Posted November 28, 2007
Last modified July 25, 2018
Informal Geometry and Topology Seminar Questions or comments?
12:40 pm – 1:30 pm 143 Lockett HallFramed knot contact homology
Posted December 3, 2007
Last modified July 25, 2018
Informal Geometry and Topology Seminar Questions or comments?
12:40 pm Lockett 119Reading Seminar
Posted May 6, 2008
Last modified July 25, 2018
Informal Geometry and Topology Seminar Questions or comments?
12:30 pm – 1:30 pm Lockett 112Reading Seminar
Posted January 11, 2017
Informal Geometry and Topology Seminar Questions or comments?
10:00 am Lockett 233Organizational meeting
Posted January 17, 2017
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted January 25, 2017
Informal Geometry and Topology Seminar Questions or comments?
10:30 am – 12:00 pm Lockett 233
Kyle Istvan, Louisiana State University
Invariants of Singular Knots
Posted February 3, 2017
Informal Geometry and Topology Seminar Questions or comments?
10:30 am – 12:30 pm Lockett 233
Ryan Leigon, Louisiana State University
First Examples in Bordered Floer Homology
Posted February 3, 2017
Informal Geometry and Topology Seminar Questions or comments?
10:30 am – 12:30 pm Lockett 233
Jose Ceniceros, Louisiana State University
Open Books and Contact Geometry
Posted February 3, 2017
Informal Geometry and Topology Seminar Questions or comments?
10:30 am – 12:30 pm Lockett 233
Federico Salmoiraghi, Department of Mathematics, LSU
TBD
Posted February 3, 2017
Informal Geometry and Topology Seminar Questions or comments?
10:30 am – 12:30 pm Lockett 233
Andrew Holmes, Louisiana State University
TBD
Posted August 23, 2017
Last modified August 29, 2017
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted August 23, 2017
Last modified September 12, 2017
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted September 20, 2017
Last modified March 2, 2021
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted August 23, 2017
Last modified September 11, 2017
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted October 3, 2017
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted August 23, 2017
Last modified October 3, 2017
Informal Geometry and Topology Seminar Questions or comments?
10:30 am – 12:00 pm Lockett 233
Kent Vashaw, Louisiana State University
TBD
Posted October 6, 2017
Last modified October 16, 2017
Informal Geometry and Topology Seminar Questions or comments?
10:30 am – 12:00 pm Lockett 233
Robin Koytcheff, University of Louisiana, Lafayette
Finite-type invariants of knots, links, and string links
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.
Posted October 24, 2017
Informal Geometry and Topology Seminar Questions or comments?
10:30 am – 12:00 pm Lockett 233
Kent Vashaw, Louisiana State University
TBD
Posted August 23, 2017
Last modified October 24, 2017
Informal Geometry and Topology Seminar Questions or comments?
10:30 am – 12:00 pm Lockett 233
Rima Chatterjee, Louisiana State University
TBD
Posted November 7, 2017
Informal Geometry and Topology Seminar Questions or comments?
10:30 am – 12:00 pm Lockett 233
Nurdin Takenov, Louisiana State University
Vassiliev Invariants
Posted August 25, 2017
Last modified November 15, 2017
Informal Geometry and Topology Seminar Questions or comments?
10:30 am – 12:00 pm Lockett 233
Sudipta Ghosh, Louisiana State University
Seiberg-Witten invariants of 4-manifolds with free circle actions
Posted August 23, 2017
Last modified January 23, 2018
Informal Geometry and Topology Seminar Questions or comments?
10:30 am – 12:00 pm Lockett 233
Rob Quarles, Louisiana State University
The Alexander module
Posted January 24, 2018
Last modified January 30, 2018
Informal Geometry and Topology Seminar Questions or comments?
10:00 am – 12:00 pm Lockett 233
Rima Chatterjee, Louisiana State University
Transverse universal links
Posted January 24, 2018
Informal Geometry and Topology Seminar Questions or comments?
10:00 am – 12:00 pm Lockett 233
Ryan Leigon, Louisiana State University
TBD
Posted February 20, 2018
Informal Geometry and Topology Seminar Questions or comments?
10:30 am – 12:00 pm Lockett 233Configuration 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.
Posted January 24, 2018
Last modified February 27, 2018
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted January 24, 2018
Last modified February 27, 2018
Informal Geometry and Topology Seminar Questions or comments?
