{"id":5,"date":"2012-10-25T22:04:15","date_gmt":"2012-10-25T22:04:15","guid":{"rendered":"http:\/\/pages.charlotte.edu\/template-faculty01\/?page_id=5"},"modified":"2026-04-01T15:09:26","modified_gmt":"2026-04-01T15:09:26","slug":"home","status":"publish","type":"page","link":"https:\/\/pages.charlotte.edu\/otseminar\/","title":{"rendered":"Optimal Transport Seminar"},"content":{"rendered":"\n<figure class=\"wp-block-image size-large is-resized\"><a href=\"https:\/\/i0.wp.com\/pages.charlotte.edu\/otseminar\/wp-content\/uploads\/sites\/1357\/2025\/09\/ot.png?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"386\" src=\"https:\/\/i0.wp.com\/pages.charlotte.edu\/otseminar\/wp-content\/uploads\/sites\/1357\/2025\/09\/ot-1024x386.png?resize=1024%2C386&#038;ssl=1\" alt=\"\" class=\"wp-image-50\" style=\"width:588px;height:auto\" srcset=\"https:\/\/i0.wp.com\/pages.charlotte.edu\/otseminar\/wp-content\/uploads\/sites\/1357\/2025\/09\/ot.png?resize=1024%2C386&amp;ssl=1 1024w, https:\/\/i0.wp.com\/pages.charlotte.edu\/otseminar\/wp-content\/uploads\/sites\/1357\/2025\/09\/ot.png?resize=300%2C113&amp;ssl=1 300w, https:\/\/i0.wp.com\/pages.charlotte.edu\/otseminar\/wp-content\/uploads\/sites\/1357\/2025\/09\/ot.png?resize=768%2C289&amp;ssl=1 768w, https:\/\/i0.wp.com\/pages.charlotte.edu\/otseminar\/wp-content\/uploads\/sites\/1357\/2025\/09\/ot.png?w=1288&amp;ssl=1 1288w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/a><\/figure>\n\n\n\n<p><strong>Organizers:<\/strong> <a href=\"https:\/\/chrisgartland.wordpress.com\/\" data-type=\"link\" data-id=\"https:\/\/chrisgartland.wordpress.com\/\">Chris Gartland<\/a> &amp; <a href=\"https:\/\/pages.charlotte.edu\/kevin-mcgoff\/\">Kevin McGoff<\/a><\/p>\n\n\n\n<p><strong>Overview:<\/strong> This Fall 2025-Spring 2026 seminar will cover a broad range of topics related to optimal transport, determined by the interests of the participants. There will be an emphasis on expository talks, and graduate students are encouraged to attend and to give talks. References for external reading are provided. The typical location and time are Fretwell 302, Tuesdays 4-5pm.<\/p>\n\n\n\n<p><strong>External Reading:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Chapter 3 of <em>Lipschitz Algebras II<\/em> by Nik Weaver<\/li>\n\n\n\n<li>Chapters 1, 4-6 of <em>Optimal Transport, Old and New<\/em> by Cedric Villani<\/li>\n\n\n\n<li><em>Transportation Cost Spaces and their Embeddings into&nbsp;L<sup>1<\/sup><\/em>, <em>a Survey<\/em> by Thomas Schlumprecht <a href=\"https:\/\/arxiv.org\/abs\/2309.09313\">https:\/\/arxiv.org\/abs\/2309.09313<\/a><\/li>\n\n\n\n<li><em>Computational Optimal Transport<\/em> by Cuturi and Peyr\u00e9 <a href=\"https:\/\/arxiv.org\/pdf\/1803.00567\">https:\/\/arxiv.org\/pdf\/1803.00567<\/a><\/li>\n\n\n\n<li><em>Statistical Optimal Transport<\/em> by Chewi, Niles-Weed, and Rigollet <a href=\"https:\/\/arxiv.org\/pdf\/2407.18163\">https:\/\/arxiv.org\/pdf\/2407.18163<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/pythonot.github.io\/\">https:\/\/pythonot.github.io\/<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/colab.research.google.com\/drive\/1SgG91NA8-h7PgzdwEi8SzHDWsfkqVSHQ?usp=sharing\">https:\/\/colab.research.google.com\/drive\/1SgG91NA8-h7PgzdwEi8SzHDWsfkqVSHQ?usp=sharing<\/a> (download &#8216;manhattan.npz&#8217; to run the cafe and bakery example)<\/li>\n\n\n\n<li><a href=\"https:\/\/colab.research.google.com\/drive\/1A_XvmkHR9Gp0FCLx4W91Ctml0EgNy-Ag?usp=sharing\">https:\/\/colab.research.google.com\/drive\/1A_XvmkHR9Gp0FCLx4W91Ctml0EgNy-Ag?usp=sharing<\/a> (visualization of stochastic embedding of cycle into path)<\/li>\n\n\n\n<li><a href=\"https:\/\/colab.research.google.com\/drive\/19-vcoi5-sR3cBcMtT_7RSDsjT9ho7Q7H?usp=sharing\">https:\/\/colab.research.google.com\/drive\/19-vcoi5-sR3cBcMtT_7RSDsjT9ho7Q7H?usp=sharing<\/a><br>(gradient flow used in sampling applications, including warm-up Sinkhorn by using the gradient of W2 space)<\/li>\n\n\n\n<li><em>Ill-Posed and Inverse Problems<\/em> by Michael Klibanov <a href=\"http:\/\/pages.charlotte.edu\/otseminar\/wp-content\/uploads\/sites\/1357\/2026\/03\/ill-posed.pdf\">http:\/\/pages.charlotte.edu\/otseminar\/wp-content\/uploads\/sites\/1357\/2026\/03\/ill-posed.pdf<\/a><\/li>\n<\/ul>\n\n\n\n<p><strong>Upcoming Talk:<\/strong> <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Tuesday April 7, 2026<\/strong><\/li>\n\n\n\n<li><strong>Time: <\/strong>4:00pm<\/li>\n\n\n\n<li><strong>Location:<\/strong> Fret 302<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Speaker<\/span>: Sebastien Bossu<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Title<\/span>: <a href=\"https:\/\/arxiv.org\/abs\/2510.16148\" target=\"_blank\" rel=\"noreferrer noopener\">Fitting an escalier to a curve<\/a><\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Abstract<\/span>: We analyze the inverse problem of fitting a <em>fonction en escalier<\/em> or multi-step function to a curve in L^2 Hilbert space.