MathematicsSeminar |
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 Sn. 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→Md(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.
The discovery came from a CSU reading group on functional programming. We will highlight a few ways that abstract algebra is being used in modern computing and how on occasion it teaches us things about algebra to which we aren't paying attention. Reports on joint work with I. Kessler, H. Kvinge.
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.