Calendar
Posted February 3, 2025
Last modified April 22, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm
Nilangshu Bhattacharyya, Louisiana State University
Proof of h-cobordism, Whitney trick and issues in the 4 dimension.
In this presentation, I will begin by recapping the complete proof of the h-cobordism theorem, which states that in dimensions greater than four, a homotopically trivial, simply connected cobordism between two simply connected compact manifolds is smoothly trivial. As a corollary, this implies the higher-dimensional Poincaré conjecture. A central tool in the proof is the Whitney trick, which is effective in higher dimensions. However, in dimension four, a framing obstruction naturally arises, presenting significant challenges. In the latter part of the presentation, I will discuss some of the technical aspects and difficulties associated with applying the Whitney trick.
Posted May 14, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:00 pm Lockett 233Organizational Meeting
We will pick a topic/book to follow and decide days and times for the Summer Informal Geometry and Topology Seminar. Here is a link to join by Zoom. https://lsu.zoom.us/j/98838338874?pwd=dlBYTVJ0WmdlaU0yall3SXVONHNhUT09
Posted May 15, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:00 pm Lockett Hall 233
Krishnendu Kar, Louisiana State University
TBD
TBD
Posted May 15, 2025
Last modified June 3, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:00 pm Lockett Hall 233
Sayani Mukherjee, Louisiana State University
Continuing our Discussion on K-Theory
We are following Inna Zakharevich's notes on K-theory and Characteristic Classes.
Posted May 15, 2025
Last modified June 3, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:00 pm Lockett Hall 233
Evan Short, Louisiana State University
Continuing our Discussion on K-Theory
We are following Inna Zakharevich's notes on K-theory and Characteristic Classes.
Posted May 15, 2025
Last modified June 10, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:00 pm Lockett Hall 233
Matthew Lemoine, Louisiana State University
Continuing our Discussion on K-Theory
We are following Inna Zakharevich's book on K-theory and Characteristic Classes. Link to book: https://pi.math.cornell.edu/~zakh/book.pdf
Posted May 15, 2025
Last modified June 12, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:00 pm Lockett Hall 233
Krishnendu Kar, Louisiana State University
Continuing our Discussion on K-Theory
We are following Inna Zakharevich's book on K-theory and Characteristic Classes. Link to book: https://pi.math.cornell.edu/~zakh/book.pdf
Posted May 15, 2025
Last modified June 15, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:00 pm Lockett Hall 233
Gargi Patil, Louisiana State University
Continuing our Discussion on K-Theory
We are following Inna Zakharevich's book on K-theory and Characteristic Classes. Link to book: https://pi.math.cornell.edu/~zakh/book.pdf
Posted May 15, 2025
Last modified June 20, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:00 pm Lockett Hall 233
Anurakti Gupta, Louisiana State University
Continuing our Discussion on K-Theory
We are following Inna Zakharevich's book on K-theory and Characteristic Classes. Link to book: https://pi.math.cornell.edu/~zakh/book.pdf
Posted May 15, 2025
Last modified June 20, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:00 pm Lockett Hall 233
Nilangshu Bhattacharyya, Louisiana State University
Continuing our Discussion on K-Theory
We are following Inna Zakharevich's book on K-theory and Characteristic Classes. Link to book: https://pi.math.cornell.edu/~zakh/book.pdf
Posted May 15, 2025
Last modified June 23, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:00 pm Lockett Hall 233
Sayani Mukherjee, Louisiana State University
Continuing our Discussion on K-Theory
We are following Inna Zakharevich's book on K-theory and Characteristic Classes. Link to book: https://pi.math.cornell.edu/~zakh/book.pdf
Posted May 15, 2025
Last modified June 27, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:00 pm Lockett Hall 233
Benjamin Appiah, Louisiana State University
Knot invariant and the Reidemeister theorem.
In this talk, I will provide a brief introduction of knot theory and the concept of knot invariant. Then explore the concept of Reidemeister moves as well as the Reidemeister theorem. For clarity, some specific examples will be provided where necessary.