&nbsp; We propose a two-stage optimization approach whereby the step positions are initially fixed, corresponding to a classic linear least-squares problem with closed-form solution, and then are allowed to vary, leading to first-order conditions that can be solved recursively. We explain how, subject to regularity conditions, the speed of convergence is linear as the number of steps <em>n<\/em> goes to infinity, and we develop a simple algorithm to compute the global optimum fit.&nbsp; Our numerical results based on a sweep search implementation show promising performance in terms of speed and accuracy.&nbsp;Joint with Andrew Papanicoalou and Nour El Hatto.<\/li>\n<\/ul>\n\n\n\n<p><strong>Full Schedule:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Tuesday April 7, 2026<\/strong><\/li>\n\n\n\n<li><strong>Time: <\/strong>4:00pm<\/li>\n\n\n\n<li><strong>Location:<\/strong> Fret 302<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Speaker<\/span>: Sebastien Bossu<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Title<\/span>: <a href=\"https:\/\/arxiv.org\/abs\/2510.16148\" target=\"_blank\" rel=\"noreferrer noopener\">Fitting an escalier to a curve<\/a><\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Abstract<\/span>: We analyze the inverse problem of fitting a <em>fonction en escalier<\/em> or multi-step function to a curve in L^2 Hilbert space.\u00a0 We propose a two-stage optimization approach whereby the step positions are initially fixed, corresponding to a classic linear least-squares problem with closed-form solution, and then are allowed to vary, leading to first-order conditions that can be solved recursively. We explain how, subject to regularity conditions, the speed of convergence is linear as the number of steps <em>n<\/em> goes to infinity, and we develop a simple algorithm to compute the global optimum fit.\u00a0 Our numerical results based on a sweep search implementation show promising performance in terms of speed and accuracy.\u00a0Joint with Andrew Papanicoalou and Nour El Hatto.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Tuesday Mar 31, 2026<\/strong><\/li>\n\n\n\n<li><strong>Time: <\/strong>4:00pm<\/li>\n\n\n\n<li><strong>Location:<\/strong> Fret 302<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Speaker<\/span>: Robert Murray-Gramlich<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Title<\/span>: An introduction to Ollivier Curvature<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Abstract<\/span>: Ollivier curvature provides a synthetic framework for studying the &#8220;geometry&#8221; of Markov chains by measuring the contraction of probability measures under the Wasserstein metric. This talk offers a self-contained introduction to the theory, highlighting how this geometric perspective provides a tractable approach to analyzing complex problems in Markov theory. We will highlight the functional consequences of positive curvature, specifically its applications to concentration of measure and the convergence of Markov semigroups. Time permitting, we will conclude by stating some open conjectures relating to Ollivier Curvature.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Tuesday Mar 24, 2026<\/strong><\/li>\n\n\n\n<li><strong>Time: <\/strong>4:00pm<\/li>\n\n\n\n<li><strong>Location:<\/strong> Fret 302<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Speaker<\/span>: Michael Klibanov<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Title<\/span>: <em>Introduction to the theory of Ill-Posed Problems<\/em><\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Abstract<\/span>: Michael will continue with his introduction to the theory of Ill-Posed Problems<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Tuesday Mar 17, 2026<\/strong><\/li>\n\n\n\n<li><strong>Time: <\/strong>4:00pm<\/li>\n\n\n\n<li><strong>Location:<\/strong> Fret 302<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Speaker<\/span>: Michael Klibanov<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Title<\/span>: <em>Introduction to the theory of Ill-Posed Problems<\/em><\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Abstract<\/span>: Consider an operator equation A(x)=y. The problem of the solution of this equation is called &#8220;ill-posed&#8221; if small perturbation of y cause large perturbation of the solution x. Typically A is a compact operator. In the mean time&nbsp;ill-posed problems are playing a rapidly&nbsp;increasing role in the modern science.&nbsp;In my first presentation, I will introduce some practical examples of IIl-Posed Problems including the classical example of&nbsp;Hadamard. Then I will prove the fundamental theorem of Andrey N. Tikhonov (1943), which has laid the foundation of the&nbsp;theory of Ill-Posed problems.