Email: erebrova@umich.edu

Mailing address: 2013 Huron Pkwy, #8, Ann Arbor, MI
48104, USA

## Hi!

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

## Research

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.

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

Undergraduate research: I was studying functions of bounded variation on infinite dimensional spaces for my masters thesis at Moscow State University. I considered several classes of functions (bounded variation and bounded semivariation), investigated their properties and compared them. Related publication:

Functions of bounded variation on infinite-dimensional spaces with measures (with V.Bogachev)

## Talks and presentations

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

## Teaching

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).

## Random likes

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)