Research
My PhD work can be summarized in the first two papers, which are also essentially my PhD thesis.
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
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.
