This Week in Mathematics


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Entries for this week: 8

Monday November 03, 2025

Financial Math ATE/Candidacy Exam
High-Dimensional Covariance Estimation and Eigenstructure Inference
- Navid Bahadoran, FSU
Time: 3:30pm Room: LOV 204-A

Tuesday November 04, 2025

Applied and Computational Math seminar
Symmetrization and Isoperimetric Problems under Anisotropic Gaussian Measures
- Kuan Ting Yeh, Purdue
Time: 3:05 Room: LOV306
Abstract/Desc: Isoperimetric inequalities play a fundamental role in various areas such as analysis, probability, geometry, and even in data analysis. Among the many tools used to study isoperimetric problems, symmetrization method provides a powerful geometric approach. In this talk, we highlight how isoperimetric inequalities bridge several fields and present recent results on symmetrization and isoperimetric problems under anisotropic Gaussian measures.

Geometry and Topology [url]
Partially hyperbolic diffeomorphisms and ergodicity in dimension 3
- Sergio Fenley, FSU
Time: 3:05 Room: 231
More Information
Abstract/Desc: Partially hyperbolic diffeomorhisms (PH) are maps which have 3 invariant bundles which are contracting, expanding, or in between. This talk will be on PH in dimension 3. They are very important because they are essentially the only ones that can be robustly transitive and stably ergodic. We will discuss the structure of such diffeomorhisms, and also the ergodicity conjecture for such systems in dimension 3.

Thursday November 06, 2025

Financial Math
Weak OT, Stochastic Orders and Bermudan Contracts
- Dominykas Norgilas, North Carolina State University
Time: 3.05 Room: 105
Abstract/Desc: We investigate the maximal possible price of a Bermudan option consistent with a given set of liquid vanilla option prices. This question is formulated as a weak optimal transport problem, which we solve completely in a two-period setting under general convex payoffs and a set of structural yet natural assumptions on the marginal distributions. A surprising phenomenon emerges: it is insufficient to work with the canonical filtration alone, additional randomization is required, even when the marginals are absolutely continuous. Finally, our analysis suggests a natural pathway for extending the framework to multi-period settings

Algebra seminar
Global p-Curvatures of Linear Recurrence Operators
- Marcus Lawson, FSU
Time: 3:05pm Room: LOV 0231
Abstract/Desc: Linear Recurrence Operators appear as objects of interest in the study differential equations, number theory and a variety of other areas. One property that we may look at is the p-curvature. If for all but finitely many primes, the characteristic polynomial of the p-curvature of an operator is the image of some fixed polynomial over Q, then we say that our operator has a global p-curvature. It would appear that many linear recurrences appearing in the OEIS (Online Encyclopedia of Integer Sequences) have a global p-Curvature. The purpose of this study is to find necessary and sufficient criteria for an operator to have a global p-Curvature. Along the way, we will explore examples which outline proofs needed to determine their global p-curvatures.

Friday November 07, 2025

Ph.D. thesis defense
An Uncertainty Quantification and Reduction Framework for Machine Learning
- Ryan Bausback, Florida State University
Time: 12:50pm Room: LOV204A
Abstract/Desc: Artificial intelligence is becoming more important in everyday life, requiring vast amounts of data with which to train new models. However, data in the wild is frequently obscured by noise, so quantifying the level of uncertainty present is of paramount importance. In this dissertation, we present novel approaches to uncertainty quantification in operator learning, with applications to machine learning in general. Our Stochastic Operator Network (SON) method leverages the Stochastic Neural Network (SNN), which utilizes the Stochastic Maximum Principle (SMP) from stochastic optimal control, in conjunction with the Universal Approximation Theorem for Operators realized in the DeepONet. The novel SON therefore maps from a space of functions into another noisy space of functions, allowing it to replicate the output of systems closer to SDEs than previous works. Its performance is demonstrated on noisy operators in both two and three dimensions. In the traditional operator learning framework, predictions are time independent, but in many contexts this is not the case. Therefore, we also reformulate operator learning as a sequential, forward-simulation problem, where a sequence of curves is pushed forward in time, representing the state of a dynamical system. This allows the Ensemble Score Filter (EnSF) to be employed when tracking the state in the output domain, resulting in more stable and accurate predictions than traditional filtering methods across many training and observation scenarios.

Data Science and Machine Learning Seminar
Academic Job Market Discussion
- Rocío Díaz Martín (FSU), Ali Kara (FSU), Zhe Su (Auburn), Zezhong Zhang (Auburn), FSU and Auburn
Time: 1:20pm Room: Love 106
Abstract/Desc: This week's seminar will be a panel discussion with recently hired tenure track faculty from FSU and Auburn. The speakers from Auburn are FSU alumni. This will be an informal discussion that should be especially beneficial to graduate students who are preparing to enter the job market. Please bring questions for the panelists!

Mathematics Colloquium [url]
Alumni Colloquium
- Zhe Su and Zezhong Zhang, Auburn
Time: 3:05 Room: Lov 101
Abstract/Desc: Zhe Su Title: Topological data analysis on manifolds via de Rham-Hodge Theory Abstract: Topological data analysis (TDA) provides powerful tools for understanding the structure of complex, high-dimensional data, yet most existing methods focus on points, graphs, or simplicial complexes. In this talk, I will present our recently developed de Rham-Hodge-based frameworks for analyzing data on manifolds. These methods provide effective and efficient ways to capture both the topological and geometric information of data and are well-suited for integration with machine learning tasks. I will also demonstrate their usefulness through applications in mathematical biology, including protein-ligand binding affinity prediction, single-cell RNA velocity analysis, medical image classification, and B-factor analysis. Zezhong Zhang Title: Generative AI for Data Assimilation Abstract: Generative AI models, especially diffusion models, are transforming how we approach high-dimensional nonlinear filtering and data assimilation. In this talk, I will introduce our recently developed class of score-based filtering framework that leverage diffusion models to represent and evolve complex posterior densities, achieving both high dimensionality and nonlinearity. Traditional methods store distributional information either in the form of the mean and covariance under Gaussian assumptions or as finite Monte Carlo ensembles. In contrast, our approach stores information in a score function rather than discrete samples, effectively overcoming the weight degeneracy issues that limit the particle-based filters and the poor performance of Kalman-based filters under nonlinear systems. I will also highlight the Ensemble Score Filter (EnSF), which employs a training-free score estimation scheme to make the method highly efficient and scalable, capable of effectively tracking chaotic systems with millions of dimensions. Through benchmark studies on Lorenz systems, I will demonstrate how generative AI can fundamentally enhance uncertainty quantification and scalability in modern data assimilation.

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This Week in Mathematics