This Week in Mathematics


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Entries for this week: 5

Tuesday September 16, 2025

Applied and Computational Math
A Priori and a Posteriori Error Estimate for Pressure Robust Schemes for Incompressible Flow
- Lin Mu, University of Georgia
Time: 3:05pm Room: LOV 0306
Abstract/Desc: The incompressible fluid model is widely used in various fields in engineering and science and their numerical solutions are of prominent importance in understanding complex, natural, engineered, and societal systems. There has been considerable interest in mathematical modeling and algorithm development. One of the critical challenges is the development of the pressure robust scheme and achieve the desired mass conservation with low cost. Our effort aims at designing the low-cost divergence preserving finite element method and in turn, achieve viscosity independent velocity error estimates. Translating this result to the incompressible fluid equations, our algorithm is robust with varying viscosity permeability values and large pressure gradients. In this talk, we shall present our algorithm development, and then demonstrate the stability and convergence analysis theoretically and numerically. The profiles of benchmark tests indicate that our algorithm outperforms other non-divergence preserving numerical schemes.

Geometry and Topology [url]
Classification of SL(n,R)-actions on closed manifolds
- Miri Son, Rice University
Time: 3:05 Room: 231
More Information
Abstract/Desc: Recently, Fisher and Melnick classified SL(n,R)-actions on n-dimensional manifolds for n≥3. In this talk, we generalize this result by classifying smooth or real-analytic SL(n,R)-actions on m-dimensional manifolds for 3≤n≤m≤2n-3. This work is motivated by the Zimmer program and is central to it, as Lie group actions restrict to their lattice actions. This classification relies on the linearization of SL(n,R)-actions when there is a global fixed point. The analytic case was proved by Guillemin—Sternberg and Kushinirenko. We discuss the smooth case which is ongoing joint work with Insung Park.

Wednesday September 17, 2025

Biomathematics Journal Club
Scale-Free Brain Functional Networks
- Greg Owanga, FSU
Time: 5:00 Room: Dirac Library

Thursday September 18, 2025

Algebra seminar
Geometry of contact loci of semihomogenous singularities
- Kent Huang, University of Waterloo
Time: 3:05pm Room: Zoom
Abstract/Desc: Contact loci record arcs that meet a singularity with certain order. In this talk I’ll outline recent results for semihomogeneous isolated hypersurface singularities: (1) a proof of the arc–Floer conjecture for all but a few special cases, identifying the compactly supported cohomology of restricted m-contact loci with fixed-point Floer cohomology of the m-th iterate of the Milnor monodromy; (2) a complete solution of the embedded Nash problem in this setting, describing the irreducible components of m-contact loci and the associated valuations. No Floer theory background is needed.

Friday September 19, 2025

Data Science and Machine Learning Seminar
The Barycentric Coding Model in Optimal Transport
- Rocío Díaz Martín, FSU Mathematics
Time: 1:20 Room: Love 106
Abstract/Desc: The context of this seminar will be the theory of Optimal Transport and its applications. We will consider the problem of estimating a point, either a distribution or a network, under the Barycentric Coding Model with respect to the Wasserstein (W) or Gromov-Wasserstein (GW) distance functions. Specifically, assuming that the target belongs to the set of W or GW barycenters of a finite collection of known templates, we aim to estimate the unknown barycentric coordinates with respect to those templates. In other words, the goal is to determine the right combination of templates (or barycentric coordinates) that best reconstructs the target. From the perspective of harmonic analysis, computing barycenters can be seen as a 'synthesis problem', whereas retrieving their coordinates corresponds to solving an 'analysis problem'. We will review the general theory for the classical case, i.e., using the Wasserstein metric, and then delve into the Gromov-Wasserstein case. For the latter, we focus on algorithms for finding barycentric coordinates (analysis), leveraging existing techniques for constructing barycenters (synthesis) that rely on fixed-point iteration (G. Peyré, M. Cuturi, and J. Solomon, 2016) and differentiation approaches via a blow-up method (S. Chowdhury and T. Needham, 2020). Applications will include covariance estimation, classification, compression, and data imputation.

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Department of Mathematics

This Week in Mathematics