# Calendar

Time interval: Events:

Thursday, November 29, 2007

Posted November 28, 2007

12:40 pm - 1:30 pm 143 Lockett Hall

Framed knot contact homology

Tuesday, December 4, 2007

Posted December 3, 2007

12:40 pm Lockett 119

Thursday, May 8, 2008

Posted May 6, 2008

12:30 pm - 1:30 pm Lockett 112

Wednesday, January 11, 2017

Posted January 11, 2017

10:00 am Lockett 233

Organizational meeting

Wednesday, January 18, 2017

Posted January 17, 2017

10:30 am - 12:00 pm Lockett 233

Shea Vela-Vick, Louisiana State University
A brief introduction to Heegaard Floer invariants

In this talk, we introduce some of the basic definitions and tools used in Heegaard Floer theory, with an emphasis on applications to knot theory.

Wednesday, January 25, 2017

Posted January 25, 2017

10:30 am - 12:00 pm Lockett 233

Kyle Istvan, Louisiana State University
Invariants of Singular Knots

Wednesday, February 1, 2017

Posted February 3, 2017

10:30 am - 12:30 pm Lockett 233

Ryan Leigon, Louisiana State University
First Examples in Bordered Floer Homology

Wednesday, February 8, 2017

Posted February 3, 2017

10:30 am - 12:30 pm Lockett 233

Jose Ceniceros, Louisiana State University
Open Books and Contact Geometry

Wednesday, February 22, 2017

Posted February 3, 2017

10:30 am - 12:30 pm Lockett 233

Federico Salmoiraghi, Department of Mathematics, LSU
TBD

Wednesday, March 15, 2017

Posted February 3, 2017

10:30 am - 12:30 pm Lockett 233

Andrew Holmes, Louisiana State University
TBD

Wednesday, August 30, 2017

Posted August 23, 2017

10:30 am - 12:00 pm Lockett 233

Federico Salmoiraghi, Department of Mathematics, LSU
An introduction to Heegaard Floer homology

Abstract: In 2001 Ozsvath and Szabo introduced Heegaard Floer homology, an invariant of three manifolds that can be calculated from a particular class of Heegaard diagram for the manifold. In this talk, after a brief outline of the construction of the invariant, I will introduce some of the different versions of Heegaard Floer homology and compute some example.

Wednesday, September 13, 2017

Posted August 23, 2017

10:30 am - 12:00 pm Lockett 233

Ryan Leigon, Louisiana State University
Bordered Heegaard Floer Homology

Abstract: Heegaard Floer theory yields powerful invariants of 3-manifolds, but it is often difficult to compute. Bordered Floer allows us to do computations by cutting a 3-manifold into simple pieces, where computations are easy, and then pasting the pieces back together. I will provide a brief introduction to the theory before giving an accessible yet non-trivial example.

Wednesday, September 20, 2017

Posted September 20, 2017

10:30 am - 12:00 pm Lockett 233

Ryan Leigon, Louisiana State University
Federico Salmoiraghi, Department of Mathematics, LSU
Equivalence of gluing maps in Heegaard Floer theory

We show that the gluing mas in Heegaard Floer theory defined by Honda, Kazez and Matic and by Zarev are equivalent.

Wednesday, September 27, 2017

Posted August 23, 2017

10:20 am - 11:50 am Lockett 233

Yu-Chan Chang, Louisiana State University
Introduction to bounded cohomology of discrete groups

Abstract: In this introductory talk, we will focus on bounded cohomology of discrete groups with real or integer coefficient. I will talk about the bounded cohomology of Gromov hyperbolic groups and amenable groups. Also, we will discuss the comparison map, which is the map from the bounded cohomology to the usual cohomology.

Wednesday, October 4, 2017

Posted October 3, 2017

10:20 am - 11:20 am Lockett 233

Yu-Chan Chang, Louisiana State University
Introduction to bounded cohomology of discrete groups II

Abstract: We continue our discussion from last week. In this talk, I will describe the construction of non-trivial quasimorphisms on free groups. This shows that free groups have non-trivial second bounded cohomology groups while the usual cohomology groups are trivial. We will also discuss the quasi-morphism on abelian groups. If time permits, I will talk about Gromov hyperbolic groups.

