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.

Algebra Seminar at Penn.
Galois Seminar at Penn.

Slides of some selected talks

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.