This Week in Mathematics


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Today:

Topology seminar [url]
A Construction of Hurwitz spaces via Artin’s Actions on Nielsen Classes
- Yuxiang Yao, UC Irvine
Time: 3:05PM Room: LOV232
Abstract/Desc: Branched covers of the projective line over the complex numbers can be studied through the topology of the complement of the branch locus. For a fixed branch locus, such covers are encoded by Nielsen classes, namely equivalence classes of local monodromy tuples around the branch points. When the branch points vary in families, the corresponding monodromy data are related by Artin’s braid group action on Nielsen classes. This point of view not only describes individual covers, but also organizes families of covers into moduli objects: over the complex numbers, the braid action on Nielsen classes gives rise to Hurwitz spaces, and more generally Hurwitz stacks while the branched cover has nontrivial automorphisms. Hurwitz spaces parametrize families of branched covers with prescribed discrete monodromy data. In this talk, I first recall the topological case parametrizing families Y -> X x P^1 of degree d branched covers with n branch points and fixed monodromy data, with branch locus disjoint from infinity. Time permitting, I will then conclude by briefly discussing an arithmetic analogue over Fq and relate it with the unordered configuration space, together with Frobenius action.

Applied and Computational Mathematics
FEMOnet & EnSF
- Kapil Chawla & Toan Huynh, Florida State University
Time: 3:05 Room: LOV 231

Entries for this week: 9

Monday April 13, 2026

Stochastic Computing and Optimization
Federated Learning: Training Together While Staying Apart
- Jingqiao Tang, FSU
Time: 3:05PM Room: LOV 232
Abstract/Desc: Federated learning allows multiple clients to collaboratively train a shared global model while keeping their raw data localized. This talk introduces the core ideas behind federated learning, discusses its convergence properties, and presents numerical experiments demonstrating its performance under various data distribution settings. We also highlight current limitations and open challenges in the field.

Tuesday April 14, 2026

Topology seminar [url]
A Construction of Hurwitz spaces via Artin’s Actions on Nielsen Classes
- Yuxiang Yao, UC Irvine
Time: 3:05PM Room: LOV232
Abstract/Desc: Branched covers of the projective line over the complex numbers can be studied through the topology of the complement of the branch locus. For a fixed branch locus, such covers are encoded by Nielsen classes, namely equivalence classes of local monodromy tuples around the branch points. When the branch points vary in families, the corresponding monodromy data are related by Artin’s braid group action on Nielsen classes. This point of view not only describes individual covers, but also organizes families of covers into moduli objects: over the complex numbers, the braid action on Nielsen classes gives rise to Hurwitz spaces, and more generally Hurwitz stacks while the branched cover has nontrivial automorphisms. Hurwitz spaces parametrize families of branched covers with prescribed discrete monodromy data. In this talk, I first recall the topological case parametrizing families Y -> X x P^1 of degree d branched covers with n branch points and fixed monodromy data, with branch locus disjoint from infinity. Time permitting, I will then conclude by briefly discussing an arithmetic analogue over Fq and relate it with the unordered configuration space, together with Frobenius action.

Applied and Computational Mathematics
FEMOnet & EnSF
- Kapil Chawla & Toan Huynh, Florida State University
Time: 3:05 Room: LOV 231

Wednesday April 15, 2026

Biomath Seminar
Population Growth and Control in Stochastic Models of Cancer Development/Opinion perception reshapes infectious disease spread
- Tanulata Halder/Afolabi Ariwayo, FSU Mathematics
Time: 3:05 Room: Love 232

Biomathematics Journal Club
Uncovering Disease-Disease Relationships Through the Incomplete Interactome
- James Thornham, FSU
Time: 5:00 Room: Dirac Library

