This Week in Mathematics


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Entries for this week: 7

Tuesday September 03, 2024

ACM [url]
PDE Foundation Model: Generalization, Meta-learning and Learning to Learn
Time: 3:05 pm Room: 0231
Abstract/Desc: In this talk, we develop and explore a foundational model for solving Partial Differential Equations (PDEs) with an emphasis on building a versatile, robust framework capable of addressing multiple PDE operators simultaneously. Our objective is to create a single model that not only handles various operators but also demonstrates the ability to generalize to new, unseen physical phenomena in a "zero-shot" manner. We present numerical examples to demonstrate the model's ability to generalize physical phenomena in a "zero-shot" manner. We introduce LeMON, a Learning to Learn Multi-Operator Network pipeline, which integrates both pre-training and fine-tuning processes. Furthermore, we investigate a new scaling law specifically tailored to PDE foundation models, providing insights into optimizing model performance as it scales. Finally, we improve the LeMON pipeline by integrating LoRA and meta-learning strategies.

Geometry and Topology [url]
Rigidity of convex subsets in symmetric spaces
- Thang Nguyen, FSU
Time: 3:05 Room: 301
Abstract/Desc: Symmetric spaces are manifolds with many rigidity phenomena. In this talk, I will present a phenomenon that Riemannian metric on convex subsets of symmetric spaces is unique once we keep either the same upper bound or lower bound on curvature as of the symmetric metric. Ideas of the work come from classical comparison theorems of Rauch and of Toponogov together with Berger's theorem for Blaschke conjecture. This is from a joint work with C. Connell, M. Islam, and R. Spatzier.

Wednesday September 04, 2024

Biomathematics Seminar
Current Research Topics of the Bertram lab
- Richard Bertram, FSU
Time: 3:05 Room: 232 Love

Biomath Journal Club [url]
Organizational Meeting
Time: 5:00 PM Room: Dirac 216

Thursday September 05, 2024

Financial Mathematics Seminar
One-Dimensional McKean-Vlasov Stochastic Variational Inequalities and Coupled BSDEs with Locally Holder Noise Coefficients
- Ning Ning (Patricia), Texas A&M University, College Station
Time: 3:05 Room: Zoom
More Information
Abstract/Desc: In this article, we investigate three classes of equations: the McKean-Vlasov stochastic differential equation (MVSDE), the MVSDE with a subdifferential operator referred to as the McKean-Vlasov stochastic variational inequality (MVSVI), and the coupled forward-backward MVSVI. The latter class encompasses the FBSDE with reflection in a convex domain as a special case. We establish the well-posedness, in terms of the existence and uniqueness of a strong solution, for these three classes in their general forms. Importantly, we consider stochastic coefficients with locally Holder continuity and employ different strategies to achieve that for each class. Short bio: Dr. Ning Ning is currently an Assistant Professor (and PhD adviser) in the Department of Statistics at Texas A&M University, College Station. Additionally, she holds affiliations with the Institute of Data Science and the Institute for Quantum Science and Engineering, and is the co-founder of the Stochastic Processes Seminar within the Department of Mathematics. She earned her PhD from the Department of Statistics and Applied Probability at the University of California, Santa Barbara. Prior to her current position, Dr. Ning held a one-year position as a Postdoctoral Research Associate in the Department of Applied Mathematics at the University of Washington, Seattle, followed by a three-year position as a Postdoctoral Research Fellow in the Department of Statistics at the University of Michigan, Ann Arbor. Dr. Ning's research interests span across various domains including stochastic processes, Markov chains, time series, networks, machine learning, and quantum computing.

Algebra seminar [url]
Rational torsion and reducibility for abelian varieties associated to newforms
- Matthew Winters, FSU
Time: 3:05PM Room: LOV 301
Abstract/Desc: Let f be a newform and A its associated abelian variety. We have shown before that for certain primes r, if A is an optimal semistable elliptic curve with reducible torsion subgroup A[r], then A has rational r-torsion. In this talk we define necessary terms and how this result generalizes to other abelian varieties. We will sketch the proof and discuss the differences that arise when A is not necessarily an elliptic curve.

Friday September 06, 2024

Data Science and Machine Learning Seminar
Generalized Dimension Reduction Using Semi-Relaxed Gromov-Wasserstein Distance
- Tom Needham, FSU Math
Time: 1:20 Room: Love 106
Abstract/Desc: Dimension reduction techniques typically seek an embedding of a high-dimensional point cloud into a low-dimensional Euclidean space which optimally preserves the geometry of the input data. Based on expert knowledge, one may instead wish to embed the data into some other manifold or metric space in order to better reflect the geometry or topology of the point cloud. We propose a general method for manifold-valued multidimensional scaling based on concepts from optimal transport. In particular, we establish theoretical connections between the recently introduced semi-relaxed Gromov-Wasserstein (srGW) framework and multidimensional scaling by solving the Monge problem in this setting. We also derive novel connections between srGW distance and Gromov-Hausdorff distance. We apply our computational framework to analyze ensembles of political redistricting plans for states with two Congressional districts, achieving an effective visualization of the ensemble as a distribution on a circle which can be used to characterize typical neutral plans, and to flag outliers.

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