Seminars and Conferences
In this section I collected all the seminars and conferences I attended. On the left, you can find specific links to material I prepared for the talks.
This is a comprehensive list of the seminars that took place at University of Pisa. For a detailed description of the topics, you can go to the CULT page.
In this section I collected all the seminars and conferences I attended. On the left, you can find specific links to material I prepared for the talks.
This is a comprehensive list of the seminars that took place at University of Pisa. For a detailed description of the topics, you can go to the CULT page.
This seminar was centered around the book [BS] of which we've read the first three chapters.
I specifically gave a talk on Section 3.5 and 3.6 where face lattices of polyhedron are studied using Möbius functions from which one arrives at a proof for Zaslavski's theorem.
References:
This seminar was focused on the basics of matroids. We followed some lecture notes by Victor Reiner [VR], reading about several axioms from which matroids can be defined and some elementary constructions.
I gave a talk on the definition of oriented matroids and ways to work with them using covectors and chirotopes (see Section 1.8, 1.9 and 1.10).
References:
This seminar focused on hyperplane arrangements. We followed some lecture notes on the topic written by Richard Stanley.
In particular, I gave a talk on Zaslavski's Theorem that shows how to count the (bounded) regions of the hyperplane arrangement by means of the characteristic polynomial.
Here you can find my notes and an outline of my talk.
Some toric varieties can be constructed starting from a rational fan in $\mathbb{R}^d$.
Leveraging this explicit construction, one can use a combinatorial approach to describe the features of such toric varieties.
In particular, we focused on the Chow ring and its combinatorial counterpart, as an example of how a combinatorial structure can simplify computations and give a more intuitive point of view on a subject!
This seminar followed two references:
Take a polytope in $\mathbb{R}^n$ with vertices on the integer lattice. What can we say about its volume? And the integer points contained in the polytope?
These are some of the questions posed by Ehrhart theory and they reveal interesting combinatorial and algebraic structures.
Motivated by some classical results, Victor Reiner and Brendon Rhoades try to find a q-analogue version of the Ehrhart series, a particular series that encodes a lot of information on the polytope itself. Some analogous results are conjectured for this q-analogue series and to try proving these a new algebraic structure is introduced: the Harmonic Algebra.
In [RR] properties of this Harmonic Algebra are studied, hoping to get a clearer picture on the main conjecture.
This seminar followed two references: