### Ethan Epperly

**Program Year:**3**Academic Institution:**California Institute of Technology**Field of Study:**Applied and Computational Mathematics**Academic Advisor:**Joel Tropp**Practicum(s):**

Lawrence Berkeley National Laboratory (2021)**Degree(s):**

B.S. Mathematics, and B.S. Computing, University of California, Santa Barbara, 2020**Personal URL:**http://ethanepperly.com

#### Summary of Research

Ethan's research is focused on the design and analysis of novel algorithms to solve large-scale linear algebra problems, which have applications in materials science, continuum mechanics, and data and network science. His work up to this point has primarily focused on rank-structured matrix techniques, for which Ethan developed a novel method of solving overlapping block low-rank completion problems. Ethan has also worked on computational models of plastic deformation in solid solution systems, where he showed that continuum diffusion can be used to explain important features of dynamic strain aging. Currently, Ethan is very excited by the potential of randomized algorithms in solving computational problems that are intractable with existing methods and is excited to begin research in this area at Caltech.#### Publications

Y. Chen, E. N. Epperly, J. A. Tropp, & R. J. Webber (2022). Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 [math.NA].E. N. Epperly & J. A. Tropp (2022). Jackknife variability estimation for randomized matrix computations. arXiv preprint arXiv:2207.06342 [math.NA].

E. N. Epperly, L. Lin, & Y. Nakatsukasa (2022). A theory of quantum subspace diagonalization. SIAM Journal of Matrix Analysis and Applications.

Nithin Govindarajan, E. N. Epperly, & Lieven De Lathauwer (2022). (Láµ£,Láµ£,1) decompositions, sparse component analysis, and blind source separation. SIAM Journal of Matrix Analysis and Applications.

E. N. Epperly, N. Govindarajan, & S. Chandrasekaran (2021). Minimal rank completions for overlapping blocks. Linear Algebra and its Applications.

E. N. Epperly, A. T. Barker, and R. D. Falgout (2020). Smoothers for matrix-free algebraic multigrid preconditioning of high-order finite elements. LLNL Technical Report.

E. N. Epperly & R. B. Sills (2020). Transient solute drag and strain aging of dislocations. Acta Materialia.

E. N. Epperly & R. B. Sills (2020). Comparison of continuum and cross-core theories of dynamic strain aging. Journal of the Mechanics and Physics of Solids, 103944.

S. Chandrasekaran, E. N. Epperly, & N. Govindarajan (2019). Graph-induced rank structures and their representations. arXiv preprint arXiv:1911.05858 [math.NA].

#### Awards

Thomas A. Tisch Prize for Graduate Teaching in CMS, 2022UCSB Mathematics Department Raymond L Wilder Award, 2020

UCSB Chancellor's Award for Excellence in Undergraduate Research, 2020

2020 Hertz Foundation Fellowship Finalist

2020 NSF Graduate Research Fellowship (declined in favor of DOE CSGF)

Achievement in Mathematics Award, Las Positas College, 2016