My current research focuses on the Baum-Connes conjecture, including its connections to Kazhdan’s property (T). More generally, I am interested in the interaction between operator algebras, group theory, and algebraic topology, with the first one being in the centre. In my dissertation, I have studied the Baum-Connes assembly map for certain discrete groups involving their K-theory and (Davis-Lück’s picture of) equivariant K-homology. Previously, I have been working on simplicity and the unique trace property of group Lp-operator algebras.
Preprints and papers in preparation
- Equivariant K-homology and K-theory for some discrete planer affine groups. (with R. Flores, A. Valette), arXiv
- Higher Kazhdan projections: K-theory and L² Betti numbers, Part I. (with H. Wang) (in preparation)
- Higher Kazhdan projections: K-theory and L² Betti numbers, Part II. (with H. Wang) (in preparation)
Published and accepted articles
- Higher Kazhdan projections, L2 Betti numbers, and Baum-Connes conjectures. (with K. Li, and P. Nowak ), J. Noncommut. Geom., to appear, arXiv
- K-theory and K-homology of the wreath products of finite with free groups. Illinois J. Math. 63 (2019), no. 2, 317–334, doi, arXiv
Remark: the title of the article was printed mistakenly as
“K-theory and K-theory of finite wreath products with free groups”
- K-theory and K-homology for the lamplighter groups of finite groups. (with R. Flores, and A. Valette), Proc. Lond. Math. Soc. (3) 115 (2017), no. 6, 1207-1226. doi, arXiv
- K-theory for the C*-algebras of solvable Baumslag-Solitar groups. (with A. Valette), Glasg. Math. J. 60 (2018), no. 2., 481-486. doi, arXiv
- Simple Lp-operator crossed products with unique trace property. (with S. Hejazian), J. Operator Theory 74 (2015), no. 1., 133-147. doi, arXiv
- An explicit approach to the Baum-Connes conjecture for some semi-direct products.
- Commutators of Operators. (In Persian)