10:00 am – 12:00 pm Lockett 233
Federico Salmoiraghi, Department of Mathematics, LSU
TBD
Posted January 24, 2018
Informal Geometry and Topology Seminar Questions or comments?
10:00 am – 12:00 pm Lockett 233
Sudipta Ghosh, Louisiana State University
TBD
Posted March 19, 2018
Informal Geometry and Topology Seminar Questions or comments?
10:30 am – 12:00 pm Lockett 233
Kent Vashaw, Louisiana State University
TBD
Posted January 24, 2018
Last modified March 19, 2018
Informal Geometry and Topology Seminar Questions or comments?
10:00 am – 12:00 pm Lockett 233
Nurdin Takenov, Louisiana State University
TBD
Posted August 27, 2018
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted August 16, 2018
Last modified September 7, 2018
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted August 27, 2018
Last modified September 7, 2018
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Ryan Leigon, Louisiana State University
TBA
Posted August 27, 2018
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Ryan Leigon, Louisiana State University
TBA
Posted August 27, 2018
Last modified September 24, 2018
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 12:00 am Saturday, September 15, 2018 Lockett 233
Yilong Wang, Louisiana State University
TBA
Posted August 27, 2018
Last modified March 2, 2021
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Kent Vashaw, Louisiana State University
TBA
Posted August 27, 2018
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Lucas Meyers, Louisiana State University
TBA
Posted August 27, 2018
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Sudipta Ghosh, Louisiana State University
TBA
Posted August 27, 2018
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Rima Chatterjee, Louisiana State University
TBA
Posted November 8, 2018
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm
Rima Chatterjee, Louisiana State University
Branches covers of contact manifolds II
Posted August 27, 2018
Last modified November 8, 2018
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Rob Quarles, Louisiana State University
TBA
Posted August 27, 2018
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Natthawut Phanachet, Louisiana State University
TBA
Posted August 27, 2018
Last modified November 8, 2018
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Nurdin Takenov, Louisiana State University
TBA
Posted January 16, 2019
Last modified May 8, 2021
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted January 22, 2019
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted January 27, 2019
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Scott Baldridge, Louisiana State University
TBA
Posted January 27, 2019
Last modified February 5, 2019
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted January 27, 2019
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Andrew Zimmer, Louisiana State University
TBA
Posted January 27, 2019
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Ryan Leigon, Louisiana State University
TBA
Posted January 27, 2019
Last modified February 21, 2019
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted January 27, 2019
Last modified March 13, 2019
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted January 27, 2019
Last modified March 26, 2019
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted January 27, 2019
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Sean Bibby, Louisiana State University
TBA
Posted January 27, 2019
Last modified March 2, 2021
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted September 11, 2019
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Shea Vela-Vick, Louisiana State University
An introduction to low-dimensional topology and contact geometry
Posted September 11, 2019
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted September 11, 2019
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Justin Murray, Louisiana State University
TBD
Posted September 11, 2019
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Ryan Leigon, Louisiana State University
TBD
Posted September 11, 2019
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Jiten Ahuja, Louisiana State University
TBD
Posted September 11, 2019
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Sudipta Ghosh, Louisiana State University
TBD
Posted September 11, 2019
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Amit Kumar, Louisiana State University
TBD
Posted September 11, 2019
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Rima Chatterjee, Louisiana State University
TBD
Posted September 11, 2019
Last modified October 29, 2019
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted September 11, 2019
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Rob Quarles, Louisiana State University
TBD
Posted September 11, 2019
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Abel Lopez, Louisiana State University
TBD
Posted September 11, 2019
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Emma Lien, Louisiana State University
TBD
Posted December 1, 2019
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Charles Livingston, Indiana University
Four-dimensional approaches to some problems in classical knot theory
Posted September 8, 2021
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted September 8, 2021
Informal Geometry and Topology Seminar Questions or comments?
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
Posted September 8, 2021
Last modified October 13, 2021
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Amit Kumar, Louisiana State University
TBD
Posted September 17, 2021
Last modified September 21, 2021
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted September 8, 2021
Last modified September 29, 2021
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted September 9, 2021
Last modified October 6, 2021
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted September 9, 2021
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 3:00 pm Lockett 233
Jackson Knox, Louisiana State University
TBD
Posted November 3, 2021
Last modified November 5, 2021
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted February 24, 2022
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted March 25, 2022
Last modified March 31, 2022
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted January 27, 2023
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted January 30, 2023
Last modified February 6, 2023
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted January 30, 2023
Last modified February 10, 2023
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233
Adithyan Pandikkadan, Louisiana State University
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.
