Yekaterina Epshteyn

Professor at the Department of Mathematics
The University of Utah


Numerical and Applied Analysis, Scientific Computing, Applied Mathematics  


CV pdf

Brief Version of the Research Statement pdf

I am fortunate to be recognized as one of the

Simons Fellows in Mathematics 2025, Simons Foundation

and given an amazing opportunity to dedicate more time to the research in 2025-2026

About Our DMREF Project link

(Upcoming) Co-Organizer National Science Foundation (NSF) CompMath PI Meeting 2025, Salt Lake City, The University of Utah, May 8 - May 9, 2025, NSF CompMath Meeting 2025

Co-organized BIRS Workshop on "Mathematics of Multiscale and Multiphysics Phenomena in Materials Science" at Banff, Canada, June 16 - June 21, 2024, link

Watch a presentation given at the IPAM Workshop "Scale-Bridging Materials Modeling at Extreme Computational Scales" at UCLA on April 18th, 2023, link

Service Statement (Brief Version) pdf

Research Interests:  

  • Numerical Methods for PDEs, Scientific Computing, Applied Mathematics, Applied and Numerical Analysis
  • Development and Analysis of Structure-Preserving Models and Numerical Algorithms
  • Interdisciplinary Research and Collaboration
  • Mathematical and Computational Modeling of Materials
  • Shallow Water Models
  • Computational Fluid Dynamics
  • Biomedical Applications
  • Finite Volume, Finite Difference Schemes, Finite Element Methods
  • Particle Methods
  • Difference Potentials Method
  • Stochastic Galerkin and Uncertainty Quantification Methods
Publications

  • Current Second-Year PhD Graduate Students:
      Caleb Albers (Summer 2023 - present)
      Yinqian Yu (Fall 2023 - present, jointly with Akil Narayan)
  • Alumni:
    • Postdocs:
        • Bohyun Kim (Fall 2023 - Spring 2024)
        Kamala (Chang) Liu (Fall 2021 - Fall 2022), Currently: China (due to family reasons)
        Michael Medvinsky (Postdoc, Fall 2013 - Spring 2015), Current Position: Research Assistant Professor, Department of Mathematics, North Carlina State University
    • Ph.D. Graduate Students:
        Dihan Dai (Ph.D student Fall 2017 - Spring 2022, co-advised with A. Narayan)
        First Job After Ph.D: Applied Scientist I (L4) at Amazon
        Thuong Nguyen (Ph.D student Fall 2016 - Summer 2022)
        First Job After Ph.D: Postdoctoral Fellow at the UT Southwestern Medical Center
        Qing Xia (Ph.D student Fall 2014 - Spring 2019)
        First Job After Ph.D: Postdoctoral Researcher at the Department of Mathematical Sciences at Rensselaer Polytechnic Institute (RPI). Dahlquist Research Fellow at KTH Royal Institute of Technology, Stockholm, Sweden.
        Kyle Steffen (Ph.D. student Fall 2013 - Spring 2018, co-advised with K. Golden)
        First Job After Ph.D: Postdoctoral Fellow at UT Austin Oden Institute for Computational Engineering and Sciences
        Jason Albright (Ph.D. student Fall 2011 - Spring 2016), First Job After Ph.D: Postdoctoral Fellow at the Theoretical Division at Los Alamos National Lab (LANL)
        R&D Staff Scientist 2 at the Theoretical Division at Los Alamos National Lab (LANL)
        Group Alumni Jason Albright took part (at around 1:20 in a video) in a video about Los Alamos National Laboratory
        Article about Group Alumni Jason Albright article
        Patrick Bardsley (Ph.D. student Fall 2011 - Spring 2016; co-mentor: F. Guevara Vasquez), First Job After Ph.D: Postdoctoral Fellow at the Department of Mathematics and Oden Institute for Computational Engineering and Sciences at the University of Texas at Austin
        Currently: Machine Learning Engineer at Cirrus Logic
        Gustav Ludvigsson (Currently Ph.D. student at Uppsala University under Prof. Gunilla Kreiss. Collaboration on a joint research project in 2016 - 2017, and a visiting Ph.D student in Spring 2017)
        Simon Sticko (Ph.D. student at Uppsala University under Prof. Gunilla Kreiss, defended his Ph.D in Spring 2018. Collaboration on a joint research project in 2016 - 2017, and a visiting Ph.D student in Spring 2017)
        First Job After Ph.D: Applied Researcher, Fraunhofer-Chalmers Centre for Industrial Mathematics
        Siyang Wang (Ph.D. student at Uppsala University under Prof. Gunilla Kreiss, defended his Ph.D in Spring 2017. Collaboration on a joint research project in 2016 - 2017),
        First Job After Ph.D: Postdoctoral Fellow at the Department of Mathematics at Chalmers University of Technology
    • REU Students:
        James Eckstein (Spring 2020 and Spring-Summer 2021), REU project "Numerical Algorithms for Automated Dynamic Grain Boundary Network Identification"
        Ph.D. student in Applied Physics at Columbia University since Fall 2023
        Camille Humphries (Spring 2019-Fall 2019), REU project "Fast Numerical Algorithms for Models with Nonlinear Diffusion"; (May 2013 - May 2014): REU project "Central-Upwind Schemes for Shallow Water Models"
        Charlotte Blake (REU student, Fall 2018 - Spring 2019): Project "Numerical Algorithms with Application to Data Processing in Materials Science (Polycrystalline Materials)"
        Ph.D student in Mathematics at the University of Illinois at Urbana-Champaign since Fall 2019
        Gabrielle Legaspi (Spring 2019), REU project; (Summer 2017): Introduction to Research
        Current Position: Biostatistician, New York, NY
        Alex Henabray (REU student, Fall 2014): REU project "Numerical Methods for Interface Problems"
        Spencer Phippen (REU student, May 2013 - January 2014): Project "Difference Potentials Method for Interface Problems"
        Current Position: Software Engineer at Google


        Recent Research Talks to Middle School Students, Spring 2013:

        Project Youth - University of Utah (for 6th Graders from local schools), Spring 2013, Slides

        The presentation "Fun Adventure in Applied Mathematics or What is Applied Mathematics?" was illustrated by experiments:
      • Generating waves in a pan with a whole milk
      • And experiments using soap bubbles


        • Affiliated Faculty Member, Center for Quantitative Biology, html

      Current Teaching:

      • Spring 2025, Math 6630 jointly with Math 6910-044: Numerical Solutions of Partial Differential Equations: Selected Advanced Topics in PDEs and in Numerical Methods for PDEs
      • Spring 2025, Math 6620: Analysis of Numerical Methods II
      • Fall 2024, Math 6610: Analysis of Numerical Methods I
      • Spring 2024, Math 6630: Numerical Solutions of Partial Differential Equations: Selected Numerical Methods
      • Fall 2023, Math 6610: Analysis of Numerical Methods I
      • Fall 2023, Math 2210-5: Calculus III
      • Spring 2023, Math 6620: Analysis of Numerical Methods II
      • Fall 2022, Math 5440-6850: Introduction to Partial Differential Equations
      • Fall 2022, Math 2210-4: Calculus III
      • Spring 2022, Math 6630: Numerical Solutions of Partial Differential Equations: Selected Numerical Methods
      • Spring 2022, Math 4800: REU-Selected Numerical Algorithms and Their Analysis
      Contact Information

      Department of Mathematics
      The University of Utah
      Salt Lake City, UT 84112
      e-mail: epshteyn@math.utah.edu
      phone: (801) 585 - 1644