&nbsp;In the future presentations I will introduce main ideas of the regularization theory of Tikhonov: how to actually solve those unstable&nbsp;problems. If time will allow, then I will introduce in my future presentations beginnings of the theory of Coefficient Inverse Problems problems for Partial Differential Equations, which are both&nbsp;the most challenging and the most important part of the theory of Ill-Posed Problems.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Tuesday Mar 3, 2026<\/strong><\/li>\n\n\n\n<li><strong>Time: <\/strong>4:00pm<\/li>\n\n\n\n<li><strong>Location:<\/strong> Fret 302<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Speaker<\/span>: Chris Gartland<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Title<\/span>: <em>Introduction to Wasserstein Metrics V<\/em><\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Abstract<\/span>: I will continue with the introduction to Wasserstein-1 metrics and transportation cost norms on graphs and metric spaces.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Tuesday Feb 24, 2026<\/strong><\/li>\n\n\n\n<li><strong>Time: <\/strong>4:00pm<\/li>\n\n\n\n<li><strong>Location:<\/strong> Fret 302<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Speaker<\/span>: Helen Li<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Title<\/span>: <em>A quick introduction to Wasserstein gradient flow and some applications<\/em><\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Abstract<\/span>: In this talk, I will begin with a brief overview of the geometry of the Wasserstein\u20132 space of probability measures, including its formal Riemannian manifold structure, Wasserstein variations, and gradient flows in the sense of Otto calculus.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Tuesday Feb 17, 2026<\/strong><\/li>\n\n\n\n<li><strong>Time: <\/strong>4:00pm<\/li>\n\n\n\n<li><strong>Location:<\/strong> Fret 302<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Speaker<\/span>: Chris Gartland<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Title<\/span>: <em>Introduction to Wasserstein Metrics IV<\/em><\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Abstract<\/span>: I will continue with the introduction to Wasserstein-1 metrics and transportation cost norms on graphs and metric spaces.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Tuesday Feb 10, 2026<\/strong><\/li>\n\n\n\n<li><strong>Time: <\/strong>4:00pm<\/li>\n\n\n\n<li><strong>Location:<\/strong> Fret 302<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Speaker<\/span>: Kevin McGoff<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Title<\/span>: A look at Brenier\u2019s Theorem<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Abstract<\/span>: In this expository talk, I will discuss Brenier\u2019s Theorem. This theorem provides an answer to Monge\u2019s original optimal transport problem, and it has had some interesting modern statistical applications. I will also describe some of the ideas in the proof, which relies on the analysis of convex functions and the notion of cyclical monotonicity.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Tuesday Jan 20, 2026<\/strong><\/li>\n\n\n\n<li><strong>Time: <\/strong>4:00pm<\/li>\n\n\n\n<li><strong>Location:<\/strong> Fret 302<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Speaker<\/span>: Chris Gartland<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Title<\/span>: <em>Introduction to Wasserstein Metrics III<\/em><\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Abstract<\/span>: I will continue with the introduction to Wasserstein-1 metrics and transportation cost norms on graphs and metric spaces.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Friday Nov 14, 2025<\/strong><\/li>\n\n\n\n<li><strong>Time: <\/strong>3:00pm<\/li>\n\n\n\n<li><strong>Location: <\/strong>Fret 302<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Speaker<\/span>: Helen Li<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Title<\/span>: <em>A Quick Introduction to Diffusion Models, Schr\u00f6dinger Bridges, and Entropy-Regularized Optimal Transport<\/em><\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Abstract<\/span>: In this talk, I will begin with a tutorial overview of diffusion models and their applications in generative AI. I will then introduce a particular class of diffusion models known as diffusion bridges, focusing on the details of a special case\u2014the Schr\u00f6dinger bridge\u2014and its connection to entropy-regularized optimal transport (EOT). Finally, I will discuss results from the paper <em>\u201cPlug-in Estimation of Schr\u00f6dinger Bridges (<\/em><a href=\"https:\/\/arxiv.org\/pdf\/2408.11686\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/arxiv.org\/pdf\/2408.11686<\/a><em>),\u201d<\/em> which proposes a novel non-iterative method that yields a natural plug-in estimator of the time-dependent drift defining the bridge between the source and target measures.