My main area of research is Algebra. In particular, I am interested in the following:
Hopf algebras, weak Hopf algebras.
Fusion categories, monoidal categories, dualities.
Homological algebra, Cyclic homology.
Frobenius actions on cohomology.
Hom-associative algebras.
Lie algebras and their cohomology.
Orbifold invariants.
Groups with symplectic self-duality.
Representations of affine Kac-Moody Lie algebras arizing from D-modules.
Preprints on the arxiv
Papers
Hopf Cyclic Cohomology and Beyond, (with M. Khalkhali), Proceedings of Symposia in Pure Mathematics.
Mixed vs stable anti-Yetter-Drinfeld contramodules, SIGMA: Symmetry Integrability Geom. Methods Appl., doi.org/10.3842/SIGMA.2021.026.
Polarized-VAE: Proximity Based Disentangled Representation Learning for Text Generation, (with V. Balasubramanian, I. Kobyzev, H. Bahuleyan, O. Vechtomova), EACL 2021, 8 pages.
Categorified Chern character and cyclic cohomology, 32 pages.
Anti-Yetter-Drinfeld modules for quasi-Hopf algebras, (with I. Kobyzev), SIGMA: Symmetry Integrability Geom. Methods Appl., doi.org/10.3842/SIGMA.2018.098.
A categorical approach to cyclic cohomology of quasi-Hopf algebras and Hopf algebroids, (with I. Kobyzev), Appl. Categ. Structures, doi.org/10.1007/s10485-018-9544-0.
Extensions and duality, 16 pages.
On the anti-Yetter-Drinfeld module-contramodule correspondence, J. Noncommut. Geom., doi.org/10.4171/JNCG/327.
Invariance properties of cyclic cohomology with coefficients, J. of Algebra, doi.org/10.1016/j.jalgebra.2019.10.034.
Monoidal Categories, 2-Traces, and Cyclic Cohomology (with M. Hassanzadeh, M. Khalkhali), Canad. Math. Bull., doi.org/10.4153/CMB-2018-016-4.
Cyclic homology for Hom-associative algebras (with M. Hassanzadeh, S. Sutlu), J. Geom. Phys., Volume 98 (2015), 40-56.
On the relative dual of an $S^1$-gerbe over an orbifold (with X. Tang, H. Tseng), Advances in Mathematics 270 (2015), 1-20.
Frobenius map and the $p$-adic Gamma function, Journal of Number Theory, Volume 132, Issue 8, (2012), 1770–1779.
Locally compact abelian groups with symplectic self-duality (with A. Prasad, M. K. Vemuri), Advances in Mathematics 225 (2010), no. 5, 2429–2454.
Frobenius map for quintic threefolds, International Mathematics Research Notices (2009), Volume 2009, Number 13, 2519–2545.
Frobenius map on local Calabi-Yau manifolds, Journal of Mathematical Physics 50 (2009), no. 2, 022302, 14 pp.
The BRST reduction of the chiral Hecke algebra, Advances in Mathematics 220 (2009), no. 6, 1657–1688.
Twisted de Rham cohomology, homological definition of the integral and "Physics over a ring" (with A. Schwarz), Nuclear Physics B, Volume 809 (2009), no. 3, p. 547–560.
$p$-adic superspaces and Frobenius (with A. Schwarz), Communications in Mathematical Physics, Volume 282 (2008), Number 1, p. 87–113.
Gelfand-Fuchs cohomology of invariant formal vector fields (with X. Tang), Mathematical Research Letters Volume 15 (2008), Number 1, p. 129–149.
Supergeometry and Arithmetic Geometry (with A. Schwarz), Nuclear Physics B, Volume 756 (2006), Issue 3, p. 207–218.
Some remarks on Gopakumar-Vafa invariants (with A. Schwarz), Pure and Applied Mathematics Quarterly Vol 1 (2005), Number 4, p. 817–826.
