My research is mainly focused at investigation of internal structure of string and M-theory and of supergravity as their field-theoretical effective formulation. One of the possible descriptions of such structure can be given by presenting classes of solutions and listing their properties. For that one searches and classifies explicit solutions of 11D and of lower dimensional supergravity as well as looks for duality symmetries of the theory that relates different solutions. The duality implies that the string and/or the membrane does not distinguish between backgrounds related by such transformations rendering the same physics for dramatically different solutions.

Among these one finds such fascinating objects as black holes, black rings, exotic branes and many others, which appear in physics in various aspects, such as black objects’ thermodynamics, information paradox, searches of de Sitter string vacua, near-horizon geometry, worldvolume gauge theories etc.

Among the tools I use in my research are the techniques of special geometry (special holonomy, Killing spinors etc.) and those of Double/Exceptional Field theory. The latter allow to address the problem in a more duality-covariant way, construct exotic objects and even catch some non-perturbative features.

1. Non-abelian fermionic T-dualities (Ilya Bakhmatov, Lev Astrakhantev) 2101.08206

2. Deformations of supergravity backgrounds, gravity-Yang-Baxter correspondence, generalized supergravity in 11D (Ilya Bakhmatov, Kirill Gubarev) 1811.09056, 1906.09052, 2002.01915

3. Non-abelian U-duality (Kirill Gubarev, Yuho Sakatani) 2007.01213, 2012.13263

4. Dynamics of exotic and D-branes in doubled and extended space (Chris Blair, Axel Kleinschmidt, Eric Bergshoeff, Fabio Riccioni), 1712.01739, 1903.05601

5. Non-geometric fluxes and U-duality orbits in xFT (David Berman, Ray Otsuki, Ilya Bakhmatov, Axel Kleinschmidt), 1710.09740, 1806.00430, Review

6. Exotic branes in Double Field Theory and their geometric properties (Axel Kleinschmidt, Ilya Bakhmatov), 1607.05450,

7. Exceptional field theories (Henning Samtleben, Ilya Bakhmatov, Aidar Abzalov), 1412.7286, 1504.01523, 1512.02163