Wednesday, October 11, 2017

Posted August 23, 2017

10:30 am - 12:00 pm Lockett 233

Kent Vashaw, Louisiana State University
TBD

Wednesday, October 18, 2017

Posted October 6, 2017

10:30 am - 12:00 pm Lockett 233

Robin Koytcheff, University of Louisiana, Lafayette

Abstract: Finite-type knot invariants (a.k.a. Vassiliev invariants) are an important class of invariants in that they conjecturally approximate all knot invariants and hence separate knots. They may also be defined for (closed) links and string links, and they are known to separate string links up to link homotopy. In other words, they are a complete invariant of string links where each component may pass through itself. This parallels (and is related to) a story about the kappa invariant, which conjecturally separates closed links up to link homotopy. In joint work with F. Cohen, Komendarczyk, and Shonkwiler, we showed that the kappa invariant separates string links up to link homotopy. In this talk, we will focus on the elementary, purely combinatorial description of finite-type invariants.

Wednesday, October 25, 2017

Posted October 24, 2017

10:30 am - 12:00 pm Lockett 233

Kent Vashaw, Louisiana State University
TBD

Wednesday, November 1, 2017

Posted August 23, 2017

10:30 am - 12:00 pm Lockett 233

Rima Chatterjee, Louisiana State University
TBD

Wednesday, November 8, 2017

Posted November 7, 2017

10:30 am - 12:00 pm Lockett 233

Nurdin Takenov, Louisiana State University
Vassiliev Invariants

Wednesday, November 15, 2017

Posted August 25, 2017

10:30 am - 12:00 pm Lockett 233

Sudipta Ghosh, Louisiana State University
Seiberg-Witten invariants of 4-manifolds with free circle actions

Wednesday, January 24, 2018

Posted August 23, 2017

10:30 am - 12:00 pm Lockett 233

Rob Quarles, Louisiana State University
The Alexander module

Wednesday, January 31, 2018

Posted January 24, 2018

10:00 am - 12:00 pm Lockett 233

Rima Chatterjee, Louisiana State University

Wednesday, February 7, 2018

Posted January 24, 2018

10:00 am - 12:00 pm Lockett 233

Ryan Leigon, Louisiana State University
TBD

Wednesday, February 21, 2018

Posted February 20, 2018

10:30 am - 12:00 pm Lockett 233

Configuration Spaces and Graph Realizability

Abstract: Embed a graph G generically into R^n as a bar framework (edges are rigid straight bars which are free to rotate around vertices). Fixing the edge lengths given by the embedding, what is the smallest integer d such that G can embed into R^d with the same edge lengths? As an example, no n-simplex can be generically embedded into R^{n-1}. Viewing the n-simplex as a complete graph, we see that the non-realizability of the n-simplex is a property of the complete graph. Are simplicies the minimal objects in some sense with regards to realizability? No, we can find generic 4-dim embeddings of the octahedron which do not admit 3-dim realizations. We will demonstrate a proof of this fact and examine several different characterizations of this correspondence between graphs and certain simplicial complexes as we try to build towards more complex and higher dimensional objects. This is a work in progress.

Wednesday, February 28, 2018

Posted January 24, 2018

10:00 am - 12:00 pm Lockett 233

Yu-Chan Chang, Louisiana State University
Simplicial Volume

Abstract: Gromov introduced the simplicial volume in 1982, it is an invariant of manifolds. While several vanishing and non-vanishing results for the simplicial volume are known by now, the exact value of non-vanishing simplicial volumes is difficult to compute. In this talk, the bounded cohomology of spaces will be defined, then we will discuss some basic properties of simplicial volume and some celebrated results by Gromov and Thurston.

