This Week in Mathematics


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Today:

Mathematics Colloquium [url]
Metrics Based on Optimal Transport
- Rocío Díaz Martín, Tufts University
Time: 3:05 Room: Lov 101
Abstract/Desc: The optimal transport (OT) problem seeks the most efficient way to transport a distribution of mass from one configuration to another, minimizing the associated transportation cost. This framework has found diverse applications in machine learning due to its ability to define meaningful distances, known as Wasserstein distances, between probability distributions. However, Wasserstein distances can be computationally expensive, particularly in high-dimensional settings. In this talk, we will introduce new OT-based metrics designed to address these computational challenges. These metrics preserve the desirable properties of the Wasserstein distance while offering significant improvements in efficiency, making them more suitable for large-scale applications.

Entries for this week: 7

Monday January 13, 2025

Mathematics Colloquium [url]
Metrics Based on Optimal Transport
- Rocío Díaz Martín, Tufts University
Time: 3:05 Room: Lov 101
Abstract/Desc: The optimal transport (OT) problem seeks the most efficient way to transport a distribution of mass from one configuration to another, minimizing the associated transportation cost. This framework has found diverse applications in machine learning due to its ability to define meaningful distances, known as Wasserstein distances, between probability distributions. However, Wasserstein distances can be computationally expensive, particularly in high-dimensional settings. In this talk, we will introduce new OT-based metrics designed to address these computational challenges. These metrics preserve the desirable properties of the Wasserstein distance while offering significant improvements in efficiency, making them more suitable for large-scale applications.

Tuesday January 14, 2025

Geometry and Topology Seminar [url]
Organizational meeting
- General, FSU
Time: 3:05 Room: 232
More Information
Abstract/Desc: We will discuss speakers and schedules of the seminar this semester.

Wednesday January 15, 2025

Biomathematics Journal Club
Are Physiological Oscillations Physiological?
- Richard Bertram, FSU
Time: 5:00 Room: Dirac Library

Biomathematics Seminar
Introduction to Delay Differential Equations
Time: 3:05 PM Room: LOV 232

Thursday January 16, 2025

Algebra seminar
Glueing invariants of Donaldson--Thomas type
- Benjamin Hennion, University Paris-Saclay (Orsay)
Time: 8:30AM Room: Zoom
Abstract/Desc: Donaldson--Thomas invariants are numerical invariants associated to Calabi--Yau varieties. They can be obtained by glueing singularity invariants from local models of a suitable moduli space. By studying the moduli of such local models, we will explain how to recover Brav--Bussi--Dupont--Joyce--Szendroi's perverse sheaf categorifying the DT-invariants, as well as how to glue more evolved singularity invariants, such as matrix factorizations (thus answering a conjecture of Kontsevich and Soibelman). This is joint work with M. Robalo and J. Holstein.

Financial Mathematics Seminar
How to give, and how not to give, a slide talk
- Alec Kercheval, FSU
Time: 3:05 Room: 0231

Friday January 17, 2025

Machine Learning and Data Science Seminar [url]
- Zhe Su, Michigan State University
Time: 1:20 Room: zoom
Abstract/Desc: Artificial intelligence (AI) has dramatically reshaped various scientific fields over the years, providing significant advances in understanding biological complexities. However, AI-based biological discovery often faces challenges arising from high dimensionality, intricate complexity, and nonlinearity associated with biological systems. These challenges can be effectively tackled by incorporating mathematical theories from algebraic topology, differential geometry, and differential topology. In various fields, mathematical AI models have shown superior performance compared to previous studies, highlighting the need for developing new mathematical models. In this talk, I will primarily focus on our recently developed de Rham Hodge-enabled frameworks for volumetric data using differential forms, which have proven to be effective, efficient, and convenient for machine learning use. Additionally, I will discuss my earlier work in geometric shape analysis for curves and surfaces. The frameworks we have developed provide deep insights into both the topological and geometric information of manifold-based data, promising to enhance our understanding of complex datasets.

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Department of Mathematics

This Week in Mathematics