Research

Lafforgue variety and irreducibility of induced representations

We construct the Lafforgue variety, an affine variety parametrizing the simple modules of a non-commutative algebra $R$ for which the center $Z(R)$ is finitely generated and $R$ is finite as a $Z(R)$-module. Using our construction in the case of Hecke algebras, we provide a characterization for irreducibility of induced representations via the vanishing of a generalized discriminant. We explicitly compute this discriminant in the case of an Iwahori-Hecke algebra. We construct well-behaved maps from the Lafforgue variety to Solleveld’s extended quotient and in the case $R$ is a complex finite type algebra to the primitive ideal spectrum.

Kostas I. Psaromiligkos. (2022). https://arxiv.org/abs/2211.11834

Character sheaves in characteristic $p$ have nilpotent singular support

In 1988, Mirkovic and Vilonen and independently Ginzburg proved that, in characteristic $0$, a $G$-equivariant irreducible perverse sheaf is a character sheaf if and only if it has nilpotent singular support. In this paper, we prove that character sheaves have nilpotent singular support in any characteristic.

Kostas I Psaromiligkos. (2022). https://arxiv.org/abs/2211.11126

Branchwidth is (1,g)-self-dual

G. Kontogeorgiou, A. Leivaditis, K.I. Psaromiligkos, G. Stamoulis, D. Zoros. (2024). Discrete Applied Mathematics 350, pp.1-9.

Directed Lovász local lemma and Shearer’s lemma

L. Kirousis, J. Livieratos, K.I. Psaromiligkos. (2020). Annals of Mathematics and Artificial Intelligence 88 (1), pp.133-155.

Acyclic Edge Coloring through the Lovász Local Lemma

I. Giotis, L. Kirousis, K.I. Psaromiligkos and D.M. Thilikos. (2017). Theoretical Computer Science 665, pp.50-60.