Wednesday, March 7, 2018

Posted January 24, 2018

10:00 am - 12:00 pm Lockett 233

Federico Salmoiraghi, Department of Mathematics, LSU
TBD

Wednesday, April 4, 2018

Posted January 24, 2018

10:00 am - 12:00 pm Lockett 233

Sudipta Ghosh, Louisiana State University
TBD

Wednesday, April 11, 2018

Posted March 19, 2018

10:30 am - 12:00 pm Lockett 233

Kent Vashaw, Louisiana State University
TBD

Wednesday, April 18, 2018

Posted January 24, 2018

10:00 am - 12:00 pm Lockett 233

Nurdin Takenov, Louisiana State University
TBD

Wednesday, August 29, 2018

Posted August 27, 2018

1:30 pm - 3:00 pm Lockett 233

Ignat Soroko, Louisiana State University
Right-angled Artin groups and their subgroups

I will define right-angled Artin groups, consider few examples and talk about some interesting classes of their subgroups: special subgroups in the sense of Haglund and Wise, and Bestvina-Brady kernels.

Wednesday, September 5, 2018

Posted August 16, 2018

1:30 pm - 3:00 pm Lockett 233

Andrew Zimmer, Louisiana State University
Metrics in several complex variables

Abstract: In this talk I'll define three classical metrics in several complex variables: the Kobayashi metric, the Bergman metric, and the K{\"a}hler-Einstein metric. After introducing these metrics, I'll describe how their geometric properties can be used to solve problems. The talk won't assume any prior background in complex analysis.

Wednesday, September 12, 2018

Posted August 27, 2018

1:30 pm - 3:00 pm Lockett 233

Ryan Leigon, Louisiana State University
TBA

Wednesday, September 19, 2018

Posted August 27, 2018

1:30 pm - 3:00 pm Lockett 233

Ryan Leigon, Louisiana State University
TBA

Wednesday, September 26, 2018

Posted August 27, 2018

1:30 pm - 12:00 am Saturday, September 15, 2018 Lockett 233

Yilong Wang, Louisiana State University
TBA

Wednesday, October 3, 2018

Posted August 27, 2018

1:30 pm - 3:00 pm Lockett 233

Kent Vashaw, Louisiana State University
TBA

Wednesday, October 17, 2018

Posted August 27, 2018

1:30 pm - 3:00 pm Lockett 233

Lucas Meyers, Louisiana State University
TBA

Wednesday, October 24, 2018

Posted August 27, 2018

1:30 pm - 3:00 pm Lockett 233

Sudipta Ghosh, Louisiana State University
TBA

Wednesday, October 31, 2018

Posted August 27, 2018

1:30 pm - 3:00 pm Lockett 233

Rima Chatterjee, Louisiana State University
TBA

Wednesday, November 7, 2018

Posted November 8, 2018

1:30 pm - 3:00 pm

Rima Chatterjee, Louisiana State University
Branches covers of contact manifolds II

Wednesday, November 14, 2018

Posted August 27, 2018

1:30 pm - 3:00 pm Lockett 233

Rob Quarles, Louisiana State University
TBA

Wednesday, November 28, 2018

Posted August 27, 2018

1:30 pm - 3:00 pm Lockett 233

Nurdin Takenov, Louisiana State University
TBA

Wednesday, November 28, 2018

Posted August 27, 2018

1:30 pm - 3:00 pm Lockett 233

Natthawut Phanachet, Louisiana State University
TBA

Wednesday, January 16, 2019

Posted January 16, 2019

1:30 pm - 3:00 pm Lockett 233

Shea Vela-Vick, Louisiana State University
Arnold's dream: in search for higher-order helicity invariants

Arnold dreamed of a hierarchy of helicity invariants which could provide lower bounds for the $L_2$-energy of a vector field under appropriate deformations. Ordinary helicity is a field analogue of the standard linking number between curves, and this correspondence quickly leads to an integral expression for helicity. The general expectation is that higher-order helicity invariants should be obtained as field generalizations of higher order linking invariants, of which Milnor's triple-linking number is the first in line. In this talk, I'll survey some of the history behind helicity invariant and show how one can use configuration space techniques to obtain a geometrically natural integral expression for the Milnor triple-linking number.

