Research
My research sets the Baum-Connes conjecture (BC) in noncommutative geometry (NCG) as a starting point and aims to study C*-algebras, K-theory, and representation theory from various angles. My current research topics include representation theory on symmetric spaces from the viewpoint of NCG and applications of ideas in NCG into the study of algebraic K-theory.
Publications and Preprints
Bernoulli shifts on additive categories and algebraic K-theory of wreath products, with Julian Kranz, preprint (2024)
Slow exponential growth representations of Sp(n, 1) at the edge of Cowling's strip, with Pierre Julg, accepted by JOT (2023)
K-theory of noncommutative Bernoulli shifts, with Sayan Chakraborty, Siegfried Echterhoff and Julian Kranz, Math. Ann. published online (2023)
K-theory of Bernoulli shifts of finite groups on UHF-Algebras, with Julian Kranz, submitted (2022)
Crossed product approach to equivariant localization algebras, submitted (2022)
Sp(n,1) admits a proper 1-cocycle for a uniformly bounded representation, submitted (2022)
On the Baum-Connes Conjecture for Groups Acting on CAT(0)-Cubical Spaces, with Jacek Brodzki, Erik Guentner and Nigel Higson, IMRN, published online (2020)
Groups with Spanier-Whitehead duality, with Valerio Proietti, Ann. K-theory 5 (2020), 465-500
Direct Splitting Method for the Baum-Connes Conjecture, JFA 277 (2019), 2259-2287
A correction to a paper of Higson and Kasparov, JNCG 13 (2019), 797-803
On the Lifting of the Dirac Elements in the Higson-Kasparov Theorem (Master thesis), preprint (2016)
Dissertation (Penn State University, defended on February 24, 2020)
Direct splitting method for the Baum-Connes conjecture and groups acting on CAT(0)-cubical spaces
Miscellaneous
Proper Kasparov Cycles and the Baum-Connes Conjecture (2020) was withdrawn: there are unfixable mistakes in the proof of Proposition 1.6 (at the last equality, page 9) and in the proof of Lemma 1.34 (at the first line, page 30). Lemma 1.34 was crucial for the proof of main theorems, namely Theorem A and B.