This Week in Mathematics

Department of Mathematics

This Week in Mathematics


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Current Week [Feb 15, 2026 - Feb 21, 2026]

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Entries for this week: 9

Tuesday February 17, 2026

Topology seminar
Symmetric products of curves, scalar curvature, and positivity in algebraic geometry
- Luca Di Cerbo, University of Florida
Time: 3:05PM Room: LOV 232
Abstract/Desc: In this talk, I will present a detailed study of the curvature and symplectic asphericity properties of symmetric products of curves. I demonstrate that these spaces can be utilized to address nuanced questions arising in the study of closed Riemannian manifolds with positive scalar curvature. For example, symmetric products of curves sharply distinguish between two distinct notions of macroscopic dimension introduced by Gromov and Dranishnikov. As a natural generalization of this circle of ideas, I will also address the Gromov–Lawson and Gromov conjectures in the Kaehler projective setting and draw new connections between the theories of the minimal model, positivity in algebraic geometry, and macroscopic dimensions. This is joint work with Alexander Dranishnikov and Ekansh Jauhari.

Applied and Computational Mathematics [url]
Non-potential mean-field games à la Benamou-Brenier
- Dr. Levon Nurbekyan, Emory University
Time: 3:05 Room: 231
Abstract/Desc: Mean-field games (MFG) theory is a mathematical framework for studying large systems of agents who play differential games. In the PDE form, MFG reduces to a Hamilton-Jacobi equation coupled with a continuity or Kolmogorov-Fokker-Planck equation. Theoretical analysis and computational methods for these systems are challenging due to the absence of strong regularizing mechanisms and coupling between two nonlinear PDE. One approach that proved successful from both theoretical and computational perspectives is the variational approach, which interprets the PDE system as KKT conditions for suitable convex energy. MFG systems that admit such representations are called potential systems and are closely related to the dynamic formulation of the optimal transportation problem due to Benamou-Brenier. Unfortunately, not all MFG systems are potential systems, limiting the scope of their applications. I will present a new approach to tackle non-potential systems by providing a suitable interpretation of the Benamou-Brenier approach in terms of monotone inclusions. In particular, I will present advances on the discrete level and numerical analysis and discuss prospects for the PDE analysis.

Wednesday February 18, 2026

Biomath lab meetings
Mathematical modelling of immune evasion and resistance in cancer therapy
- Naz Mokari, FSU
Time: 2:00 Room: LOV102
Abstract/Desc: The evolutionary and ecological dynamics of tumors under immune responses and therapeutic interventions pose major challenges to long-term treatment success. A major problem in cancer treatment is the emergence of resistance. Although treatment may initially achieve short-term disease control, resistant cancer cell subpopulations often arise leading to relapse with more aggressive and treatment-resistant forms of the disease. Here, we develop and analyze mathematical models describing the interactions among effector immune cells, effector-sensitive tumor cells, and effector-resistant tumor cells under distinct immune-evasion strategies. The models incorporate ecological and evolutionary processes, including competition and cooperation between resistant and sensitive tumor subpopulations. We identify threshold conditions governing tumor persistence, elimination, and phenotype dominance under varying therapeutic intensities. These findings provide a theoretical framework for designing targeted and combination therapies and offer insights into strategies for mitigating the treatment resistance.

Biomath Seminar
Adaptive Cancer Therapy Modeling
- Nazanin Mokari, FSU Mathematics
Time: 3:05 Room: Love 232
Abstract/Desc: The evolutionary and ecological dynamics of tumors under immune responses and therapeutic interventions pose major challenges to long-term treatment success. A major problem in cancer treatment is the emergence of resistance. Although treatment may initially achieve short-term disease control, resistant cancer cell subpopulations often arise leading to relapse with more aggressive and treatment-resistant forms of the disease. Here, we develop and analyze mathematical models describing the interactions among effector immune cells, effector-sensitive tumor cells, and effector-resistant tumor cells under distinct immune-evasion strategies. The models incorporate ecological and evolutionary processes, including competition and cooperation between resistant and sensitive tumor subpopulations. We identify threshold conditions governing tumor persistence, elimination, and phenotype dominance under varying therapeutic intensities. These findings provide a theoretical framework for designing targeted and combination therapies and offer insights into strategies for mitigating the treatment resistance.

Biomathematics Journal Club
A Positive Mood, a Flexible Brain
- Gus Jennetten, FSU
Time: 5:00 Room: Dirac Library

Thursday February 19, 2026

Algebra seminar
Ekedahl-Oort Types of Double Covers in Characteristic Two
- Jeremy Booher, University of Florida
Time: 3:05pm Room: LOV 232
Abstract/Desc: Let X be a smooth projective curve over a perfect field of characteristic two and Y be a ramified double cover of X. If X is ordinary, we compute the Ekedahl-Oort type of Y in terms of the ramification of the cover generalizing results of Elkin and Pries and of Voloch. If X is not ordinary, we bound the Ekedahl-Oort type in terms of the ramification of the cover. We do so by analyzing the de Rham cohomology of the cover with its Frobenius and Verschiebung and establishing a local-to-global principle for the effects of each point of ramification. This is joint work with Joe Kramer-Miller and Steven Groen.

Friday February 20, 2026

Data Science and Machine Learning Seminar [url]
Geometric Perspective on Concentration Phenomena in Frame Theory
- Ferhat Karabatman, FSU
Time: 1:20 Room: Lov 106
Abstract/Desc: Frames are fundamental structures in many areas, and tight frames are particularly valued for their stability and robustness properties. In this work, we establish concentration phenomena for Parseval frames, i.e. tight frames with frame bound 1, under isotropic distributions supported on the sphere and the Euclidean ball, showing that epsilon-nearly Parseval frames are prevalent in these probabilistic models. We further introduce a distinguished subclass of Parseval frames and prove that they are both robust under the Bernoulli-type erasure model and prevalent within the space of Parseval frames. As an application of our results, we derive a high-probability upper bound of order o(epsilon d) for the Paulsen problem.

Mathematics Colloquium [url]
Bridging Schroedinger and Bass for generative diffusion modeling
- Nizar Touzi, NYU
Time: 3:05 Room: Lov 101
Abstract/Desc: Generative models aim to approximate an unknown probability distribution mu on Rd using a finite sample of independent draws from mu. Motivated by variance-preserving score-based diffusion models, we introduce a new diffusion-based transport plan on path space that is optimal with respect to a criterion combining entropy minimization and stabilization of the quadratic variation. The resulting transport plan can be interpreted as an interpolation between the Schroedinger bridge and the Bass solution from martingale optimal transport. The proposed method has a computational complexity comparable to that of state-of-the-art approaches, while yielding a significant improvement in generation quality.

Mathematics Colloquium [url]
Bridging Shrödinger and Bass for generative diffusion modeling
- Nizar Touzi, NYU
Time: 3:05 Room: 101
Abstract/Desc: Generative models aim to approximate an unknown probability distribution μ on Rd using a finite sample of independent draws from μ. Motivated by variance-preserving score-based diffusion models, we introduce a new diffusion-based transport plan on path space that is optimal with respect to a criterion combining entropy minimization and stabilization of the quadratic variation. The resulting transport plan can be interpreted as an interpolation between the Schrödinger bridge and the Bass solution from martingale optimal transport. The proposed method has a computational complexity comparable to that of state-of-the-art approaches, while yielding a significant improvement in generation quality.

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