Wednesday, January 23, 2019

Posted January 22, 2019

1:30 pm - 3:00 pm Lockett 233

Mike Wong, Louisiana State University
GRID invariants obstruct decomposable Lagrangian cobordisms

Abstract: Ozsvath, Szabo, and Thurston defined several combinatorial invariants of Legendrian links in the 3-sphere using grid homology, which is a combinatorial version of knot Floer homology. These, collectively called the GRID invariants, are known to be effective in distinguishing some Legendrian knots that have the same classical invariants. In this talk, we describe a recent result that the GRID invariants provide an obstruction to the existence of decomposable Lagrangian cobordisms between Legendrian links. This obstruction is stronger than the obstructions from the Thurston-Bennequin and rotation numbers, and is closely related to a recent result by Golla and Juhasz. This is joint work with John Baldwin and Tye Lidman.

Wednesday, January 30, 2019

Posted January 27, 2019

1:30 pm - 3:00 pm Lockett 233

Scott Baldridge, Louisiana State University
TBA

Wednesday, February 6, 2019

Posted January 27, 2019

1:30 pm - 3:00 pm Lockett 233

Anton Zeitlin, LSU
Hidden Homotopy Symmetries of Einstein Field Equations

Abstract: We demonstrate that the Einstein field equations with extra fields known as B-field and dilaton, have a nontrivial underlying algebraic structure, known as homotopy Gerstenhaber algebra. Such homotopy algebra is a natural object associated to Courant algebroid in the vertex algebra formalism. We show that the Einstein equations coincide with the Maurer-Cartan equations for the L-infinity part of such Gerstenhaber algebra.

Wednesday, February 13, 2019

Posted January 27, 2019

1:30 pm - 3:00 pm Lockett 233

Andrew Zimmer, Louisiana State University
TBA

Wednesday, February 20, 2019

Posted January 27, 2019

1:30 pm - 3:00 pm Lockett 233

Ryan Leigon, Louisiana State University
TBA

Wednesday, February 27, 2019

Posted January 27, 2019

1:30 pm - 3:00 pm Lockett 233

Yu-Chan Chang, Louisiana State University
Introduction to handlebody groups

Abstract: Handlebody group is the mapping class group of a 3-dimensional handlebody, it is a subgroup of the mapping class group of the boundary surface of that handlebody. In this introductory talk, I will talk about some properties of handlebody groups and how different they are from the surface mapping groups.

Wednesday, March 13, 2019

Posted January 27, 2019

1:30 pm - 3:00 pm Lockett 233

Nurdin Takenov, Louisiana State University
3-coloring and other invariants of knots

Abstract: 3 coloring invariant is, perhaps, the simplest knot invariant. Nevertheless, as shown by Przytycki, it can be strengthened and is connected to other knot invariants, like uncrossing number and Jones polynomial. In my talk I will describe these results.

Wednesday, March 27, 2019

Posted January 27, 2019

1:30 pm - 3:00 pm Lockett 233

Rima Chatterjee, Louisiana State University
Classification of Legendrian Torus Knots

Abstract: Legendrian Knots have played important role in Contact Geometry. A natural question in Contact Geometry is which knots are Legendrian Simple that is which Legendrian Knots can be classified using their classical invariants. In this talk, I will give a brief overview of the classical invariants of Legendrian Knots and discuss about Legendrian torus knots which is one of the few examples of Legendrian simple knot type.

Wednesday, April 10, 2019

Posted January 27, 2019

1:30 pm - 3:00 pm Lockett 233

Sean Bibby, Louisiana State University
TBA

Wednesday, April 24, 2019

Posted January 27, 2019

1:30 pm - 3:00 pm Lockett 233

Federico Salmoiraghi, Department of Mathematics, LSU
Sutured Floer Homology and TQFT

In this talk I will describe a result by Juhasz. He introduces a natural notion of cobordism between sutured manifolds, and shows that such a cobordism induces a map on sutured Floer homology. This map is a common generalization of the hat version of the closed 3-manifold cobordism map in Heegaard Floer theory, and the contact gluing map defined by Honda, Kazez, and Matic.

