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.

Exploration of Grothendieck-Teichmueller(GT)-shadows and their action on Grothendieck's child's drawings

The term "GT-shadow" could have been introduced in paper Approximating Galois orbits of dessins by David Harbater and Leila Schneps from 1997. The authors used a different (but equivalent) definition of the Grothendieck-Teichmueller group but all the original ideas for "approximations" can be found in their paper.
Algebra Seminar at Penn.
Galois Seminar at Penn.

Slides of some selected talks

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.