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papers

Publications

Publications 2025 Kim, H.-Y., Kim, M.-Y., & Kim, Y.-J. (2025). Fractionation by persistent random walk and two-coefficient diffusion law. Physica A: Statistical Mechanics and Its Applications, 674, 130718. handle doi Liu, W., & Sofiani, M. (2025). Bifurcation and stability of stationary shear flows of Ericksen-Leslie model for nematic liquid crystals. arxiv Liu, H., & Tzavaras, A. E. (2025). Variational structure of Fokker-Planck equations with variable mobility handle arxiv AlNajjar, A., Spirito, S., & Tzavaras, A. E. (2025). Asymptotic limits for strain-gradient viscoelasticity with

Teaching

Teaching

Courses Real Analysis - AMCS 235 ​​​​​This is a basic introductory graduate level course on Real Analysis. It starts with a review of notions connected with the real analysis of continuous functions including the Ascoli-Arzela Theorem on compactness of sequences of continuous functions, and the Stone-Weierstrass Theorem for the approximation of continuous functions. The main body of the course will be the theory of measure and integration. The last part of the course deals with various topics in Real Analysis, like Differentiation, approximation of $L^p$ functions, and Fourier Series. The

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Applied PDE Research Group

Applied Partial Differential Equations Research Group Professor Athanasios Tzavaras leads the Applied PDE group, which stands for Applied Partial Differential Equations Research group areas of expertise and current scientific interests: analysis of partial differential equations, mathematical modeling, and numerical methods Our group is interested in mathematical modeling, analysis and the development of numerical methods for evolutionary partial differential equations in fluid and solid mechanics. Subjects of current interest include: ​Relative entropy and the comparison of thermomechanical

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Research topics

We study a class of nonlinear kinetic equations derived from a generalized Vlasov-Poisson model under certain physical assumptions. We prove the local existence and uniqueness of solutions in a framework of analytic functions using the Banach fixed-point theorem. Vlasov equations, analytic solutions, analytic norms, fixed point method. Effect of anisotropic diffusivity, development of gradients due to discontinuities in diffusivity. Diffusion of multicomponent systems, cross diffusion systems, mathematical properties, renormalized solutions, uniqueness of weak solutions. Thermodynamics, Soret

Talks Alexey Miroshnikov

Dr. Alexey Miroshnikov, Senior Principal Research Scientist, Discover Financial Services Stability analysis of game-theoretic feature attributions for machine learning models Seminar Event Start: 2024-11-11 - 16:00 Event End: 2024-11-11 - 17:00 Location: Building 1, Level 3, Room 3119 Abstract In this work, we study the feature attributions of machine learning (ML) models originating from linear game values and coalitional values, defined as operators on appropriate functional spaces. The main focus is on random games based on conditional and marginal expectations. It is well-known from the

Talks Anastasia Molchanova

Dr. Anastasia Molchanova, Postdoctoral Fellow, TU Wien, Austria Sobolev Homeomorphisms in Nonlinear Elasticity Mathematics and Applications Colloquium Event Start: 2024-10-22 - 16:00 Event End: 2024-10-22 - 17:00 Location: Building 1, Level 3, Room 3119 Abstract Sobolev homeomorphisms play a fundamental role in geometric function theory, calculus of variations, and continuum mechanics. In this talk, we discuss key properties of these mappings that are crucial from both modeling and analytical perspectives, such as continuity, injectivity, and Lusin's (N) and (N-1) conditions. We then present a
visitors

Visitors

Visitors 2025 Saud Alraddadi, Purdue University, USA Summer 2025 2024 Dr. Alexey Miroshnikov, Senior Principal Research Scientist, Discover Financial Services November 2024 Seminar Stability analysis of game-theoretic feature attributions for machine learning models Graduate Seminar Mathematics of Explainable AI with Applications to Finance Dr. Anastasia Molchanova, Postdoctoral Fellow, Institute of Analysis and Scientific Computing, TU Wien, Austria October 2024 Mathematics and Applications Colloquium Sobolev Homeomorphisms in Nonlinear Elasticity Seminar Limits of Sobolev Homeomorphisms

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Visitors 2023 Professor Jose Carrillo, University of Oxford, UK January 8th - January 19th Mathematics and Applications Colloquium AMCS CEMSE Nonlocal Aggregation-Diffusion Equations: entropies, gradient flows, phase transitions and applications Prof. Jose Carrillo, Department of Mathematics, University of Oxford, UK Tuesday, January 10, 2023, 15:30 - 17:00 Building 2, Level 5, Room 5209 Fokker-Planck equations Cucker-Smale orientation dynamics McKean-Vlasov equations Keller-Segel-type models Contact Person Athanasios Tzavaras This talk will be devoted to an overview of recent results in