Wednesday, September 4, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

Shea Vela-Vick, Louisiana State University
An introduction to low-dimensional topology and contact geometry

Wednesday, September 11, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

Scott Baldridge, Louisiana State University
An introduction to Mirror Symmetry, Calabi-Yau manifolds, and Special Lagrangian Cones

Abstract: In this talk we look at the history of mirror symmetry as it came out of string theory (i.e., a 10-dimensional universe where particles are "strings"). We use that historical account to explain some of the motivation behind studying Calabi-Yau manifolds and special Lagrangian fibrations of these manifolds, which lead to my studying of special Lagrangian cones in my work. The goal is to use this narrative to introduce and discuss common terms (symplectic forms, Lagrangian, fiber bundles and fibrations, etc.) that will be used throughout the graduate student seminar this year. In that sense, this is not going to be an overly technical talk.

Wednesday, September 18, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

Justin Murray, Louisiana State University
TBD

Wednesday, September 25, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

Ryan Leigon, Louisiana State University
TBD

Wednesday, October 2, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

Jiten Ahuja, Louisiana State University
TBD

Wednesday, October 9, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

Sudipta Ghosh, Louisiana State University
TBD

Wednesday, October 16, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

Amit Kumar, Louisiana State University
TBD

Wednesday, October 23, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

Rima Chatterjee, Louisiana State University
TBD

Wednesday, October 30, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

Nurdin Takenov, Louisiana State University
Braid group and its representation(s)

Abstract: In my presentation I will talk about braid group and its representations. In particular, I will talk about Burau representation and (if there will be enough time) about its generalization.

Wednesday, November 6, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

Rob Quarles, Louisiana State University
TBD

Wednesday, November 13, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

Abel Lopez, Louisiana State University
TBD

Wednesday, November 20, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

Emma Lien, Louisiana State University
TBD

Wednesday, December 4, 2019

Posted December 1, 2019

1:30 pm - 3:00 pm Lockett 233

Charles Livingston, Indiana University
Four-dimensional approaches to some problems in classical knot theory

Wednesday, September 8, 2021

Posted September 8, 2021

1:30 pm - 3:00 pm Lockett 233

Rob Quarles, Louisiana State University
A generating set of knots

Abstract: In this (informal) talk we will explore a normalization of the (Conway-normalized) Alexander polynomial that contains some interesting properties. In particular we will construct a generating set of knots that will give us the Alexander polynomials of any given n-crossing knot, using no knots with more than n crossings. We will then explore the connection between this set of knots and a strong, simple knot invariant given by Bar-Natan and van der Veen.

Wednesday, September 15, 2021

Posted September 8, 2021

1:30 pm - 3:00 pm Lockett 233

Roland van der Veen, Bernoulli Institute, University of Groningen
A tale of tangles and tensors

Abstract: In this informal talk I will emphasize the analogies between the algebraic structure found in tangles and that of the tensor powers of some algebra H. In both cases one has to deal with a lot of legs, indices and strands. We build bigger tangles by gluing strands of smaller ones just like we contract indices of tensors to make new ones. Then there are other operations on tangles such as doubling a strand or reversing it and this extra structure translates to the algebra H being a Hopf algebra so if you didn't know about Hopf algebras yet, tangles will teach you! Many meaningful topological notions such as genus and ribonness can be formulated in terms of tangles and their operations so given a suitable Hopf algebra and the above dictionary we should be able to shed some light on those. Time permitting some of this will be demonstrated using Mathematica. This is joint work with Dror Bar-Natan and I will discuss (part of) sections 4 and 7 of our recent preprint: https://arxiv.org/abs/2109.02057

Wednesday, September 22, 2021

Posted September 8, 2021

1:30 pm - 3:00 pm Lockett 233

Amit Kumar, Louisiana State University
TBD

Wednesday, September 22, 2021

Posted September 17, 2021

1:30 pm - 3:00 pm Lockett 233

Sudipta Ghosh, Louisiana State University
Connected sum formulas in knot Floer homology

Knot Floer homology is an invariant of knot which was first introduced in the context of Heegaard Floer homology and later extended other Floer theories. In this talk, we discuss a new approach to the connected sum formula using direct limits. Our methods apply to versions of knot Floer homology arising in the context of Heegaard, instanton and monopole Floer homology. This is joint work with Ian Zemke.

