# Boris Shapiro: Around generalized zonotopal algebras of graphs

**Time: **
Mon 2022-03-14 15.00 - 16.00

**Location: **
Zoom

**Video link: **
Meeting ID: 617 5356 8496

**Participating: **
Boris Shapiro (SU)

### Abstract

This project is joint with I. Smirnov and A. Vaintrob and so far results are mainly computational. For a given (multi)graph *G*, I will recall the definition of its external zonotopal algebra \(C_G\) which is a graded subalgebra in the space of “square free edges” generated by the vertices where to each vertex one associates the natural sum of its adjacent edges with plus and minus signs. This algebra has been well understood and its Hilbert series is a specialisation of the Tutte polynomial of *G*.

We discuss a natural family of deformations of \(C_G\) parameterised by univariate polynomials of degree not exceeding the maximal valency among the vertices of *G*. Some theoretical and many computational results will be presented.