Yakov (Yasha) Berchenko-Kogan

Postdoctoral Scholar, Pennsylvania State University

CV

Appointments

• Pennsylvania State University, postdoctoral scholar with Vladimir Itskov, 2021–present.
• University of Hawaii at Manoa, temporary assistant professor with Evan Gawlik, 2019–2021.
• Washington University in St. Louis, Chauvenet postdoctoral lecturer with Ari Stern, 2016–2019.
• MIT, Ph.D. under Tom Mrowka, 2016.
• Caltech, B.S. Mathematics with a minor in Control and Dynamical Systems, 2011.

Research Publications

• Y. I. Berchenko-Kogan, Symmetric bases for finite element exterior calculus spaces, arXiv:2112.06065, 2021.
• Y. I. Berchenko-Kogan and E. Gawlik, Finite element approximation of the Levi–Civita connection and its curvature in two dimensions, arXiv:2111.02512, 2021.
• Y. I. Berchenko-Kogan, Numerically computing the index of mean curvature flow self-shrinkers, Results in Mathematics, 77, 17, 2022.
• Y. I. Berchenko-Kogan, Duality in finite element exterior calculus and Hodge duality on the sphere, Foundations of Computational Mathematics, 21, 1153–1180, 2021.
• Y. I. Berchenko-Kogan and A. Stern, Charge-conserving hybrid methods for the Yang–Mills equations, SMAI Journal of Computational Mathematics, 7, 97–119, 2021.
• Y. I. Berchenko-Kogan and A. Stern, Constraint-preserving hybrid finite element methods for Maxwell's equations, Foundations of Computational Mathematics, 21, 1075–1098, 2021.
• Y. I. Berchenko-Kogan, Bounds on the index of rotationally symmetric self-shrinking tori, Geometriae Dedicata, 213, 82–106, 2021.
• Y. I. Berchenko-Kogan, The entropy of the Angenent torus is approximately 1.85122, Journal of Experimental Mathematics, 2019.
• Y. I. Berchenko-Kogan, Duality in finite element exterior calculus, arXiv:1807.01161, 2018.
• Y. I. Berchenko-Kogan, Yang–Mills Replacement, Journal of Geometric Analysis 28 (4), 3603–3656, 2018.
• D. Shi, Y. I. Berchenko-Kogan, D. V. Zenkov, and A. M. Bloch, Hamel’s formalism for infinite-dimensional mechanical systems, Journal of Nonlinear Science 27 (1), 241–283, 2017.
• Y. I. Berchenko-Kogan, Minimum product set sizes in nonabelian groups, Journal of Number Theory 132 (10), 2316–2335, 2012.
• Y. I. Berchenko-Kogan, Uncovering the Lagrangian from observations of trajectories, Caltech senior thesis, 2011.
• Y. I. Berchenko-Kogan, Distance in the ellipticity graph, arXiv:1006.4853, 2010.

General Audience Publications

• Y. I. Berchenko-Kogan, More than math: The lasting benefits of summer programs, Imagine 21 (2), 20–21, 2013.
• Y. I. Berchenko-Kogan, What do grad students in math do all day, Math Horizons 20 (3), 18–19, 2013. (français, 日本語, português)

Selected Presentations

• Numerically computing the entropy and index of mean curvature flow self-shrinkers, Geometric Analysis Festival, 2021. (recording) (slides)
• Duality in finite element exterior calculus and the Hodge star on the sphere, AMS sectional meeting, University of Hawaii, special session on numerical methods for PDEs, 2019. (slides) (slides with overlays)
• Numerical methods in geometric PDE, colloquium, 2019. (slides with overlays) (embedded videos)
• Duality in finite element exterior calculus, Finite Element Circus, 2018. (slides) (slides with overlays)
• Hamel's formalism for infinite-dimensional mechanical systems, Foundations of Computational Mathematics, 2017. (poster)
• Yang-Mills replacement, Simons Center for Geometry and Physics, mathematics of gauge fields seminar, 2017. (video recording)
• Yang-Mills replacement, AMS sectional meeting, Rutgers, special session in geometric analysis, 2015. (slides) (slides with overlays)
• Uncovering the Lagrangian of a system from discrete observations, JMM, AMS session on dynamical systems, 2012. (slides) (slides with overlays)
• Distance in the ellipticity graph, JMM, AMS session on group theory, 2011. (slides) (slides with overlays)

Teaching

• Linear Algebra and Differential Equations, spring 2021.
• Numerical Analysis, spring 2021.
• Calculus II, fall 2020.
• Calculus III, fall 2020.
• Calculus III, spring 2020.
• Accelerated Calculus III, spring 2020.
• Partial Differential Equations, fall 2019.
• Calculus III, fall 2019.
• Measure Theory and Functional Analysis II, spring 2019.
• Introduction to Lebesgue Integration, spring 2019.
• Measure Theory and Functional Analysis I, fall 2018.
• Mathematics for the Physical Sciences, spring 2018.
• Calculus II, fall 2017.
• Differential equations, fall 2016.
• Topology, fall 2016.
• Notes on Stallings Foldings, Mathcamp, 2012.