Wednesday, September 29, 2021

Posted September 8, 2021

1:30 pm - 3:00 pm Lockett 233

Nilangshu Bhattacharyya, Louisiana State University
Construction of Khovanov (Co)chain complex

Abstract: The talk will be based on Bar-Natan's construction of the Khovanov (Co)chain complex of link/knot. We would discuss that the graded Euler Characteristic of the (Co)Chain Complex is the same as the Jones Polynomial of oriented knot.

Wednesday, October 6, 2021

Posted September 9, 2021

1:30 pm - 3:00 pm Lockett 233

Justin Murray, Louisiana State University
Colored Ruling Polynomials and Colored Kauffman Polynomials

Abstract: In this talk, I will give definitions of m-graded n-colored ruling polynomials and discuss some relations to DGA representations, and other colored knot polynomials. Along the way I’ll probably define (smooth) BMW algebras and a Legendrian BMW algebra.

Wednesday, November 10, 2021

Posted September 9, 2021

1:30 pm - 3:00 pm Lockett 233

Jackson Knox, Louisiana State University
TBD

Wednesday, November 10, 2021

Posted November 3, 2021

1:30 pm Lockett 233

Assaf Bar-Natan, University of Toronto
Grand Arcs and Infinite-Type Surfaces

A surface S is called infinite-type if it has an infinite pair-of-pants decomposition (and a really funny name). Some examples are the flute surface (plane minus the natural numbers), the Cantor tree (sphere minus a Cantor set), Jacob's Ladder (infinite tori glued in a bi-directional line), or even the Loch Ness Monster (infinite tori glued in a line but only in one direction). The mapping class group, or, the group of homeomorphisms of a surface up to homotopy is a mysterious object for finite-type surfaces, and even more mysterious for infinite-type. One way to study this group is to find a good graph upon which it acts. We will do exactly that in this talk by introducing the grand arc graph. This is based on joint work with Y. Verberne. This talk should be accessible to anyone familiar with the classification of finite-type surfaces.

Wednesday, March 9, 2022

Posted February 24, 2022

1:30 pm Lockett 233

Sam Shepherd, Vanderbilt University
Cubulating groups

I will explain what it means to cubulate a group, and discuss some properties of cubulated groups. I will then describe a strategy for cubulating groups using wallspaces.

Wednesday, April 6, 2022

Posted March 25, 2022

1:30 pm Lockett 233

Dan Rutherford, Ball State University
Introduction to Legendrian contact homology for surfaces

Legendrian contact homology is an algebraic invariant of Legendrian knots and surfaces that arises from the Morse theory of the symplectic action functional. My goal in this talk will be to make this construction accessible to a general mathematical audience. I will begin with a brief introduction to homology via the simplicial homology of a space and then explain a beautiful connection between homology and calculus known as Morse theory. Next, I will introduce Legendrian surfaces in R^5 and explain how to view them via their front projections which are singular surfaces in R^3. After explaining the original Morse/Floer theory definition of Legendrian contact homology, I will conclude the talk by presenting a recent simplicial reformulation of the invariant that is joint work with Mike Sullivan.

Wednesday, February 1, 2023

Posted January 27, 2023

1:30 pm Lockett 233

Amit Kumar, Louisiana State University
Invariants and Moduli

This talk will be an introduction to Theory of invariants and its evolution to the theory of moduli spaces. I will begin from the works of the invariant triple: Cayley, Sylvester, and Soloman, and will end at David Mumford's point of view that gives us the theory of Moduli spaces. No specific prerequisite is required.

Wednesday, February 8, 2023

Posted January 30, 2023

1:30 pm Lockett 233

Justin Murray, Louisiana State University
On the Homotopy Cardinality of the Legendrian Representation Category

Given a Legendrian knot in the standard contact R^3, one can assign an n-dimensional representation category. This A-infinity category encodes n-dimensional representations of the Legendrian contact homology DGA (LCH DGA). In this talk, I will discuss the relationship between a categorical count of representations, and other holomorphic curve invariants called colored ruling polynomials. In particular, I will present a formula relating these two invariants. This formula is generalizes results known for augmentations (1-dimensional representations). Towards the end I will discuss some related applications to concordance and a few open conjectures.