Posted May 15, 2025
Last modified June 23, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:00 pm Lockett Hall 233
Evan Short, Louisiana State University
Continuing our Discussion on K-Theory
We are following Inna Zakharevich's book on K-theory and Characteristic Classes. Link to book: https://pi.math.cornell.edu/~zakh/book.pdf
Posted May 15, 2025
Last modified June 23, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:00 pm Lockett Hall 233
Matthew Lemoine, Louisiana State University
Continuing our Discussion on K-Theory
We are following Inna Zakharevich's book on K-theory and Characteristic Classes. Link to book: https://pi.math.cornell.edu/~zakh/book.pdf
Posted May 15, 2025
Last modified July 6, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:00 pm Lockett Hall 233
Emmanuel Astante, Louisiana State University
TBD
Posted May 15, 2025
Last modified July 8, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:00 pm Lockett Hall 233
Gargi Patil, Louisiana State University
Continuing our Discussion on K-Theory
We are following Inna Zakharevich's book on K-theory and Characteristic Classes. Link to book: https://pi.math.cornell.edu/~zakh/book.pdf
Posted May 15, 2025
Last modified July 2, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:00 pm Lockett Hall 233
Anurakti Gupta, Louisiana State University
Continuing our Discussion on K-Theory
We are following Inna Zakharevich's book on K-theory and Characteristic Classes. Link to book: https://pi.math.cornell.edu/~zakh/book.pdf
Posted May 15, 2025
Last modified July 21, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:00 pm Lockett Hall 233
Nilangshu Bhattacharyya, Louisiana State University
Categorification of colored Jones polynomial
Given an oriented framed link L whose components are colored by integer $n$ corresponding to the $(n+1)$-dimensional irreducible representation of $U_q(sl_2)$, the colored Jones polynomial $J_n(L)$ takes values in $\mathbb{Z}[q,q^-1]$. In this talk, we will describe Khovanov's categorification of the colored Jones polynomial.
Posted May 15, 2025
Last modified July 2, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:00 pm Lockett Hall 233
Matthew Lemoine, Louisiana State University
Continuing our Discussion on K-Theory
We are following Inna Zakharevich's book on K-theory and Characteristic Classes. Link to book: https://pi.math.cornell.edu/~zakh/book.pdf
Posted May 15, 2025
Last modified July 2, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:00 pm Lockett Hall 233
Sayani Mukherjee, Louisiana State University
Continuing our Discussion on K-Theory
We are following Inna Zakharevich's book on K-theory and Characteristic Classes. Link to book: https://pi.math.cornell.edu/~zakh/book.pdf
Posted May 15, 2025
Last modified August 1, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:00 pm Lockett Hall 233
Krishnendu Kar, Louisiana State University
Continuing our Discussion on K-Theory
We are following Inna Zakharevich's book on K-theory and Characteristic Classes. Link to book: https://pi.math.cornell.edu/~zakh/book.pdf
Posted May 15, 2025
Last modified August 1, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:00 pm Lockett Hall 233
Krishnendu Kar, Louisiana State University
Continuing our Discussion on K-Theory
We are wrapping up our discussion of Inna Zakharevich's book on K-theory and Characteristic Classes. Link to book: https://pi.math.cornell.edu/~zakh/book.pdf
Posted July 21, 2025
Last modified August 17, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Krishnendu Kar, Louisiana State University
Matthew Lemoine, Louisiana State University
Organizational Meeting
Please join us for the Informal Geometry and Topology Seminar. This seminar is an opportunity for grad students to get experience talking in front of an audience and practicing giving talks. In this first meeting, we will decide which topic/book/paper that we will follow for our discussion during the Fall semester. We will also have opportunities for individual talks. For more information, feel free to contact Matthew Lemoine or Krishnendu Kar.
Posted August 27, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Rachel Meyers, Louisiana State University
TBD
TBD
Posted August 27, 2025
Last modified September 10, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Sayani Mukherjee, Louisiana State University
Khovanov Homology
Continuing our discussion of Khovanov Homology, follow Melissa Zhang's notes.
