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
- 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
- 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
The first draft of the documentation can be found
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.