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This Week in Mathematics

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Entries for this week: 10
Monday February 26, 2024

PDE seminar
Nonlocal Integrable Models
    - Nick Ossi, FSU
Time: 3:05pm Room: LOV 105
Abstract/Desc: Certain well-known dispersive partial differential equations that model the propagation of waves are known to be integrable - that is, exactly solvable. Recently, a peculiar class of integrable systems with spatial and/or temporal nonlocality has been introduced. This talk will give an overview of this class of nonlocal equations, as well as a discussion of some technical details that separate these systems from their local counterparts.

PDE seminar
Time: 3:05pm Room: LOV 105
Abstract/Desc: TBA

Tuesday February 27, 2024

Topology and Geometry Seminar
Negatively curved spaces and groups and the Cannon conjecture
    - Phil Bowers, FSU
Time: 3:05 Room: LOV 107
Abstract/Desc: In this talk I will define the boundary of a negatively curved space carefully, describe the combinatorial half spaces and combinatorial disks defined on the boundary of a negatively curved group, and outline Cannon’s plan for proving the Cannon conjecture using the Combinatorial Riemann Mapping Theorem.

Wednesday February 28, 2024

Applied and Computational Math Seminar -- Stochastic Computing and Optimization
Stochastic Computing and Optimization
    - ACM/Fin Math students,
Time: 3:05PM Room: LOV 0231
Abstract/Desc: Students from ACM and Financial Math will present their research progress. Some invited speakers may also present their research.

Biomathematics Seminar
Mathematical Optimization of Drug Regimens
    - Helen Moore, University of Florida
Time: 3:00 Room: 232 Love
Abstract/Desc: Improvements in drug regimens can make a difference in both clinical trial success and patient outcomes. Optimal control can be used to mathematically optimize regimens, which can then be tested experimentally and clinically. Before we run optimization, we first evaluate the dynamics model to make sure it behaves as expected. I will show examples of the evaluation and optimization, and discuss some of the work that remains to be done.

Industry Seminar
Math in the Biopharma Industry
    - Helen Moore, University of Florida
Time: 4:00 Room: 204 Love
Abstract/Desc: I will discuss several aspects of math modeling jobs in the biopharma industry. This includes the types of problems industry math modelers work on, and how their jobs compare with academic jobs. I will also discuss how to get a math modeling job in biopharma.

Joint Math Major Seminar / Undergraduate Colloquium
What is turbulence?
    - Aseel Farhat, FSU
Time: 3:05pm Room: LOV 101
Abstract/Desc: Turbulence is something we all are familiar with but is incredibly hard to describe. It happens in liquids, think of breaking waves and raging rivers, as well as gases, for example air streaming around a car or plane. Despite this complexity, scientists believe that fluid flow is described by the Navier-Stokes equations. The same equations describe the motion of the water in a cup of coffee, the evolution of a hurricane, the behavior of the ocean currents and even the atmosphere of Jupiter. The solutions to the three-dimensional Navier-Stokes equations are hard to find and we still don't know if they involve oddities, such as discontinuities or infinities. The answer to this question can win you a million dollars from the Clay Mathematics Institute. In this talk, I will introduce the Navier-Stokes equations and we will discuss some mathematical aspects of turbulence and some of the outstanding challenges in the study of fluids.

Thursday February 29, 2024

Algebra Seminar [url]
From Hochschild homology to traces and back
    - Maxime Ramzi, University of Copenhagen
Time: 3:05 pm Room: ZOOM
More Information
Abstract/Desc: Traces in symmetric monoidal categories are a generalization of the trace of a matrix, and they enjoy a number of pleasant properties reminiscent of the usual trace, such as cyclic invariance. In this talk, I will explain how these properties are encoded in (topological) Hochschild homology and how in turn, structural properties of Hochschild homology can be used to infer (calculational) properties of traces and related objects in classical algebraic topology. Time permitting, I will explain how to go back, and extract calculational properties of Hochschild homology. This talk is in part based on joint work with Carmeli, Cnossen and Yanovski, and partly based on joint work with Klein and Malkiewich.

Financial Math Seminar
Some recent applications of multivariate approximation via Stein's method to computational statistics
    - Thanh Dang, Florida State University
Time: 3:05pm Room: Lov 231
Abstract/Desc: Stein's method is a collection of techniques for bounding probability distance between two distributions. While Stein's method has been developed for a wide variety of univariate targets, there is much less progress regarding multivariate targets beside from the multivariate normal distribution. In this talk, we will summarize some recent theoretical advances of Stein's method in the multivariate approximation direction. We will discuss how these theoretical advances enable researchers to tackle two important problems in computational statistics. The first one is about designing a computationally tractable quality measure that compares how well any two samples approximate a target distribution. This is based on a series of papers by Jackson Gorham, Andrew Duncan, Sebastian Vollmer and Lester Mackey. The second application is about solving non-convex optimization and sampling problems. This is based on the works of two groups of researchers: Murat Erdogdu, Lester Mackey, Ohad Shamir and Xiao Fang, Qi-Man Shao, Lihu Xu. To close the talk, we will describe our own work with Lingjiong Zhu in this line of research.

Friday March 01, 2024

Machine Learning and Data Science Seminar
Non-equilibrium dynamics of complex networks
    - Ramón Nartallo-Kaluarachchi, University of Oxford
Time: 13:20 Room: Zoom
More Information
Abstract/Desc: Many real-world complex systems operate far from thermodynamic equilibrium. In particular, the dissipation of entropy to maintain a system in non-equilibrium has been proposed as a unifying, organising principle in living systems. Concurrently, network dynamics has emerged as an invaluable framework for modelling the dynamics of complex systems, yet the role of network topology in influencing the thermodynamic behaviour of the system has remained elusive. In this talk, I will present work that highlights directedness and hierarchical organisation as the key structural feature driving non-equilibrium in complex networks in both theory, real-world structural data and empirical multivariate time-series. Going beyond aggregate, system-wide measurements, I will further present a framework for quantifying the irreversibility of individual interactions in a complex system and use this approach to analyse human neuroimaging during a long-term memory task.

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