This Week in Mathematics

Department of Mathematics

This Week in Mathematics


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Current Week [Feb 01, 2026 - Feb 07, 2026]

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Entries for this week: 9

Monday February 02, 2026

Stochastic Computing and Optimization
Foundations of Data Assimilation: From Kalman Filtering to Score-Based Ensemble Methods.
- Kadesha Reynolds, Florida State University
Time: 3:05pm Room: 232
Abstract/Desc: This talk introduces the Ensemble Score Filter (EnSF), a score-based ensemble method for data assimilation in nonlinear dynamical systems. Standard approaches, such as the Kalman Filter and Ensemble Kalman Filter (EnKF), rely on Gaussian assumptions that can limit performance when system dynamics are strongly nonlinear. EnSF provides an alternative perspective by representing information through score functions estimated directly from ensembles, avoiding explicit covariance construction. The presentation outlines the core ideas behind ensemble-based filtering, the formulation of EnSF, and its relationship to existing methods.

Tuesday February 03, 2026

Applied and Computational Mathematics [url]
Graduate Research Seminar: PhD Candidates Defense Preview
- Yi-Yung Yang, Sanjeeb Poudel, Ruth Lopez,
Time: 3:05 Room: 231
Abstract/Desc: Three Ph.D. candidates defending this semester will present previews of their defenses.

Rognes’ connectivity conjecture
- Jeremy Miller, Purdue University
Time: 3:05PM Room: Zoom
Abstract/Desc: Rognes’ connectivity conjecture concerns the connectivity of a simplicial complex called the common basis complex. Rognes proved that the equivariant homology of this complex is the E^1 page of a spectral sequence converging to the homology of the algebraic K-theory spectra. I will describe joint work with Patzt and Wilson where we prove the connectivity conjecture for fields. I will explain a connection between the homology the common basis complex and the André–Quillen homology of a certain equivariant ring built out of Steinberg modules. Time permitting, I will mention variants of these results for symplectic groups (joint with Scalamadre and Sroka) and automorphism groups of free groups (joint with Bruck and Piterman).

Wednesday February 04, 2026

Biomath Seminar
Topological Data Analysis for Research in Biomathematics
- Cagatay Ayhan, FSU Mathematics
Time: 3:05 Room: Love 232
Abstract/Desc: opological Data Analysis (TDA) provides tools from applied algebraic topology to extract meaningful information from the “shape” of data. One of the most widely used tools in TDA is persistent homology (PH), which assigns a topological descriptor to data and uses this descriptor as a summary representation. Applications of persistent homology are wide-ranging, from breast cancer detection to the analysis of weather phenomena. The field remains highly active, with ongoing research focused on refining PH techniques and adapting them to specific scientific settings. In this expository talk, I will begin with an introduction to PH and present several canonical examples. I will then highlight applications, with an emphasis on problems in biomathematics. In particular, I will introduce our recent preprint:https://arxiv.org/abs/2512.08637 “A Persistent Homology Pipeline for the Analysis of Neural Spike Train Data” which is joint work with a team here at FSU. I will discuss this pipeline in detail and conclude by outlining potential directions and research opportunities for future work in TDA.

Biomathematics Journal Club
Collective Dynamics of Small-World Networks
- David Wharton, FSU
Time: 5:00 Room: Dirac Library

Thursday February 05, 2026

Financial Math
VIX Options in the Short-Maturity Regime
- Lingjiong Zhu,
Time: 3.05 Room: LOV 231
Abstract/Desc: We derive the short-maturity asymptotics for VIX option prices in local-stochastic volatility models. Both out-of-the-money (OTM) and at-the-money (ATM) asymptotics are considered. Using large deviations theory methods, the asymptotics for the OTM options are expressed as a two-dimensional variational problem, which is reduced to an extremal problem for a function of two real variables. This extremal problem is solved explicitly in an expansion in log-moneyness. We will study the VIX option pricing for Heston-type model and the SABR model in more detail. Finally, we will discuss VIX option pricing in the presence of jumps. This is based on the joint work with Desen Guo, Dan Pirjol and Xiaoyu Wang.

Algebra seminar
Weighted blow-up in nature: wall crossings for Log-Hilbert schemes of points on curves.
- Veronica Arena, Cambridge
Time: 3:05pm Room: Zoom
Abstract/Desc: Weighted blow-ups are a birational transformation that naturally appears in moduli spaces. One instance where this happens, is when studying the logarithmic Hilbert scheme of points on a curve $C$ equipped with a log structure. Today we will give a quick introduction to both weighted blow-ups and logarithmic Hilbert schemes of points on curves. Then we will focus our attention on the examples of two and three points on $(P^1|0)$ and will describe the wall crossings between the classical Hilbert scheme of points and the logarithmic ones via weighted blow-ups.

Friday February 06, 2026

Machine Learning and Data Science Seminar [url]
Finding Your Inner Qubit — Quantum Computing 101
- Eric Kubischta, FSU
Time: 1:20 Room: Lov 106
Abstract/Desc: Quantum computing has a reputation for being mysterious, but the basic model is simple: quantum states are complex vectors, gates are unitary matrices, and measurement produces random outcomes with probabilities determined by squared inner products. This talk introduces qubits and quantum circuits with minimal physics, using the Bloch sphere (the complex projective line CP^1) as a visual aid for single-qubit states, gates, and measurements. We will discuss why we need quantum mechanics at all, what is meant by a “quantum speedup,” and highlight a few canonical quantum algorithms that achieve provable advantage over classical algorithms. We will also cover the main obstacles to building large-scale quantum computers today, and time permitting, we will outline what “quantum machine learning” usually refers to and why practical advantages remain an open question.

Mathematics Colloquium [url]
Uniform, Constrained, and Composite Sampling via Proximal Sampler
- Jiaming Liang, University of Rochester
Time: 3:05 Room: Lov 101
Abstract/Desc: This talk presents proximal algorithms for three log-concave sampling problems: uniform, constrained, and composite sampling. These problems form a natural hierarchy, where constrained sampling generalizes uniform sampling, and composite sampling further extends constrained sampling through more general potential structures arising in applications such as Bayesian inference. Our algorithm design is based on a sequence of reductions that connect the more general settings back to uniform sampling in suitable lifted spaces. At the core of our approach is an efficient and implementable proximal sampler for uniform sampling, which directly applies to the more general constrained and composite settings. For all three problems, we establish mixing time guarantees measured in Rényi and Chi-squared divergences.

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February