Yekaterina Epshteyn

Professor at the Department of Mathematics
The University of Utah


Numerical Analysis, Scientific Computing, Applied Mathematics  


CV pdf

Brief Version of the Research Statement pdf

About Our New DMREF Project link

Watch a presentation given at the IPAM's 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
  • Mathematical and Computational Modeling of Materials
  • Shallow Water Models
  • Finite Volume, Finite Difference Schemes
  • Particle Methods
  • Difference Potentials Method
  • Finite Element Methods
  • Computational Fluid Dynamics
  • Biomedical Applications
Publications

  • Current Postdoctoral Collaborators/Mentees:
  • Current PhD Graduate Students:
  • Current First-Year PhD Graduate Students:
      Caleb Albers (Summer 2023 - present)
      Batuhan Bayir (Fall 2023 - present)
      Dongwan Kim (Fall 2023 - present)
      Yinqian Yu (Fall 2023 - present, jointly with Akil Narayan)
  • Alumni:
    • Postdocs:
        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
    • 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)
        Currently: 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 starting 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 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