Posted August 27, 2025
Last modified September 14, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Anurakti Gupta, Louisiana State University
Continuing our Discussion of Khovanov Homology
We are continuing our discussion of Khovanov Homology following Melissa Zhang's notes. (https://arxiv.org/abs/2501.03115)
Posted August 27, 2025
Last modified September 21, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Gargi Patil, Louisiana State University
Continuing our discussion of Khovanov Homology
We are continuing our discussion of Khovanov Homology following Melissa Zhang's notes. (https://arxiv.org/pdf/2501.03115)
Posted August 27, 2025
Last modified September 29, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Saumya Jain, Louisiana State University
Manifold models for hyperbolic graph braid groups
Given a finite graph X, the associated graph braid group B_n(X) is the fundamental group of the unordered n-point configuration space of X. For the 3-point case, Genevois classified which graph braid groups are Gromov hyperbolic and asked the question: When do these groups arise as 3-manifold groups? In this talk, we give a partial answer for B_3(X) when X is a generalized Theta graph.
Posted September 29, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:55 pm Lockett Hall 233
Yongho Lee, Louisiana State University
A representation of the holonomy Lie algebra of a matroid
Let $\mathcal{M}$ be a simple matroid for which the cardinality of each rank-two flat is at most 3. For any such matroid $\mathcal{M}$, we produce a representation of the holonomy Lie algebra of $\mathcal{M}$ using the combinatorial Laplacian.
Posted August 27, 2025
Last modified October 4, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Krishnendu Kar, Louisiana State University
Khovanov Homology
Continuing our discussion of Khovanov Homology following Melissa Zhang's notes.
Posted August 27, 2025
Last modified October 15, 2025
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm Lockett Hall 233
Adithyan Pandikkadan, Louisiana State University
Khovanov Homology
Continuing our discussion of Khovanov Homology, follow Melissa Zhang's notes.
Posted August 27, 2025
Last modified October 22, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Remi Mandal, Louisiana State University
Khovanov Homology
Continuing our discussion of Khovanov Homology following Melissa Zhang's notes.
Posted August 27, 2025
Last modified October 27, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Nilangshu Bhattacharyya, Louisiana State University
Khovanov Homology
Continuing our discussion of Khovanov Homology following Melissa Zhang's notes.
Posted August 27, 2025
Last modified October 27, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Evan Short, Louisiana State University
Khovanov Homology
Continuing our discussion of Khovanov Homology following Melissa Zhang's notes.
Posted August 27, 2025
Last modified October 27, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Matthew Lemoine, Louisiana State University
Topological Data Analysis of Mortality Patterns During the COVID-19 Pandemic (joint work with Megan Fairchild)
This talk will be a brief overview of Topological Data Analysis and will go into some of the work that Megan and I have done. Topological Data Analysis is a relatively new field of study that uses topological invariants to study the shape of data. We analyze a dataset provided by the Centers for Disease Control and Prevention (CDC) using persistent homology and MAPPER. This dataset tracks mortality week-to-week from January 2020 to September 2023 in the United States during the COVID-19 pandemic. We examine the dataset as a whole and break the United States into geographic regions to analyze the overall shape of the data. Then, to explain this shape, we discuss events around the time of the pandemic and how they contribute to the observed patterns.
Posted August 27, 2025
Last modified November 17, 2025
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm Lockett Hall 233
Nilangshu Bhattacharyya, Louisiana State University
Khovanov Homology
Continuing our discussion of Khovanov Homology following Melissa Zhang's notes.
Posted August 27, 2025
Last modified November 24, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Huong Vo, Louisiana State University
Incoherence of free-by-free groups
A group is incoherent if it has a finitely generated subgroup that is not finitely presented. In this talk, we'll look at how an amalgamated product construction and a homological condition called excessive homology show incoherence of many free-by-free groups.
Posted August 27, 2025
Last modified November 26, 2025
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm Lockett Hall 233
Krishnendu Kar, Louisiana State University
Khovanov Homology
Wrapping up our discussion on Khovanov Homology from this semester.
