## Mathematics## Seminar |

## Rocky Mountain Algebraic Combinatorics Seminar

### Upcoming Seminars Schedule

### The algebra and geometry of ordered set partitions

Brendon Rhoades

University of California, San Diego

An *ordered set partition* is a set partition with a total order on its blocks. In particular, an *n*-block ordered set partition of {1, 2, ..., *n* } may be viewed as a permutation in the s ymmetric group *S*_{n}. We will describe some algebraic and geometric properties of ordered set partitions which extend classical properties of permutations. Joint with Jim Haglund, Brendan Pawlowski, Mark Shimozono, and Andy Wilson.

### The Frobenius-Schreier-Sims Algorithm: the beginnings of black-box rings.

James Wilson

CSU

We prove a condition on **unfaithful** representations ρ:A→M_{d}(K) of algebras that implies dimA ≤ d!. This allows us to test
if elements are contained in subalgebras and if so to express them as words
in a compact generating set, even when dimA is exponentially large.
This opens the door to efficient computation with large black-box rings. It
is the "categorification" of the classic Schreier-Sims algorithm.

Weber 223

4–6 pm

Friday, Dec 6, 2019

(Refreshments in Weber 117, 3:30–4 pm)

Colorado State University

This is a joint Denver U / UC Boulder / UC Denver / U of Wyoming / CSU seminar that meets biweekly. Anyone interested is welcome to join us at a local restaurant for dinner after the talks.