Posted January 30, 2023
Last modified February 24, 2023
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted January 30, 2023
Last modified March 3, 2023
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted January 31, 2023
Last modified March 17, 2023
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted January 31, 2023
Last modified March 17, 2023
Informal Geometry and Topology Seminar Questions or comments?
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.
Posted March 29, 2023
Last modified April 3, 2023
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233
Amit Kumar, Louisiana State University
Legendrian Weaves and Manifold with decoration
In the paper titled 'Legendrian Weaves' Casals and Zaslow introduced the idea of N-graph and used it to construct Legendrian surfaces in the jet space of the surface associated with the N - graph. I will first talk about this construction and will then show that how the N-graph is an example of a more general 'manifold with decoration'. On a heuristic level a manifold with decoration is a manifold with defect where the defect facilitates decoration with other mathematical objects e.g., local systems, groups, etc. For this talk, I will focus on the decoration with groups and will show how such manifolds capture processes like Reidemeister moves. I will end the talk with an approach to TQFT of manifolds with decoration. This is research in progress.
Posted March 29, 2023
Last modified April 10, 2023
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233
Jake Murphy, LSU
Quasiconvex subgroups of Coxeter groups
A subgroup of a hyperbolic group whose inclusion map is a quasi-isometric embedding is called quasiconvex. Various algorithmic problems are decidable for these quasiconvex subgroups, such as the membership problem and computing the index of the subgroup. In this talk, I will show techniques for determining when a subgroup is quasiconvex by Dani and Levcovitz for right-angled Coxeter groups and by Schupp for extra-large type Coxeter groups.
Posted January 31, 2023
Last modified April 13, 2023
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233
Megan Farrell, Louisiana State University
Smooth versus Topological Concordance via Whitehead Doubles
We examine the difference between smooth and topological concordance using Knot Floer Homology. We do this using whitehead doubles, which can provide examples of knots which are topologically slice but not smoothly slice. We will be following Knot Floer Homology and Whitehead Doubles, written by Matt Hedden.
Posted January 31, 2023
Last modified April 28, 2023
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233
Matthew McCoy, Louisiana State University
An Introduction to Buildings and BN Pairs
This talk will introduce a special class of simplicial complexes called buildings. We will discuss some basic properties of buildings along with some examples. Then, we will discuss group actions on buildings. In particular, group actions by algebraic groups. As it turns out, algebraic groups are the historical motivation behind the study of buildings, and there are lots of relations between buildings and the structure theory of algebraic groups. In particular, we will discuss BN pairs associated with algebraic groups acting on buildings and how these BN pairs relate to the group action.
Posted September 6, 2023
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 2:30 pm Lockett 233Organizational
Posted September 6, 2023
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 2:30 pm Lockett 233
Shea Vela-Vick, Louisiana State University
Characteristic Classes - Lecture 1
Posted September 6, 2023
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 2:30 pm Lockett 233
Adithyan Pandikkadan, Louisiana State University
Characteristic Classes - Lecture 2
Posted September 6, 2023
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 2:30 pm Lockett 233
Nilangshu Bhattacharyya, Louisiana State University
Characteristic Classes - Lecture 3
Posted September 6, 2023
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 2:30 pm Lockett 233
Colton Sandvick, Louisiana State University
Characteristic Classes - Lecture 4
Posted October 6, 2023
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 2:30 pm Lockett 233
Adithyan Pandikkadan, Louisiana State University
Continuation on characteristic classes
Posted September 6, 2023
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 2:30 pm Lockett 233
Krishnendu Kar, Louisiana State University
TBA
Posted September 6, 2023
Last modified October 11, 2023
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 2:30 pm Lockett 233
Megan Fairchild, Louisiana State University
The Non-Oriented 4-Genus of Knots
The non-oriented 4-genus of a knot K in the three-sphere is defined to be the minimum first betti number of a surface F so that K bounds F. We will be discussing bounds on the non-oriented 4-genus given by knot invariants such as the signature and Arf invariant, as well as bounds given by unoriented band moves. We also will discuss obstructions to a knot bounding a Mobius band given by the double branched cover of the three-sphere branched over K.
