This Week in Mathematics


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Today:

Geometry and Topology [url]
Higher Segal spaces versus partial groups
- Philip Hackney, University of Louisiana
Time: 3:05
More Information
Abstract/Desc: This talk is about a new connection between the d-Segal spaces of Dyckerhoff and Kapranov and the partial groups of Chermak. The higher Segal conditions generalize the usual Segal condition for simplicial objects, and have applications in representation theory, K-theory, geometry, combinatorics, and elsewhere. Meanwhile, partial groups played a key role in Chermak's proof of the existence and uniqueness of centric linking systems for saturated fusion systems, a major recent result in p-local finite group theory. In this talk, I'll discuss the d-Segal conditions for simplicial spaces and introduce partial groups from the simplicial perspective. These are related via the degree of a partial group, which is the least positive integer k for which it is 2k-Segal. I'll give some examples of partial groups and their degrees, and a hint about the kinds of tools we've developed for these computations. This is all based on joint work with Justin Lynd.

Entries for this week: 5

Tuesday November 18, 2025

Geometry and Topology [url]
Higher Segal spaces versus partial groups
- Philip Hackney, University of Louisiana
Time: 3:05
More Information
Abstract/Desc: This talk is about a new connection between the d-Segal spaces of Dyckerhoff and Kapranov and the partial groups of Chermak. The higher Segal conditions generalize the usual Segal condition for simplicial objects, and have applications in representation theory, K-theory, geometry, combinatorics, and elsewhere. Meanwhile, partial groups played a key role in Chermak's proof of the existence and uniqueness of centric linking systems for saturated fusion systems, a major recent result in p-local finite group theory. In this talk, I'll discuss the d-Segal conditions for simplicial spaces and introduce partial groups from the simplicial perspective. These are related via the degree of a partial group, which is the least positive integer k for which it is 2k-Segal. I'll give some examples of partial groups and their degrees, and a hint about the kinds of tools we've developed for these computations. This is all based on joint work with Justin Lynd.

Wednesday November 19, 2025

Biomathematics Journal Club
Dynamic Cluster Field Modeling of Collective Chemotaxis
- Dana Hughes, FSU
Time: 5:00 Room: Dirac Library

Thursday November 20, 2025

Algebra seminar
Volume polynomials
- June Huh, Princeton
Time: 3:05pm Room: LOV 0231
Abstract/Desc: Volume polynomials form a distinguished class of log-concave polynomials exhibiting rich analytic and combinatorial structures, rooted in the geometry of convex bodies and projective varieties. In this talk, I will present an overview of volume polynomials, highlight their applications to the combinatorics of algebraic matroids, introduce a new class of analytic matroids, and discuss several open problems. (Based on joint work with Lukas Grund, Mateusz Michałek, Henrik Süss, and Botong Wang.)

Financial Math
Hungry Hungry HiPPOs: A Mathematical Breakdown of the Development of Deep State-Space Sequence Models
- Farez Siddiqui, Florida State University
Time: 3.05 Room: 105
Abstract/Desc: With the advent of attention heads and the subsequent transformer architecture in 2017, the field of natural language processing (as well as countless other fields) saw a boom in development. Despite its revolutionary impact, transformers have fallen short in time series analysis tasks when compared to more "traditional" models like LSTMs. However, LSTMs have been in development as far back as the 90's, and have been shown to struggle in capturing long-term dependencies. These models also are difficult to parallelize due to their recurrent/sequential nature. Surely something better must have come along by now? Within the past decade, a new family of models has seen great strides made that poses a promising alternative to not only recurrent neural networks like LSTMs, but convolutional neural networks and transformers as well! These models are known as Deep State-Space Models (SSMs) (e.g. Mamba) But the classical theory of state-space models (specifically linear time-invariant state-space equations) has been thoroughly studied since the 60's... what's new about these deep SSMs? Why is such a well-studied framework only NOW being considered as a such a strong contender to the transformer? The aim of this week's seminar is to take the attendees on a sufficiently thorough journey through the development of deep SSMs over the past 5 years. This will include the problems with recurrent neural networks they were initially trying to solve, and through most of the clever (and beautiful) iterations that came afterwards up to the seminal S4 and S5 models that gave way to Mamba. If you have every felt overwhelmed trying to dip your toes into the deep state-space model literature by the mathematical underpinnings, this talk is for you.

Friday November 21, 2025

Data Science and Machine Learning Seminar
Persistent Model of the Second Configuration Space of Metric Star Graphs
- Wenwen Li, FSU Mathematics
Time: 1:20pm Room: Love 106
Abstract/Desc: Abstract: In this talk, I will provide a brief introduction to the second configuration space of a metric graph $X$, denoted by $X_{r,L}^2$, with the restraint parameter $r$ and edge length vector $\mathbf{L}=(L, L_2, \dots, L_k)$, where $L_2, \dots, L_k$ are arbitrary but fixed positive real numbers. As the parameters r and L vary, these spaces form a natural bifiltration (denoted by $X_{-,-}^2$) that captures the evolution of topological features across two scales. In previous work, we showed that $PH_i(X_{-,-}^2; \mathbb{F})$ is isomorphic to a tame 2-parameter persistence module $N$, i.e., the restriction of $N$ to each chamber of the parameter space is a constant functor for all $i\geq 0$. Next I will specialize to $X=\mathsf{Star}_k$ (the star graph with $k$ edges) and present joint work with Murad \"Ozayd\i n on $2$-parameter persistence modules $PH_{i}((\mathsf{Star}_k)^2_{-,-};\mathbb{F})$. In this project, we investigate the indecomposable direct summands of these $2$-parameter persistence modules. We construct a bipartite weighted graph $(G_k)_{\mathbf{L}}$ with fixed edge length vector $\mathbf{L} \in (\mathbb{R}_{>0})^k$ and define filtering functions on its vertices and edges to obtain a natural filtration (denoted by $(G_k)_{-,\mathbf{L}}$). We show that the filtration $(G_k)_{-,\mathbf{L}}$ is compatible with $\mathbf{L}$ up to homotopy, hence obtain a multifiltration $(G_k)_{-,-}$ (in the homotopy category). We refer to $(G_k)_{-,\mathbf{-}}$ as the \textit{persistent bipartite model} of $(\mathsf{Star}_k)^2_{-,-}$. This construction yields an isomorphism between the associated $(k+1)$-parameter persistence modules $PH_i((\mathsf{Star}_k)^2_{-,-}; \mathbb{F}) \cong PH_i((G_k)_{-,-}; \mathbb{F})$. By leveraging the persistent bipartite model with edge length vector $\mathbf{L}=(L,L_2,\dots, L_k)$ where $L_2, \dots, L_k$ are arbitrary but fixed positive real numbers, we prove that the 2-parameter persistence module $PH_1((\mathsf{Star}_k)^2_{-,-};\mathbb{F})$ is interval-decomposable for all $k\geq 3$. (While $PH_0((\mathsf{Star}_k)^2_{-,-};\mathbb{F})$ is not interval-decomposable for all $k\geq 3$.) Furthermore, our analysis provides an explicit description of all indecomposable direct summands of $PH_1((\mathsf{Star}_k)^2_{-,-};\mathbb{F})$, up to isomorphism.

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This Week in Mathematics