Posted November 24, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Krishnendu Kar, Louisiana State University
Matthew Lemoine, Louisiana State University
Organizational Meeting
Join us for the first meeting of the Spring Semester 2026 Informal Geometry and Topology Seminar to decide which topic we will follow. The Informal Geometry and Topology Seminar is an opportunity for graduate students to get experience presenting information that they learn or have learned. We normally have a topic, paper, book, or subject that we follow and take turns presenting the information we learn, or giving independent talks about our own research. If you have any questions or would like to be added to the email list, please feel free to email Matthew Lemoine (mlemo36@lsu.edu) or Krishnendu Kar (kkar2@lsu.edu).
Posted January 15, 2026
Last modified January 20, 2026
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett Hall 233
Nilangshu Bhattacharyya, Louisiana State University
From Khovanov homology to its stable homotopy refinement
Khovanov homology assigns a knot or a link to a bigraded homology theory that categorifies the Jones polynomial. It has concrete applications, for instance Rasmussen’s $s$-invariant, extracted from Lee’s deformation, which gives a lower bound on the smooth slice genus. At the same time, while the theory is very combinatorial and closely tied to the representation theory of $U_q(\mathfrak{sl}_2)$, it can be hard to see the underlying geometric picture directly from the homology groups. The stable homotopy refinement, introduced by Lipshitz and Sarkar, upgrades Khovanov homology to a space level invariant: a spectrum whose cohomology recovers Khovanov homology while supporting additional structure that is invisible in homology. In this talk, I will start with the construction of Khovanov homology and then gradually move toward its stable homotopy refinement. My work uses this viewpoint to build and study stable homotopy types beyond classical links, including planar trivalent graphs with perfect matchings, and to connect these refinements with themes from contact geometry and Floer theoretic settings.
Posted January 15, 2026
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm – 4:30 pm 233 Lockett HallTo Be Filled In
Posted January 15, 2026
Last modified February 4, 2026
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett Hall 233
Matthew Lemoine, Louisiana State University
Sliding Window Embedding
When we are looking at a dataset that has a time-dependency and is periodic (or quasi-periodic), we are interested in noticing differences in the period. Using sliding window embeddings (also known as time-delay reconstructions), we can look at the periods of a given dataset and analyze the persistent homology to detect changes in our periods. In this talk, we will be discussing the foundational paper in this area of Topological Data Analysis by Jose Perea and John Harer (arxiv:1307.6188).
Posted February 4, 2026
Last modified February 5, 2026
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm Lockett Hall 233
Justin Lanier, Louisiana State University
Every Surface is a Leaf
We'll start by discussing the fact that every closed 3-manifold admits foliations, where the leaves are surfaces. This fact raises the question: for a given closed 3-manifold, which surfaces can appear as leaves of some foliation of that 3-manifold? Kerékjártó and Richards gave a classification up to homeomorphism of noncompact surfaces, which includes surfaces with infinite genus or infinitely many punctures. In their 1985 paper "Every surface is a leaf", Cantwell–Conlon prove a universality theorem: for every closed 3-manifold M and every orientable noncompact surface L, M has a foliation where L appears as a leaf. We will discuss their paper and the surrounding context.
Posted January 15, 2026
Last modified February 20, 2026
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett Hall 233
Hailey Garcia, Louisiana State University
The Cohomology of the Complement of Hyperplane Arrangements
We consider linear hyperplane arrangements 𝓐 in V=ℂ^n. Of interest is the complement of the arrangement M(𝓐)=M(𝓐)=V\(∪_{H_i∈𝓐}H_i). We will demonstrate the definition and some properties of the Orlik-Solomon algebra A(𝓐) of 𝓐. Then, by considering the deletion-restriction triple (𝓐',𝓐,𝓐''), we demonstrate that the cohomology ring of M(𝓐) is isomorphic to A(𝓐) and hence determined by the combinatorics of the intersection lattice L(𝓐).
Posted January 15, 2026
Last modified February 27, 2026
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett Hall 233
Benjamin Appiah, Louisiana State University
An example of color evaluation in graphene diagrams.
In this talk, I will explore the concept of decorated ribbon graphs, graphene diagrams, and virtual links. Then introduce a novel coloring technique called color evaluation. I will conclude by discussing an example of how this color evaluation is invariant in virtual link, knot, and graphene diagrams.
