This Week in Mathematics


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Today:

Special Seminar Lecture
Exploring the Gaussian Free Field
- Greg Lawler, University of Chicago
Time: 3:05 PM Room: LOV 101
Abstract/Desc: A fundamental object in probability and statistical physics is the Gaussian Free Field (GFF) along with its relation to path measures such as the Schramm-Loewner evolution (SLE) and its exponential which is sometimes called Liouville Quantum Gravity (LQG). There are many ways to view the field. I will introduce the GFF using the ``exploration’’ perspective which has been invaluable in understanding it. I will not assume previous knowledge of GFF, SLE, or LQG, but I will assume knowledge of probability: multivariate normal distributions and Brownian motion.

Entries for this week: 9

Monday April 22, 2024

ATE exam
Graph Neural Networks for the Inverse Problem
- Latira Campbell, FSU
Time: 1:00pm Room: 204A

Ruth Lopez Fajardo's ATE
Parameter Estimation for Complex Dynamical Systems
- Ruth Lopez Fajardo, Florida State University
Time: 3pm Room: 204A
Abstract/Desc: In science and engineering fields a physical phenomenon can be described by a mathematical model, often through algebraic or differential equations. These models often feature parameters that represent properties or measurable quantities. If observations of the phenomenon are available a common challenge is estimating the parameters in the model given this observations. This challenge is essentially an inverse problem: given observed outputs, we seek to deduce the inputs (parameters). A conventional approach to address this challenge is through deterministic optimization, illustrated by methods such as least squares curve fitting. However, inverse problems frequently encounter issues of ill-posedness, prompting the need for regularization techniques to be introduced. Another route, explored over recent decades, is the Bayesian approach. Here, the inherent noise in the observations and prior knowledge on the parameters are treated as random variables. This framework aims to derive a posterior distribution for the parameters by utilizing Bayes’ theorem to effectively integrate the uncertainty inherent in the model. In this presentation, we'll discuss a method that employs a recursive Bayesian approach to address the parameter estimation inverse problem within dynamical systems, all within the framework of data assimilation.

Tuesday April 23, 2024

Topology and Geometry Seminar [url]
Symmetry properties of the cubical Joyal model structure
- Brandon Doherty, FSU
Time: 3:05 Room: LOV 107
Abstract/Desc: Via the cubical Joyal model structure, cubical sets having faces, degeneracies and connections can be viewed as models for (infinity,1)-categories; in this model, homotopies are most naturally defined using the geometric product, rather than the cartesian product. This is an alternative monoidal product having convenient properties, but with the drawback that it is not symmetric. In this talk, based on work in progress joint with Tim Campion, we discuss a comparison between the less structured cubical sets on which the cubical Joyal model structure is defined and cubical sets with symmetries, which allows us to prove that the geometric product is symmetric up to natural weak equivalence in the cubical Joyal model structure. If time permits, we will also discuss applications of this comparison to the construction of a Quillen-equivalent model structure on symmetric cubical sets, and the potential application of similar techniques to proving that the cubical Joyal model structure is monoidal with respect to the cartesian product.

Wednesday April 24, 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
An introduction to social evolution
- Erol Akçay, UPenn
Time: 3:05 Room: Zoom
More Information
Abstract/Desc: This talk will survey the author's research on social evolution.

Biomathematics Journals
A Multiscale Model of Complex Endothelial Cell Dynamics in Early Angiogenesis
- James Thornham, FSU
Time: 5:00 Room: 216 Dirac Library

Thursday April 25, 2024

Special Seminar Lecture
Exploring the Gaussian Free Field
- Greg Lawler, University of Chicago
Time: 3:05 PM Room: LOV 101
Abstract/Desc: A fundamental object in probability and statistical physics is the Gaussian Free Field (GFF) along with its relation to path measures such as the Schramm-Loewner evolution (SLE) and its exponential which is sometimes called Liouville Quantum Gravity (LQG). There are many ways to view the field. I will introduce the GFF using the ``exploration’’ perspective which has been invaluable in understanding it. I will not assume previous knowledge of GFF, SLE, or LQG, but I will assume knowledge of probability: multivariate normal distributions and Brownian motion.

Friday April 26, 2024

Machine Learning and Data Science Seminar
1) Vietoris-Rips complexes of totally split-decomposable spaces; 2) Efficient computation of 1-skeleton of directed graphs
- Mario Gomez Flores and Abdullah Malik , FSU
Time: 1:20 Room: Lov 102
Abstract/Desc: 1) Split-metric decompositions are an important tool in the theory of phylogenetics, particularly because of the link between the tight span and the class of totally decomposable spaces, i.e. a generalization of metric trees whose decomposition does not have a “prime” component. The connection with tight spans has been studied at least since the introduction of split-metric decompositions by Bandelt and Dress in 1992, and culminated with the characterization of the polytopal structure of the tight span of a totally decomposable metric by Huber, Koolen, and Moulton in 2018. We use this connection, along with recent critical results on the Vietoris-Rips complex of the circle and the connection between tight spans and Vietoris-Rips complexes, to characterize the homotopy type of the Vietoris-Rips complex of a large class of totally decomposable spaces. This talk will be of interest to those studying phylogenetics. 2) Directed graphs, viewed as 1-dimensional simplicial sets, model binary relations that have found a wide variety of applications, even with the restriction that neglects any n-ary relations that might exist between n nodes. The advantage of viewing directed graphs as simplicial sets is that one is allowed to canonically identify these n-nary relationship as the 1-skeleton of the simplicial set. In this talk, we propose two algorithms that can help identify these higher dimensional relationships in an efficient way, which can then be used for downstream tasks.

Mathematics Colloquium
Random Fractals Arising in Probability and Statistical Physics
- Greg Lawler, University of Chicago
Time: 3:05 Room: Lov 101
Abstract/Desc: Many of the mathematical structures arising in statistical physics viewed at phase transitions are fractals that are random but have some kinds of “statistical self-similarity’’. One prototypical model is the “self-avoiding walk”, a path of a walker who moves ``randomly’’ except with the restriction that no place is revisited. The last twenty-five years have seen significant advances in the mathematical understanding of these fractals. I will introduce some of these focusing primarily on planar models which have been the focus of most of the successes. This talk is designed for a general mathematical audience and does not assume background in probability or statistical physics.

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Department of Mathematics

This Week in Mathematics