**Email**: erebrova@umich.edu

**Mailing address:** 2013 Huron Pkwy, #8, Ann Arbor, MI

48104, USA

I am Liza, 5-th year graduate student at the University of Michigan, Department of Mathematics. My advisor is Roman Vershynin.

I received my specialist degree (B.S.+M.S. equivalent) in Mathematics at Moscow State University under supervision of Professor Vladimir Bogachev in 2012.

Here you can find my CV (academic) and my Resume (focused on more applied projects and interests) - version November, 2017

You also can read about my

My main research interests are in high-dimensional probability and geometry, as well as their applications to the study of large high-dimensional data.

**PhD research:** my current research is concentrated around non-asymptotic random matrix
theory.

I like studying spectral structure of large, but finite random matrices. One of the challenging cases is when matrix entries distributions are heavy-tailed (comparing to the standard gaussian case). Here we've shown that in terms of invertibility heavy-tailed matrices behave exactly as nice as sub-gaussian do:

- Coverings of random ellipsoids, and invertibility of matrices with i.i.d. heavy-tailed entries (with K.Tikhomirov)
- Israel J. Math., to appear. arXiv:1508.06690

This is not the case for the operator norm of heavy-tailed matrices. In the next paper we identified the conditions when the norm of an i.i.d. square random matrix can be improved to the ''ideal'' oder \(O(\sqrt{n})\) by modifying just a small fraction of its entries. We've also identified log-optimal dependence between the size of correction and the resulting norm:

- Norms of random matrices: local and global problems (with R.Vershynin)
- Advances in Mathematics, to appear. arXiv:1608.06953

**Applied research:** in Summer 2017 I worked as an intern at Scalable Solvers Group,
Lawrence Berkeley National Lab.
I investigated applications of STRUMPACK
linear solver
to kernel matrices, as well as various
preprocessing techniques improving the efficiency of STRUMPACK usage.

More information:

- Slides from an informal final presentation within the research team.
- Final report (technical part) for NSF (who sponsored my internship).

Please see the Talks page for (almost) complete list of my public presentations, usually with abstracts and sometimes with relevant slides.

Quick links:- Invited research talks
- Expository talks at UofMichigan
- Expository Machine Learning talks at Berkeley Lab

This semester I am a TA for **Math 623 Computational Finance** at University of Michigan.
Students can find all the information on the Canvas page, or email me.

**Office hours:**

Wednesday 4 - 5:30PM

Thursday 11:30 - 1PM

in 3862 East Hall

Earlier at UofMichigan I worked as primary instructor for Math 115 (Calculus 1) and led Matlab labs and problem solving recitations for Math 216 (Differential Equations).

Back in Moscow, I worked as a calculus instructor for high school students at 57-th math school (2008-2012) and as an algebra teacher at Kolmogorov math and physics high school (2012-2013).

In addition to doing research and explaining math, I enjoy coding and playing with data. Back in Moscow, I completed two year CS program in Yandex Data Analysis school, and it was such a great time. Nowadays I infrequently participate in online contests alone or with friends.

My other interests include all that I find beautiful or challenging. For example, music, art, cats, cities, mountains, puzzles... Finally, I love talking to people, sharing experiences and drinking coffee - dark roast preferrable.

“Poirot,” I said. “I have been thinking.”

“An admirable exercise my friend. Continue
it.”

(Agatha Christie, Peril at End House)