Posted January 15, 2026
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett Hall 233
Sayani Mukherjee, Louisiana State University
TBD
TBD
Posted January 15, 2026
Last modified March 23, 2026
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett Hall 233
Saumya Jain, Louisiana State University
Right-angled Mock Reflection Groups
Right-angled Coxeter groups (RACGs) and certain groups arising from blow-ups act isometrically on CAT(0) cube complexes in a reflection-like manner. Right-angled mock reflection groups (RAMRGs) generalize this class of groups. In this talk, I will introduce RAMRGs and explain how their group structure can be encoded combinatorially using graphs with additional local data. We will also discuss examples and see a characterization of all finite RAMRGs.
Posted January 15, 2026
Last modified March 30, 2026
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett Hall 233
Krishnendu Kar, Louisiana State University
An odd Khovanov stable homotopy type
Khovanov homology admits two integral variants: the original (“even”) theory and the Ozsváth–Rasmussen–Szabó (“odd”) refinement. While both categorify the Jones polynomial and agree over \mathbb{F}_2, their algebraic structures differ in subtle ways. In this talk, I will survey homotopy-theoretic refinements of Khovanov homology, focusing on the Lipshitz–Sarkar stable homotopy type and its odd analogue. I will explain how these spectra are constructed from Burnside categories and homotopy colimits, compare key structural features of the even and odd theories, and discuss their relationship.
Posted January 15, 2026
Last modified April 7, 2026
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett Hall 233
Nilangshu Bhattacharyya, Louisiana State University
Spanning tree complex and Khovanov homology
This talk will give an introduction to the spanning tree model for Khovanov homology. Starting from a knot or link diagram, one can associate a planar graph by checkerboard coloring, and the spanning trees of this graph turn out to capture an important part of the structure of the Khovanov complex. I will explain how this viewpoint leads to a simpler complex generated by spanning trees, why it is natural from the perspective of the Jones polynomial, and how it helps illuminate the combinatorial structure underlying Khovanov homology. The emphasis will be on the main ideas and examples, with the goal of making the spanning tree complex accessible to a broad audience.
Posted January 15, 2026
Last modified April 12, 2026
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett Hall 233
Anurakti Gupta, Louisiana State University
Transverse knots distinguished by Knot Floer Homology
I will discuss a paper by Lenhard Ng, Peter Ozsváth, and Dylan Thurston, in which they use knot Floer homology to distinguish transverse knots. In particular, they show that transverse knots with the same self-linking number need not be transversely isotopic. I will describe the invariant using the combinatorial construction of knot Floer homology with coefficients in F_2.
Posted January 15, 2026
Last modified April 20, 2026
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett Hall 233
Fabian Espinoza de Osambela, Louisiana State University
Frobenius Algebra Sheaves and TQFTs over Algebraic Curves
Two-dimensional topological quantum field theories (TQFTs) over a commutative ring are classified by commutative Frobenius algebras. In joint work, we constructed explicit rank-two Frobenius algebras over Dedekind domains whose module structure is governed by the class group, revealing new arithmetic constraints in the theory. In this talk, I will present a geometric reinterpretation of these constructions in terms of Frobenius algebra sheaves over algebraic curves. First, I will introduce the construction for affine curves. Then I will provide descent data that allows the extension to any abstract algebraic curve. This perspective leads to new global phenomena: for elliptic curves, geometric constraints force the vanishing of certain trace components in the untwisted setting. If time permits, I will explain how this obstruction can be resolved by introducing twisted Frobenius structures, in which the trace takes values in a line bundle, and illustrate the resulting theory through explicit examples. Finally, I will describe a natural extension to Cl(O)-graded TQFTs, which removes the order-two restriction and suggests a Picard-graded, geometrically dependent class of theories. This framework is still under development, but the examples indicate a rich interaction between arithmetic, geometry, and TQFT.
Posted January 15, 2026
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett Hall 233
Huong Vo, Louisiana State University
TBD
TBD