Sortable sets and sortable simplicial complexes
Abstract: Sortable sets of monomials is a concept which was introduced by Bernd Sturmfels. Toric algebras whose monomial generators are sortable have the nice property that their defining toric ideal has a quadratic Gröbner basis and squarefree initial ideal, and this has remarkable consequences for the \;toric algebra and also for the ideal generated by this sortable set of monomials. We will also introduce sortable simplicial complexes \;and show that the proper interval graphs are precisely the graphs whose independence complex is sortable.My lecture is based on  \;joint papers with my coauthors Viviana Ene, Takayuki Hibi, Fahimeh Khosh-Ahang, Somayeh Moradi, Masoomeh Rahmbeigi, Marius Vladoiu, Ayesha Asloob Qureshi and Guangjun Zhu.Link to Zoom meeting:
Title: Unconditional Reflexive Polytopes
Abstract: A convex body is unconditional if it is symmetric with respect to reflections in all coordinate hyperplanes. In this talk, we investigate unconditional lattice polytopes with respect to geometric, combinatorial, and algebraic properties. In particular, we characterize unconditional reflexive polytopes in terms of perfect graphs. As a prime example, we study a type-B analogue of the Birkhoff polytope. This talk is based on joint work with McCabe Olsen and Raman Sanyal.
Link to Zoom meeting: