# About me

## Currently...I am an assistant professor above the merit bar at School of Mathematics of Trinity College Dublin, and a fellow of Trinity College Dublin. In 2017-19 I serve as the Director of Undergraduate Teaching and Learning at School of Mathematics. I am also a member of the Executive Committee of Hamilton Mathematics Institute.## Career to date- Solomon Lefschetz Chair of mathematics at CINVESTAV, while on a research leave from Trinity College Dublin (2016-2017)
- Assistant professor in pure maths at Trinity College Dublin (2012- )
- Research fellow at University of Luxembourg (2011-12)
- Lecturer in mathematics, Trinity College Dublin (2010-11)
- Research fellow at Dublin Institute for Advanced Studies (2008-10)
- Lecturer in mathematics, Trinity College Dublin (2007-08)
During the above periods, I also held shorter visiting positions in Max-Planck institute for mathematics in Bonn (visiting fellow, "Higher Structures in Geometry and Physics" programme, 2016), Isaac Newton Institute for Mathematical Sciences in Cambridge (visiting fellow, "Grothendieck-Teichmüller Groups, Deformations and Operads" programme, 2013) and University Lyon 1 (professeur invité, 2012). ## Prior to a full time academic positionI was born in Moscow in 1981. My primary and secondary school was a specialised English language school, Moscow School 1239, and my high school was a specialised mathematics school, Moscow State School 57. Upon graduation from high school, I did most of my studies both at Moscow State University and at Independent University of Moscow; my supervisors during those studies were Boris Feigin and Mikhail Zaicev. After I graduated from those universities in 2003, I continued working with my supervisors towards a Ph.D. in maths, which I got from Moscow State University in 2007. During my last year of Ph.D. studies, I held a Marie Curie fellowship at the maths department of Budapest Technical University, my mentor there was Andras Szenes. |
(photo by "Face2Face with Marriage Equality" project) |

# For Junior Freshman students

As a Director of Undergraduate Teaching and Learning (2017-19), I gave welcome presentations to incoming maths and TSM students. Here they are: maths and TSM. Very similar presentations were prepared previously by Paschalis Karageorgis; probably all nice things in these PDF files are his work, and all misprints are mine.

# Finding relevant info on my homepage

After investing some time into organising this page, I ended up putting so much stuff online, that I myself need some guidelines about where everything is, and it would be unfair to assume that whoever is reading this has a better idea about it. So here it goes. This main page (button "Home" above) contains brief info about me and an outline of my research interests. The button "Research" links to info about my research: publications and preprints, seminar and conference talks (including materials of those where appropriate), research-related travel, and, last but not the least, some words addressed to prospective postgraduate students. The button "Teaching" links to information and materials for courses I taught since 2007. The button "Links" contains links to pages of some friends and colleagues (that selection is somewhat sporadic and rarely updated, my sincere apologies for that), and also a selection of pages I check out from time to time (which is mostly for me to find easily). The "Contact me" button is mostly self-explanatory (although one very useful bit on the page it links to is maybe an unexpected bonus: detailed directions to my office in TCD).

# Research interests

My main research area is homotopical algebra and its applications; I am also really interested in operads, Gröbner bases, combinatorics, homological algebra, representation theory, deformation theory.

The figure on top of this page is actually connected to all of these: it shows how one proves that the Jacobi identity, the defining property of Lie algebras, forms a Gröbner basis of the shuffle operad corresponding to the operad

*Lie*controlling Lie algebras. There is a fair bit of combinatorics lurking around here all the time, since computations in shuffle operads are related to patterns in labelled trees. Homological and homotopical algebra manifest themselves in the fact that this computation is the easiest way to show that the operad

*Lie*is Koszul (that is possesses extremely nice homological properties), and subsequently to study the homotopy category of differential graded Lie algebras, which in turn is crucial for the purposes of deformation theory, since deformation questions are controlled by homotopy Lie algebras. Representation theory appears here only sideways: the Koszul property of the operad

*Lie*allows, by computing the Euler characteristics of some chain complexes, to calculate in one easy go the characters of the symmetric group representations in the spaces

*Lie(n)*for all

*n*.

I am often asked about a good reading reference on operads. There are two suggestions that I have. A wonderful comprehensive reference book is a recent textbook Algebraic operads by Jean-Louis Loday and Bruno Vallette. A companion textbook which might be a more accessible reading for undergraduate and postgraduate students making their first steps in the subject is the book Algebraic operads: an algorithmic companion which I wrote in collaboration with Murray Bremner.

# Some popular maths lectures

- "Using residues to count trees", a talk at the CINVESTAV summer school for prospective postgraduate students, July 2017: YouTube Video.
- "Exploring the neighbourhood of infinity", a talk at the Science Open Day at Trinity College Dublin, November 2015: YouTube Video
- "Mathematics of complexity research theme at Trinity", not quite a lecture, but a video in making of which I participated in 2014: YouTube Video
- "Algebra meets geometry, or counting with pictures", TCD Open Day, December 1, 2012. Beamer presentation: PDF.

# On research funding priorities etc.

It is fairly well known that it gets more and more difficult for researchers in pure science to be funded in Ireland. I do believe that all the staff of major research funding agencies who decide to not even send pure science proposals for peer review, claiming that those proposals are not "relevant" or "do not fall into remit", must spend some of their precious time listening to the following song of relevant as ever Tom Lehrer.