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Today

Di Qi, Purdue University, Statistical reduced-order models and machine learning-based closure strategies for turbulent dynamical systems

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The capability of using imperfect statistical reduced-order models to capture crucial statistics in complex turbulent systems is investigated. Much simpler and more tractable block-diagonal models are proposed to approximate the complex and high-dimensional turbulent dynamical equations using both parameterization and machine learning strategies. A systematic framework of correcting model errors with empirical information theory is…

Jonathan Zhu, Princeton, Waists, widths and symplectic embeddings

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Waists and widths measure the size of a manifold with respect to measures of families of submanifolds. We’ll discuss related area estimates for minimal submanifolds, as well as applications to quantitative symplectic camels. Zoom invitation is sent to the geometry and topology seminar list. If you are not on the list, please, contact Peter McGrath…

Ivan Yotov, University of Pittsburgh, A nonlinear Stokes-Biot model for the interaction of a non-Newtonian fluid with poroelastic media

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A nonlinear model is developed for fluid-poroelastic structure interaction with quasi-Newtonian fluids that exhibit a shear-thinning property. The flow in the fluid region is described by the Stokes equations and in the poroelastic medium by the quasi-static Biot model. Equilibrium and kinematic conditions are imposed on the interface. A mixed Darcy formulation is employed, resulting…

Daniel Sanz-Alonso, University of Chicago, Department of Statistics and CCAM, Finite Element and Graphical Representations of Gaussian Processes

SAS 4201

Gaussian processes (GPs) are popular models for random functions in computational and applied mathematics, statistics, machine learning and data science. However, GP methodology scales poorly to large data-sets due to the need to factorize a dense covariance matrix. In spatial statistics, a standard approach to surmount this challenge is to represent Matérn GPs using finite…

Mikhail Karphukin, Caltech, Eigenvalues of the Laplacian and min-max for the energy functional

SAS 4201

The Laplacian is a canonical second order elliptic operator defined on any Riemannian manifold. The study of optimal upper bounds for its eigenvalues is a classical problem of spectral geometry going back to J. Hersch, P. Li and S.-T. Yau. It turns out that the optimal isoperimetric inequalities for Laplacian eigenvalues are closely related to…

Juan Carlos, Centro de Modelización Matemática, Ecuador, Bilevel learning for inverse problems

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In recent years, novel optimization ideas have been applied to several inverse problems in combination with machine learning approaches, to improve the inversion by optimally choosing different quantities/functions of interest. A fruitful approach in this sense is bilevel optimization, where the inverse problems are considered as lower-level constraints, while on the upper-level a loss function based…

Gloria Mari Beffa, University of Wisconsin, Discrete Geometry of Polygons and Soliton Equations

SAS 4201

 In this talk we will discuss the connection between invariant evolutions of polygons and completely integrable discrete systems via polygonal geometric invariants. We will give examples and show how some open problems for bi-Hamiltonian structures of discrete systems were made easier and solved using this correspondence. If time allows we will discuss some open problems.…

Kamala Dadashova, NC State, Parameter subset selection for a mathematical model of antibody therapies for neurological diseases

SAS 1220

A significant challenge in the development of drugs to treat central nervous system (CNS) disorders is to attain sufficient delivery of antibodies across blood-brain barriers (BBB). Since not all antibodies can pass through BBB, it is crucial to understand antibody exposure in the CNS quantitatively to construct drug characteristics and identify proper dosing regimens. We…

Alexey Miroshnikov, Discover Financial Services, Wasserstein-based fairness interpretability framework for machine learning models

SAS 4201

The objective of this talk is to introduce a fairness interpretability framework for measuring and explaining the bias in classification and regression models at the level of a regressor distribution. In our work, we measure the model bias across sub-population distributions in the model output using the Wasserstein metric. To properly quantify the contributions of…

Daniel Stern, University of Chicago, Steklov Eigenvalues on Surfaces

SAS 4201

As described in the previous week's talk by Mikhail Karpukhin, there is a rich interplay between isoperimetric problems for Laplace eigenvalues on surfaces and the study of harmonic maps and minimal surfaces in spheres. Over the last 10-15 years, a program initiated by Fraser and Schoen has revealed a similar relationship between isoperimetric problems for the…

Stéphane Gaubert, École Polytechnique, France, What tropical geometry tells us about linear programming and zero-sum games

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Tropical convex sets arise as ``log-limits'' of parametric families of classical convex sets. The tropicalizations of polyhedra and spectrahedra are of special interest, since they can be described in terms of deterministic and stochastic games with mean payoff. In that way, one gets a correspondence between classes of zero-sum games, with an unsettled complexity, and classes…