Publications

"Surprising identities for the hypergeometric 4F3 function.", joint work with J. D'Aurizio, Bollettino dell'Unione Matematica Italiana, vol.11, pages 403–409 (2018). DOI
"On Reeder's Conjecture for type B and C Lie algebras. ", Algebras and Representation Theory, 25, pages 25–51 (2022, On Line 2020). DOI

In the paper we present a proof of Reeder's Conjecture on the graded multiplicities of small representations in the exterior algebra Λg for the simple Lie algebras of type B and C.

"Reeder's Conjecture for even orthogonal Lie algebras", Algebras and Representation Theory, 26, 881–900 (2023). DOI

In the paper we complete a case by case proof Reeder's Conjecture started in our previous work, proving the conjecture for the simple Lie algebras of type D and for the Exceptional Cases .

4."Combinatorial and Topological Aspects of Path Posets, and Multipath Cohomology ", with L. Caputi and C. Collari, Journal of Algebraic Combinatorics, 57, 617–658 (2023). DOI The aim of this paper is to explore some combinatorial properties of the path posets, in order to provide new insights and computations. In particular, we develop acyclicity criteria for multipath cohomology, and compute it for oriented linear graphs. To conclude, we interpret multipath cohomology as the cohomology of a certain simplicial complex, and we investigate which spaces may or may not arise this way.

5."Multipath cohomology of directed graphs." (Accepted, to appear on Algebraic and Geometric Topology) , joint work with Luigi Caputi and Carlo Collari. In this paper we introduce a new cohomology theory for (directed) graphs, which we call multipath cohomology. Our construction interpolates between the chromatic homology, introduced by L. Helme-Guizon and Y. Rong, and the homology for directed graphs introduced by P. Turner and E. Wagner. We prove that the multipath cohomology satisfies some functorial properties and we describe its connection with chromatic homology.

6. "Classification of Real and Complex 3-qutrit States." joint work with Willem de Graaf and Alessio Marrani , Journal of Mathematical Physics (Vol.64, Issue 9) (2023) DOI

In this paper we classify the orbits of the group SL(3, F)^3 on the space F^3⊗F^3⊗F^3 for F = C and F = R. This is known as the classification of complex and real 3-qutrit states. We also give an overview of physical theories where

these classifications are relevant.

7. "On the Spectrum of Exterior Algebra, and Generalized Exponents of Small Representations" Bollettino dell'Unione Matematica Italiana (2023) DOI

8. "On the homotopy type of multipath complexes" joint work with Carlo Collari, Luigi Caputi and Jason P. Smith. Mathematika (2023) DOI

Preprints

1. "On the Smooth Locus in Flat Linear Degenerations of Flag Varieties" (Submitted)

Computations for "Reeder's Conjecture for even orthogonal Lie algebras": an explicit proof of Reeder Conjecture for simple Lie Algebras of type E6,E7,E8 and F4.

PhD Thesis: "Reeder's Conjecture for Lie algebras of type C"

In Preparation

On the Singular Locus in Flat Linear Degenerations