Wednesday, February 15, 2023

Posted January 30, 2023

1:30 pm Lockett 233

On the Contact Class in Heegaard Floer Homology

Ozsvath and Szabo defined an invariant of a contact 3-manifold, an element in the Heegaard Floer Homology of the manifold. In this talk, I will give an alternate description of this contact invariant which was introduced by K. Honda, W.H. Kazez, and G. Matic in their paper “On the Contact Class in Heegaard Floer Homology”. We will also see how the contact class helps to prove certain properties of the contact structure.

Wednesday, March 1, 2023

Posted January 30, 2023

1:30 pm Lockett 233

Nilangshu Bhattacharyya, Louisiana State University
Morse theory and Flow Category

The aim is to discuss the basics of Morse theory with an eye towards understanding the flow category of a Morse function. For a compact Riemannian manifold, the classifying space of the flow category of a Morse function on that manifold completely captures the topological structure of the manifold up to Homotopy (result by Cohen-Jones-Segal). I will try to show a few examples.

Wednesday, March 8, 2023

Posted January 30, 2023

1:30 pm Lockett 233

Aneek Maiti, Louisiana State University
Kazhdan-Lusztig polynomials

Intersection cohomology is an important tool in the theory of Perverse sheaves. It satisfies Poincare duality and the Kunneth formula. For a Schubert variety corresponding to a reductive linear algebraic group the computation of the Intersection cohomology is not very easy without extra tools. During the 1970s in Kazhdan Lusztig conjectured (which has been proved later) a problem in representation theory of Verma modules and introduced Kazdan Lusztig polynomials. These Kazhdan Lusztig polynomials are very important tool to compute the intersection cohomology of Schubert varieties. In my talk I will give a brief overview of Kazhdan Lusztig polynomials.

Wednesday, March 22, 2023

Posted January 31, 2023

1:30 pm Lockett 233

Colton Sandvick, Louisiana State University
Singular Support of Constructible Sheaves on Manifolds

Given a sheaf F on a real manifold X, one can assign closed, conic, Lagrangian subset of the cotangent bundle T*X, called the singular support. Singular support is a powerful invariant of sheaves and behaves well with regard to many common sheaf operations. In this talk, we will discuss singular support in the context of constructible sheaves, describe many of its fundamental properties, and give some examples. As an application, we will discuss some classes of sheaves which can be described by their singular support. We will not assume any prior knowledge of sheaf theory; although, some familiarness with differential geometry and singular (or de Rham) cohomology will be helpful.

Wednesday, March 29, 2023

Posted January 31, 2023

1:30 pm Lockett 233

Colton Sandvick, Louisiana State University
Singular Support of Étale Constructible Sheaves and Applications to Representation Theory

In this talk, we will discuss a generalization of singular support for constructible sheaves on manifolds where we instead consider étale constructible sheaves on algebraic varieties. Singular support in this setting was only recently defined by Beilinson in 2015. We will detail the nuances in working with étale sheaves on algebraic varieties rather than sheaves on manifolds. We will investigate a few classical applications of singular support which provides a geometric description of character sheaves in characteristic 0. We will then use Beilinson's generalization to explain some recent work of Psaromiligkos which generalizes one of these results to character sheaves on reductive groups in positive characteristic.

Wednesday, April 5, 2023

Posted January 31, 2023

1:30 pm Lockett 233

Jake Murphy, LSU

Wednesday, April 12, 2023

Posted January 31, 2023

1:30 pm Lockett 233

Gurleen Nanda, Louisiana State University

Wednesday, April 19, 2023

Posted January 31, 2023

1:30 pm Lockett 233

Amit Kumar, Louisiana State University

Wednesday, April 26, 2023

Posted January 31, 2023

1:30 pm Lockett 233

Megan Farrell, Louisiana State University

Wednesday, May 3, 2023

Posted January 31, 2023

1:30 pm Lockett 233

Matthew McCoy, Louisiana State University