My main research interests lie in representation and character theory of finite groups. In particular, I am interested in the so-called Local-Global conjectures in modular representation theory of finite groups with a focus on the verification of the inductive conditions for quasi-simple groups of Lie type (a.k.a. finite reductive groups). This is an accessible introduction to group theory and representation theory written by Eugenio Giannelli and Jay Taylor. A more specialized survey on Local-Global conjectures written by Gunter Malle can be found here. This note, written by Radha Kessar and Gunter Malle, describes some recent achievements in this research area by focusing on the crucial case of simple groups.
Publications & Preprints
Alperin's bound and normal Sylow subgroups (with Z. Feng and J. M. Martínez), arXiv:2502.12841. (arXiv)
Submitted.
The Brown complex in non-defining characteristic and applications, arXiv:2303.13973. (arXiv)
Submitted.
Inductive local-global conditions and generalised Harish-Chandra theory. (arXiv)
To appear in Forum Math. Sigma.
On e-local structures for Z_ℓ-spetses (with J. Semeraro). (arXiv)
Int. Math. Res. Not. IMRN, Vol. 2025 (18), 2025
A reduction theorem for the Character Triple Conjecture. (arXiv)
To appear in Proc. Lond. Math. Soc.
The Alperin Weight Conjecture and the Glauberman correspondence via character triples (with J. M. Martínez, N. Rizo). (arXiv)
To appear in Algebra & Number Theory.
The Character Triple Conjecture for maximal defect characters and the prime 2. (arXiv)
Rev. Mat. Iberoam., Vol. 41 (6), 2357-2378, 2025
Webb's conjecture and generalised Harish-Chandra theory. (arXiv)
Bull. Lond. Math. Soc., Vol 57 (4), 1083-1092, 2025
A local-global principle for unipotent characters. (arXiv)
Forum Math. Sigma, Vol. 12, No. e125, 2024.
The simplicial complex of Brauer pairs of a finite reductive group. (arXiv)
Math Z., Vol. 308, No. 27, 2024.
Counting conjectures and e-local structures in finite reductive groups. (arXiv)
Adv. Math., Vol. 436, No. 109403, 61 pp., 2024.
Degree divisibility in Alperin-McKay correspondences (with J. M. Martínez). (arXiv)
J. Pure Appl. Algebra, Vol. 227 (12), No. 107449, 2023.
Monomial characters of finite solvable groups. (arXiv)
Arch. Math (Basel), Vol. 120, 339-347, 2023.
The McKay Conjecture and central isomorphic character triples. (arXiv)
J. Algebra, Vol. 618, 42-55, 2023
Character Triple Conjecture for p-solvable groups. (arXiv)
J. Algebra, Vol. 595, 165-193, 2022.
Restrictions of characters in p-solvable groups (with B. Sambale). (arXiv)
J. Algebra, Vol. 587, 130-141, 2021.
Theses
Defended: 2nd February 2022
Advisor: Britta Späth
Master's thesis
Title: Monomial characters of finite solvable groups
Defended: 18th July 2018
Advisor: Silvio Dolfi
Coauthors