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Friday Nov 7, 2025<\/strong><\/li>\n\n\n\n<li><strong>Time: <\/strong>3:00pm<\/li>\n\n\n\n<li><strong>Location: <\/strong>Fret 302<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Speaker<\/span>: Yang Xiang (UNC Chapel Hill)<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Title<\/span>: <em>Graph Joining and Disjointness<\/em><\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Abstract<\/span>: We investigate a phenomenon called disjointness within the framework of graph joinings as a means to characterize structural incompatibility between graphs. Given two weighted, undirected graphs (equivalently, reversible Markov chains), we say they are disjoint if their only possible joining\u2014that is, their only reversible Markovian coupling\u2014is the product. This perspective shifts attention from computing distances between graphs to examining the set of their joinings, thereby highlighting structural features that underlie their incompatibility.<\/li>\n<\/ul>\n\n\n\n<p><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Friday Oct 31, 2025<\/strong><\/li>\n\n\n\n<li><strong>Time: <\/strong>3:00pm<\/li>\n\n\n\n<li><strong>Location: <\/strong>Fret 302<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Speaker<\/span>: Robert Murray-Gramlich<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Title<\/span>: <em>Statistical Aspects of Wasserstein Distances<\/em><\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Abstract<\/span>: Wasserstein distances have recently become popularized in statistics due to their geometric properties (and the topology it induces) as well as the many applications to machine and statistical learning. We will discuss the &#8220;Wasserstein Law of Large Numbers&#8221; which gives an upper bound on the convergence speed of W_p on a compact&nbsp;set and give a complete proof including the bound on the logarithmic factor in the &#8220;critical case&#8221;. Given time we will also discuss some open related problems.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Friday Oct 24, 2025<\/strong><\/li>\n\n\n\n<li><strong>Time: <\/strong>3:00pm<\/li>\n\n\n\n<li><strong>Location: <\/strong>Fret 302<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Speaker<\/span>: Phuong Hoang<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Title<\/span>: <em>Optimal Graph Joining with Applications to Isomorphism&nbsp;Detection and Identification<\/em><\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Abstract<\/span>: We introduce and develop a new constrained optimal transport problem for graphs, called the optimal graph joining (OGJ) problem, and study its relation to graph isomorphism. The graphs of interest are finite, undirected, and may be weighted and labeled. Extending the idea of probabilistic couplings to the setting of graphs, we first introduce the notion of a graph joining of two graphs G and H, which is a graph K on the product of the vertex sets of G and H that has G and H as marginals in an appropriate sense. Given two graphs and a vertex-based cost function, OGJ aims to find a graph joining that minimizes the expected cost. After establishing the basic properties of the OGJ problem, we provide theoretical results connecting the OGJ problem to the graph isomorphism problem. In particular, we provide a variety of sufficient conditions on graph families under which OGJ detects and identifies isomorphisms between graphs within the family.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Friday Oct 17, 2025<\/strong><\/li>\n\n\n\n<li><strong>Time: <\/strong>3:00pm<\/li>\n\n\n\n<li><strong>Location: <\/strong>Fret 302<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Speaker<\/span>: Helen Li<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Title<\/span>: <em>Mean-Field Asymptotics of Entropic OT Hessian Spectra at Fixed Regularization on Random Point Clouds<\/em><\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Abstract<\/span>: We investigate how the eigenvalues of a canonical Hessian matrix arising in <strong>entropic optimal transport (OT)<\/strong> behave as the sample size increases. Given N uniformly sampled points from a bounded region with Lipschitz boundary&nbsp;and a fixed regularization parameter \\epsilon&gt;0, we show that the smallest nonzero eigenvalue of the associated Sinkhorn matrix scales as c_\\epsilon&nbsp;\/N with high probability. The constant c_\\epsilon&nbsp;is determined by the spectral gap of a Gaussian smoothing operator defined over \\omega. In the limit of small \\epsilon, the Gaussian smoothing operator approaches the Neumann Laplacian, revealing a geometric connection between OT regularization and diffusion. These findings provide a theoretical foundation for understanding the scaling and stability of large-scale entropic OT problems.