Aida Maraj: Symmetry Lie Algebras of Varieties with Applications to Algebraic Statistics

Abstract.

The motivation for this talk is to detect when an irreducible projective variety V is not toric. We do this by analyzing a Lie group and a Lie algebra associated with V. If the dimension of V is strictly less than the dimension of the above-mentioned objects, then V is not a toric variety. We provide an algorithm to compute the Lie algebra of an irreducible variety and use it to provide examples of non-toric statistical models in algebraic statistics. The talk is based on preprint arxiv:2309.10741  with Arpan Pal.