My current research is concerned with algebraic operads, their generalizations and related structures. The questions I am working on are motivated by the study of embedding spaces, deformation quantization, and Drinfeld's Grothendieck-Teichmueller group which, in turn, has links to the absolute Galois group of rational numbers and the theory of motives.

- My publications and preprints
- My papers available on the e-Print archive of Cornell University
- My Ph.D. thesis in mathematics
- My Ph.D. thesis in theoretical physics (if you read in Russian)

Algebra Seminar at Penn.

Galois Seminar at Penn.

- The slides of my talk "A manifestation of the Grothendieck-Teichmueller group in geometry".
- The slides of my talk "The Goldman-Millson Theorem revisited".
- The slides of my talk "The Intricate Maze of Graph Complexes".
Variations of this talk were presented
- at the Deformation Theory Seminar at Penn,
- at the Closing Conference for the Program on Higher Structures in Geometry and Physics at the Max Planck Institute for Mathematics,
- at several places in the Midwest in March of 2016, and
- at a couple of places in Boston area in April of 2016.

- The slides of my talk "Kontsevich's formality quasi-isomorphism is "demystified"" presented at the conference Cyclic Homology. Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland, October 2016.

A beta version of the software package for working with GT-shadows and their action on Grothendieck's child's drawings can be found here. The first draft of the documentation can be found here. For the introduction to GT-shadows, please see this paper.

Here is Jingfeng Xia's master thesis. It is devoted to the groupoid of GT-shadows for the gentle version of the Grothendieck-Teichmueller group. It also contains partial results about the connected components of this groupoid related to finite quotients of the full modular group.

Handwritten lectures on deformation quantization and the corresponding homework sets.

The software related to my joint paper with Geoffrey Schneider. This software allows one to compute Tamarkin's Ger-infinity structure on Hochschild cochains recursively. The documentation for this software can be found here.

The algebraic index theorem can be applied to the study of energy bands of molecular systems.

I serve on the editorial board of Tbilisi Mathematical Journal.