I’m happy to announce another seminar series many of our readers may be interested in, titled “Algebraic Matroids and Rigidity Theory”. It is at 10am EST on Thursdays and is organized by Daniel Bernstein. Please email him at [dibernst ~at ~ mit ~.~ edu] or [bernstein.daniel ~at~ gmail ~.~ com] to get on the mailing list and for the password.

We do not intend on having a talk on May 18 for Victoria Day :). Here’s the info for Rudi’s talk next week.

**Mon, May 11** 3pm EST (8pm BST, 7am Tue NZST)**Rudi Pendavingh**, Eindhoven University of Technology**Counting valuated matroid types****YouTube**

Corrected slides

**Abstract:**If $M$ is a matroid with bases $\mathcal{B}$, then a

*valuation*of $M$ is a function $\nu:\mathcal{B}\rightarrow \mathbb{R}$ satisfying the following symmetric exchange axiom:

- If $B, B’\in \mathcal{B}$ and $e\in B\setminus B’$, then there is an $f\in B’\setminus B$ so that $$\nu(B)+\nu(B’)\leq \nu(B-e+f)+\nu(B’+e-f)$$

*combinatorial type*of a given valuation essentially comprises the information for which $B,B’,e,f$ equality is attained in this definition.

*rigid*if all its valuations are of the same combinatorial type. By a theorem of Lafforge, a rigid matroid has a discrete set of linear representations over each field. By work of Bollen, Draisma, and myself, a rigid matroid which is algebraic in characteristic $p$ is also linear in characteristic $p$. More generally, if a matroid is algebraic in characteristic $p$, then the matroid has some valuation which satisfies a certain condition on its combinatorial type. Testing this condition involved enumerating the combinatorial types.