Career to date
Prior to a full time academic position
I was born in Moscow in 1981. A major life-changing event for me was passing qualifying exams to transfer from Moscow School 1239 (which was my primary and secondary school) to one of the most amazing high schools in Russia, High School 57. I did three years of studies in a specialised maths class there, and it gave me a good idea what studying to become a mathematician would be about, so I decided to stick around. 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)|
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).
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 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.