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.
Deformation Theory 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.
Handwritten lectures on deformation quantization and
the corresponding homework sets.
The software related to
my joint paper with
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.
I came from a family of mathematicians.
Few articles of my father Alexandr N. Dolgushev are available on MathSciNet.
An article of my mother
Nadezda V. Dolgusheva is also available