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Friday Oct 3, 2025<\/strong><\/li>\n\n\n\n<li><strong>Time: <\/strong>3:00pm<\/li>\n\n\n\n<li><strong>Location:<\/strong> Fret 302<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Speaker<\/span>: Chris Gartland<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Title<\/span>: <em>Introduction to Wasserstein Metrics II<\/em><\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Abstract<\/span>: I will continue with the introduction to Wasserstein-1 metrics and transportation cost norms on graphs and metric spaces.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Friday Sept 26, 2025<\/strong><\/li>\n\n\n\n<li><strong>Time: <\/strong>3:30pm<\/li>\n\n\n\n<li><strong>Location: <\/strong>Fret 302<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Speaker<\/span>: Kevin McGoff<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Title<\/span>: <em>Optimal transport in ergodic theory and dynamical systems<\/em><\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Abstract<\/span>: In this expository talk, I will provide an introduction to the use of optimal transport in the setting of ergodic theory and dynamical systems. In this setting it is natural to consider a constrained set of couplings that respect the dynamics, called joinings. Originally introduced by Furstenberg in 1967, joinings have proved to be an influential and powerful tool for studying stationary dynamics. I will describe the setting, define joinings, and describe some of the ways that optimal transport has made an impact. No prior knowledge of dynamical systems will be assumed.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Friday Sept 19, 2025<\/strong><\/li>\n\n\n\n<li><strong>Time: <\/strong>3:00pm<\/li>\n\n\n\n<li><strong>Location: <\/strong>Fret 302<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Speaker<\/span>: Helen Li<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Title<\/span>: <em>Condition number of Hessian of Entropy-Regularized OT and other types of modified optimal transport&nbsp;problem.<\/em><\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Abstract<\/span>: I will begin by discussing the condition number for the benchmark example of equally spaced points on the unit circle, and then pose questions related to datasets consisting of random samples. I will also explain the main ideas and results from&nbsp; <a href=\"https:\/\/arxiv.org\/abs\/2107.12364\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/arxiv.org\/abs\/2107.12364<\/a>. Next, I will turn to other types of modified optimal transport with improved regularity properties, focusing in particular on unbalanced OT. For this part, I will primarily follow the results presented in <a href=\"https:\/\/arxiv.org\/pdf\/2211.08775\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/arxiv.org\/pdf\/2211.08775<\/a>&nbsp;<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Friday Sept 12, 2025<\/strong><\/li>\n\n\n\n<li><strong>Time: <\/strong>2:30pm<\/li>\n\n\n\n<li><strong>Location: <\/strong>Fret 302<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Speaker<\/span>: Helen Li<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Title<\/span>: <em>Robust Numerical Differentiation for Entropy-regularized Optimal Transport (EOT) with application to Shuffled Regression<\/em><\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Abstract<\/span>: In this presentation, I will begin by introducing shuffled regression and entropic optimal transport (EOT) as one possible approach. I will then discuss the derivatives of EOT, provide a brief overview of numerical condition numbers, and explain how to compute them robustly. I will present an example of shuffled regression that could serve as a potential benchmark for future numerical algorithm comparisons. Finally, I would like to discuss future work, extensions, and possible collaborations among the audience.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Friday Sept 5, 2025<\/strong><\/li>\n\n\n\n<li><strong>Time: <\/strong>2:30pm<\/li>\n\n\n\n<li><strong>Location: <\/strong>meet at Fret 302, but may have to move if room is taken<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Speaker<\/span>: Chris Gartland<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Title<\/span>: <em>Introduction to Wasserstein Metrics<\/em><\/li>\n\n\n\n<li><span style=\"text-decoration: underline\">Abstract<\/span>: I will give an introductory talk defining Wasserstein-p metrics, mostly focused on p=1. Basic properties and interesting questions will be discussed.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Organizers: Chris Gartland &amp; Kevin McGoff Overview: This Fall 2025-Spring 2026 seminar will cover a broad range of topics related to optimal transport, determined by the interests of the participants. There will be an emphasis on expository talks, and graduate students are encouraged to attend and to give talks. References for external reading are provided. 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