd instantons on $S^4 $ via the quaternionic Hopf fibration. In the charge1 case this yields a smooth and complete 15dimensional family. The situation for higher charge is more complicated, but we are able to compute all the infinitesimal deformations.

19635

Thursday 9/12 2:00 PM

Honghao Gao, MSU

Augmentations and sheaves for links
 Honghao Gao, MSU
 Augmentations and sheaves for links
 09/12/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
We study two different invariants of framed oriented links. Augmentations are rank one representations of a noncommutative algebra, whose definition is motivated by Floer homology. Sheaves in microlocal theory can be thought of as generalizations of link group representations. We will demonstrate two constructions going back and forth between these invariants. We will also tell a motivating story behind the scene, using SFT and microlocalization correspondence in symplectic topology.

18580

Thursday 9/26 2:00 PM

David Boozer, UCLA

Holonomy perturbations of the ChernSimons functional for lens spaces
 David Boozer, UCLA
 Holonomy perturbations of the ChernSimons functional for lens spaces
 09/26/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
We describe a scheme for constructing generating sets for Kronheimer and Mrowka's singular instanton knot homology for the case of knots in lens spaces. The scheme involves Heegaardsplitting a lens space containing a knot into two solid tori. One solid torus contains a portion of the knot consisting of an unknotted arc, as well as holonomy perturbations of the ChernSimons functional used to define the homology theory. The other solid torus contains the remainder of the knot. The Heegaard splitting yields a pair of Lagrangians in the traceless $SU(2)$character variety of the twicepunctured torus, and the intersection points of these Lagrangians comprise the generating set that we seek. We illustrate the scheme by constructing generating sets for several example knots. Our scheme is a direct generalization of a scheme introduced by Hedden, Herald, and Kirk for describing generating sets for knots in $S^3$ in terms of Lagrangian intersections in the traceless $SU(2)$character variety for the 2sphere with four punctures.

18586

Thursday 10/3 2:00 PM

Rita Gitik, Michigan

On Geodesic Triangles in the Hyperbolic Plane
 Rita Gitik, Michigan
 On Geodesic Triangles in the Hyperbolic Plane
 10/03/2019
 2:00 PM  2:50 PM
 C304 Wells Hall
Let M be an orientable hyperbolic surface without boundary and
let c be a closed geodesic in M. We prove that any side of any triangle formed by distinct lifts of c in the hyperbolic plane is shorter than c. The talk will be presented for advanced undergraduate and beginning graduate students.

19632

Thursday 10/17 2:00 PM

Jesse Madnick , McMaster University

Bubble Tree Convergence of Parametrized Associative Submanifolds
 Jesse Madnick , McMaster University
 Bubble Tree Convergence of Parametrized Associative Submanifolds
 10/17/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
In symplectic geometry, part of Gromov's Compactness Theorem asserts that sequences of holomorphic curves with bounded energy have subsequences that converge to bubble trees, and that both energy and homotopy are preserved in this "bubble tree limit." In $G_2$ geometry, the analogues of holomorphic maps are the "associative Smith maps." In this talk, we'll see that familiar analytic features of holomorphic maps also hold for associative Smith maps. In particular, we'll describe how sequences of associative Smith maps give rise to bubble trees, and how energy and homotopy are again preserved in the limit. This is joint work with Da Rong Cheng and Spiro Karigiannis.

19641

Thursday 10/24 2:00 PM

Lev TovstopyatNelip, MSU

Obstructing Lagrangian link cobordisms via Heegaard Floer homology.
 Lev TovstopyatNelip, MSU
 Obstructing Lagrangian link cobordisms via Heegaard Floer homology.
 10/24/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
I'll explain how an invariant of Legendrian links in knot Floer homology can be used to obstruct the existence of decomposable Lagrangian link cobordisms in a very general setting. The argument involves braiding the ends of the cobordism about open books and appealing to an algebraic property of the Legendrian invariant called comultiplication. Much of the talk will be spent describing the topological and contact geometric ingredients.

19619

Thursday 10/31 2:00 PM

Boyu Zhang, Princeton University

Classification of links with Khovanov homology of minimal rank
 Boyu Zhang, Princeton University
 Classification of links with Khovanov homology of minimal rank
 10/31/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
In this talk, I will present a classification of links whose Khovanov homology has minimal rank, which answers a question asked by Batson and Seed. The proof is based on an excision formula for singular instanton Floer homology that allows the excision surface to intersect the singularity. We will use the excision theorem to define an instanton Floer homology for tangles on sutured manifolds, and show that its gradings detect the generalized Thurston norm for punctured surfaces. This is joint work with Yi Xie.

19628

Thursday 11/21 2:00 PM

Akram Alishahi, University of Georgia

Braid invariant relating knot Floer homology and Khovanov homology
 Akram Alishahi, University of Georgia
 Braid invariant relating knot Floer homology and Khovanov homology
 11/21/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
Khovanov homology and knot Floer homology are two knot invariants that were defined around the same time, and despite their different constructions, share many formal similarities. After reviewing the construction of Khovanov homology and some of these similarities, we will discuss an algebraic braid invariant which is closely related to both Khovanov homology and the refinement of knot Floer homology into tangle invariants. This is a joint work with Nathan Dowlin.

19621

Thursday 12/5 2:00 PM

Shelly Harvey, Rice

Pure braids and link concordance
 Shelly Harvey, Rice
 Pure braids and link concordance
 12/05/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
If one considers the set of mcomponent based links in R^3
with a 4dimensional equivalence relationship on it, called
concordance, one can form a group called the link concordance group,
C^m. Questions in concordance are important in for classification
questions in topological and smooth 4manifolds It is well known that
the link concordance group contains the isotopy class of pure braid
with m strands, P_m. That is, two braids are concordant if and only
if they are isotopic! In the late 90's Tim Cochran, Kent Orr, and
Peter Teichner defined a filtration of the knot/link concordance group
called the nsolvable filtration. This filtration gives a way to
approximate whether a link is trivial in the group. We discuss the
relationship between pure braids and the nsolvable filtration as well
as various other more geometrically defined filtrations coming from
gropes and Whitney towers. This is joint work with Aru Ray and Jung
Hwan Park.

20691

Tuesday 12/10 11:00 AM

Luca Di Cerbo, University of Florida

Price Inequalities and BenjaminiSchramm Convergence
 Luca Di Cerbo, University of Florida
 Price Inequalities and BenjaminiSchramm Convergence
 12/10/2019
 11:00 AM  12:00 PM
 C304 Wells Hall
In this talk, I will present a study of Betti numbers of sequences of compact negatively curved Riemannian manifolds BenjaminiSchramm converging to their universal covers. The main tools are a Price inequality for harmonic forms on negatively curved spaces, and an effective thickthin decomposition.
