This Week in Mathematics


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Entries for this week: 6

Tuesday December 02, 2025

Geometry and Topology [url]
A Menger Redux: Embedding Metric Spaces Isometrically in Euclidean Space (Joint with J. Bowers)
- Phil Bowers, FSU
Time: 3:05 Room: 231
More Information
Abstract/Desc: A standard tool in metric geometry is Menger's 1928 result that characterizes those abstract metric spaces that admit an isometric embedding into the n-dimensional Euclidean space. Menger's proof was rather abstract as he translated the embedability problem into abstarct logic and gave a rather opaque explanation of his result. In 2015, J. Bowers and I revisited Manger's characterization and produced an elementary geometric proof that offered insight into its tightness. In this talk, I will review Menger's result and give a beautiful characterization of those spaces that nearly, but do not quite embed isometrically. Time permitting, I will describe our recent extension of Menger's result to the realization of point sets in Minkowski space and use this to get Menger-type embedabilty theorems for point and hyperplane sets in hyperbolic space, disks sets in the sphere, and point sets in de Sitter space.

Wednesday December 03, 2025

Biomath lab meetings
A Porifera Pair: A Differential Model of a Sponge Mutualism
- John King, FSU
Time: 5:30 Room: LOV105
Abstract/Desc: It has been well known the importance of heterospecific associations between sponges in tropical waters. What is not entirely known is the stability of these systems and how sponge-hazard specialization has evolved. I will present a model that simulates two sponge species populations and their ability to mutually associate. After describing results from this model, I expand the model to include system evolution.

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

Thursday December 04, 2025

Algebra seminar
TBA
- Arash Karimi, FSU
Time: 3:05pm Room: LOV 0231
Abstract/Desc: TBA

Financial Math
Limit Order Book Simulation: A Review and Recent Progress
- Ahmer Nadeem Khan, Florida State University
Time: 3.05 Room: 105
Abstract/Desc: Limit Order Books (LOBs) are the mechanism used by most electronic trading venues across major asset classes to match buyers and sellers. Forecasting and simulating the dynamics of the LOB is crucial to many financial applications, e.g. high frequency trading, optimal execution, statistical arbitrage, and market making. A range of modeling approaches have been developed in the literature, including point processes, agent-based models, stochastic differential equations, and deep learning. I will present an overview of the statistical properties of the order book, modeling challenges e.g. market impact awareness, and a comparative review of the various modeling methods. In particular, I will discuss recent success of the recently popular autoregressive generative models (Nagy et al.) on order book message data to simulate order flow, which tokenize the LOB messages and use sequences of tokens like a Large Language Model (LLM) would use words in a language.

Friday December 05, 2025

Mathematics Colloquium [url]
Gradient flows and interacting particle dynamics for sampling in high dimensions
- Dejan Slepcev, CMU
Time: 3:05 Room: Lov 101
Abstract/Desc: Providing samples of a measure given by its density is a challenging problem, especially in high dimensions. We will first describe standard approaches based on Markov chains whose invariant measure is the desired target measure, and highlight the difficulties. At the mean-field level the distributions of particles in these processes are governed by evolution equations. In particular, the Fokker–Planck equation, the gradient flow of Kullback-Leibler (KL) divergence in Wasserstein geometry, corresponds to Langevin Monte Carlo sampling. We will consider several gradient flows of KL-divergence for sampling based on different geometries on the spaces of probability measures, including the gradient flows with respect to Stein geometry and a new, Radon-Wasserstein, geometry. In addition to discussing foundational questions regarding the flows and their asymptotic properties, we will describe the discretizations used and focus on interacting particle systems. Particular attention will be given to methods that are applicable in high dimensions. The talk is based on joint works with Lantian Xu and Elias Hess-Childs.

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This Week in Mathematics