Thursday April 16, 2026

Financial Math
Noise estimation of SDE from a single data trajectory
- Munawar Ali,
Time: 3.05 Room: LOV 231
Abstract/Desc: In this paper, we propose a data-driven framework for model discovery of stochastic differential equations (SDEs) from a single trajectory, without requiring the ergodicity or stationary assumption on the underlying continuous process. By combining (stochastic) Taylor expansions with Girsanov transformations, and using the drift function’s initial value as input, we construct drift estimators while simultaneously recovering the model noise. This allows us to recover the underlying $\mathbb P$ Brownian motion increments. Building on these estimators, we introduce the first \textit{stochastic Sparse Identification of Stochastic Differential Equation (SSISDE)} algorithm, capable of identifying the governing SDE dynamics from a single observed trajectory without requiring ergodicity or stationarity. To validate the proposed approach, we conduct numerical experiments with both linear and quadratic drift–diffusion functions. Among these, the Black–Scholes SDE is included as a representative case of a system that does not satisfy ergodicity or stationarity.

Algebra seminar
Lefschetz (1,1)-theorem for singular varieties
- Ananyo Dan, CUNEF Universidad
Time: 3:05pm Room: Zoom
Abstract/Desc: Lefschetz (1,1)-theorem states that every (1,1) class in a smooth projective variety is the first Chern class of a line bundle. Such a statement fails when the variety is singular. There have been various attempts at extending the Lefschetz (1,1) to singular varieties. The most universal statement so far is due to Arapura. However, it follows from the work of Totaro that the map studied by Arapura does not look at all the possible (1,1) classes, in the singular case. Totaro suggests looking at the Bloch-Gillet-Soule cycle class map from the operational Chow group to the space of Hodge classes. In a joint work with I. Kaur, we study this map and give a criterion under which this map is surjective, thereby giving a possible Lefschetz (1,1) theorem for singular varieties. In the talk, I plan to present these results and give various examples where the surjectivity holds.

Friday April 17, 2026

Machine Learning and Data Science Seminar [url]
The Observable Wasserstein Distance
- Washington Mio, FSU
Time: 1:20 Room: Lov 106
Abstract/Desc: Calculating the Wasserstein distance between large point clouds in metric spaces is computationally costly. In Euclidean space, the sliced Wasserstein distance provides a more accessible alternative. We develop an analogue of slicing techniques for probability measures or data in metric spaces to obtain a computationally more tractable lower bound for the Wasserstein distance, a metric that we term observable Wasserstein distance. This is joint work with T. Needham, E. dos Santos, and L. Mauri.

Mathematics Colloquium [url]
From Phase Separation in Heterogeneous Media to Learning Training Schemes for Image Denoising
- Irene Fonseca, CMU
Time: 3:05 Room: Lov 101
Abstract/Desc: What do these two themes have in common? Both are treated variationally, both deal with energies of different dimensionalities, concepts of geometric measure theory prevail in both, and higher order penalizations are considered. Will learning training schemes for choosing these penalizations in imaging may be of use in phase transitions? Phase Separation in Heterogeneous Media: Modern technologies and biological systems, such as temperature-responsive polymers and lipid rafts, take advantage of engineered inclusions, or natural heterogeneities of the medium, to obtain novel composite materials with specific physical properties. To model such situations using a variational approach based on the gradient theory of phase transitions, the potential and the wells may have to depend on the spatial position, even in a discontinuous way, and different regimes should be considered. In the critical case, where the scale of the small heterogeneities is of the same order of the scale governing the phase transition and the wells are fixed, the nteraction between homogenization and the phase transitions process leads to an anisotropic interfacial energy. The supercritical case for fixed wells is also addressed, and in the subcritical case with moving wells, where the heterogeneities of the material are of a larger scale than that of the diffuse interface between different phases, it is observed that there is no macroscopic phase separation. Learning Training Schemes for Image Denoising: Due to their ability to handle discontinuous images while having a well-understood behavior, regularizations with total variation (TV) and total generalized variation (TGV) are some of the best known methods in image denoising. However, like other variational models including a fidelity term, they crucially depend on the choice of their tuning parameters. A remedy is to choose these systematically through multilevel approaches, for example by optimizing performance on noisy/clean image training pairs. These methods with space-dependent parameters that are piecewise constant on dyadic grids are considered, with the grid itself being part of the minimization. Improved performance on some representative test images when compared with constant optimized parameters is demonstrated.

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Department of Mathematics

This Week in Mathematics