Posted September 6, 2023
Last modified October 24, 2023
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 2:30 pm Lockett 233
Jake Murphy, LSU
Bestvina Brady Morse Theory and Virtually Fibered Right-Angled Coxeter Groups
A group G is said to virtually algebraically fiber if there exists a finite index subgroup H and an epimorphism from H into Z with a finitely generated kernel. One technique used to show a group is virtually algebraically fibered is Bestvina-Brady Morse theory. In this talk I will give a brief introduction to Bestvina-Brady Morse theory and present a result by Jankiewicz, Norin, and Wise which shows that certain right-angled Coxeter groups are virtually algebraically fibered.
Posted September 6, 2023
Last modified October 29, 2023
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 2:30 pm Lockett 233
Krishnendu Kar, Louisiana State University
Glimpses on Virtual Knots and Virtual Knot Group
Virtual Knots are knots drawn on thickened surfaces, first introduced by Louis Kauffman. Virtual knots extend the study of classical knots by allowing crossings to become "virtual," which means they don't have a physical overpass or underpass. Instead, they can cross over without any physical connection. We extend the notion of knot equivalence (Reidemeister moves) to these knots to classify them. To distinguish between two virtual knots, we use virtual knot invariants analogous to classical knot invariants. One such invariant is the virtual knot group introduced by Boden in 2015, extending the idea of Wirtinger presentation. In this seminar, we will explore the properties of this virtual knot group and see examples of how this virtual knot invariant is useful.
Posted September 6, 2023
Last modified November 3, 2023
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 2:30 pm Lockett 233
Amit Kumar, Louisiana State University
Graph coloring via defect TFTs
This is the first talk in a series of two talks. I will begin by introducing how certain problems in mathematics can be interpreted as a local to global problem. First of these is the graph coloring problem where it is still less non-trivial to see. Second is the word problem in group theory, which has to be formulated as a local to global problem. The theory of bordism with defects and the corresponding TFT provide a common ground for both the problems. Next, I will review the concepts of TFT and Extended TFT. Finally, I will discuss the category of 2-Bordism with defects and its TFT. We will see in the second talk that both these problems have been approached by forming a bordism category for a given (finite) group together with a presentation.
Posted September 6, 2023
Last modified November 13, 2023
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 2:30 pm Lockett 233
Amit Kumar, Louisiana State University
TFT with defects and applications
Even though this is the second talk in the series, the first talk is NOT a prerequisite. A QFT assigns a number to a closed n-manifold and a vector space to a codimension-1 submanifolds. An (1-)extended QFT assigns a number to a closed n-manifolds, a vector space to a codimension-1 submanifolds and a 1-category to a codimension 2 submanifolds. Defects arise when considering QFT with background fields, where it manifests itself as a stable singularity of certain functions (background fields.) On a physical level, defects allow existence of regions with different theories. A very good example of a defect is the phase-diagram of water: the three lines separates three phases each with its own (different) physics. We first formulate a TFT with defects as a field theory of manifolds with defects and then use these ideas to reformulate graph coloring problem and word problem.
Posted September 6, 2023
Last modified November 28, 2023
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm – 2:30 pm Lockett 233
Gurleen Nanda, Louisiana State University
Moduli space of local systems and higher Teichmüller theory
Let G be a split semisimple algebraic group over $\mathbb{Q}$ and S be a compact oriented surface with or without boundary. In this talk we will introduce the $\mathcal{L}_{G,S}$ moduli space of G($\mathbb{C}$)-local systems on S. When S has holes we define a dual pair of local systems $\mathcal{X}_{G,S}$, $\mathcal{A}_{G,S}$, both carry positive atlas equivariant with respect to the action of mapping class group. In the remainder of the talk we will use positive configurations of flags to construct co-ordinate system on $\mathcal{X}_{G,S}$.
Posted January 18, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pmOrganizational
Posted January 18, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233
Nilangshu Bhattacharyya, Louisiana State University
Characteristic Classes
Posted January 18, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233
Adithyan Pandikkadan, Louisiana State University
Characteristic Classes
Posted January 18, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233
Colton Sandvick, Louisiana State University
Characteristic Classes
Posted January 18, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233
Shea Vela-Vick, Louisiana State University
Characteristic Classes
Posted January 18, 2024
Last modified March 3, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233
Justin Murray, Louisiana State University
Singularities of Legendrian manifolds, isotopies, and applications to cellular contact homology.
