- This event has passed.
Algebra and Combinatorics Seminar: Lorenzo Vecchi, KTH, Categorical valuative invariants of matroids
March 6 | 12:45 pm - 1:45 pm EST
In this talk we define a new category of matroids, by working on matroid polytopes and rank preserving weak maps. This lets us introduce the concept of categorical valuativity for functors, which can be seen as a categorification of the ordinary valuativity on matroid polytope decompositions.
We also show that this new theory agrees with what we know about valuative polynomials: several known valuative polynomials can be seen as Hilbert series of some interesting graded vector space (e.g. Orlik-Solomon algebras and Chow rings) and we prove that these graded vector spaces let us define a valuative functor in the new sense.
Lastly, we sketch how to categorify a Theorem by Ardila and Sanchez, which states that the convolution of two valuative invariants (respectively, valuative functors) is again valuative.
This is based on a joint project with Ben Elias, Dane Miyata and Nicholas Proudfoot.
Speaker’s website