Department of Mathematics, Washington University in St. Louis

CV

- MIT, Ph.D. under Tom Mrowka, 2016.
- Caltech, B.S. Mathematics with a minor in Control and Dynamical Systems, 2011.

- Y. I. Berchenko-Kogan and A. Stern, Constraint-preserving hybrid finite element methods for the Yang–Mills equations, in preparation.
- Y. I. Berchenko-Kogan and A. Stern, Constraint-preserving hybrid finite element methods for Maxwell's equations, in preparation.
- Y. I. Berchenko-Kogan, Duality in finite element exterior calculus and Hodge duality on the sphere, arXiv:1906.06354, 2019.
- 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.

- 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)

- 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)

- 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.