In this talk, I will review the work of Arnold on singularities and caustics. Along the way, we will review when these 3-dimensional singularities give rise to 2-dimensional Legendrian isotopies and when they do not. After this, we will provide a complete list of base projections for these resolved singularities. This list will exclude various bifurcations of the base projection that are whose sheets are "far enough" apart. Time permitting, I will discuss how one can apply these to cellular Legendrian contact homology.
Posted January 18, 2024
Last modified April 2, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Jake Murphy, LSU
Incoherent Coxeter groups
A group is coherent if every finitely generated subgroup is also finitely presented. In this talk, we will cover results of Jankiewicz and Wise showing that many Coxeter groups are incoherent using Bestvina-Brady Morse theory.
Posted January 18, 2024
Last modified March 31, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233
Neal Stoltzfus, Mathematics Department, LSU
The Free Differential Calculus tool to study Braid Automorphisms
This talk will survey applications of the Jacobian and Hessian in the free differential calculus to the study of automorphisms in low dimensions, particularly braids. This is a central technical tool in my talk next Wed. We will develop the homology of covering spaces of surfaces with boundary (ribbon graphs), study braid automorphisms using the Jacobian of the Artin map image of a braid in the free differential calculus following Birman and Cohen-Suciu. The Burau representation will be developed (with the Lawrence-Krammer-Bigelow representation explored next week). The second part of the talk will cover (Lefschetz-Poincare) duality from the free differential calculus perspective using an analog of the Hessian.
Posted January 18, 2024
Last modified April 2, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Huong Vo, Louisiana State University
The Solomon-Tits theorem
The Solomon-Tits theorem states that a spherical Tits building over a field is homotopy equivalent to a wedge of spheres of the appropriate dimension. In this talk, we will go over some specific examples that show the theorem using PL Morse Theory.
Posted January 18, 2024
Last modified April 5, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Agniva Roy, Louisiana State University
Legendrian Rainbow Closures, Sheaf Moduli, and Grassmanians
Recent advancements in computing invariants of Legendrian knots in the 3-sphere, based on seminal work of Kashiwara-Schapira and continued by Shende- Treumann-Zaslow-Casals-Williams-Gao-Shen-Weng-Hughes-Gorsky-Gorsky-Simental and many others, have uncovered deep connections between contact and symplectic geometry and various properties of algebraic varieties. In this talk, I will try to explore the simplest examples of (k,n) torus links, and show how the sheaf moduli of these links give rise to Grassmanian varieties. Also, we will see how exact Lagrangian fillings give a geometric understanding of Plucker coordinates in the (2,n) case. The talk will focus largely on pictures and examples, with a view towards conveying the fascinating interplay of ideas that happens here.
Posted January 18, 2024
Last modified April 15, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Krishnendu Kar, Louisiana State University
An Introduction to ‘Spetra’cular category
We define higher homotopy groups of a topological space $X$ by taking homotopy classes of the maps from higher dimensional spheres. These higher-homotopy groups are exponentially more difficult to compute than homology or cohomology groups due to the failure of some robust computational tools such as excision. Excision holds for these groups up to connectivity, and so does the Mayer-Vietoris sequence. The suspension map $\Sigma:X\rightarrow \Sigma X$ induces a map on higher homotopy groups $\Sigma:\pi_n(X)\rightarrow \pi_{n+1}(\Sigma X)$. A theorem by Freudenthal states that after taking enough suspensions, these homotopy groups will stabilize eventually. We call the colimit of these homotopy groups as the stable homotopy group. In the modern treatment of stable homotopy theory, spaces are replaced by spectra. In this talk, we will see some important facts, examples, and, more importantly, justification for the title.
Posted January 18, 2024
Last modified April 22, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Megan Fairchild, Louisiana State University
The Double Branched Cover of the Three-Sphere Over a Knot.
In this talk, we will examine how the double branched cover of the three-sphere over a knot is constructed and the linking form defined on its first homology. We will discuss how to calculate first homology, defining the linking form, and calculating the linking form given a knot diagram. The main goal of the talk is to better understand this object and examine its connection to non-orientable 4-genus of knots.
Posted January 31, 2024
Last modified April 23, 2024
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm Lockett 233
Morgan Weiler, Cornell University
TBA