
Combinatorics/Algebra Seminar
The seminar meets Mondays at 4.10 pm in Carver 274.
If you or a guest wish to talk, please visit the Post Office.
March 19
Gerrit Smith: Maximal green sequences of quiver mutations.
Abstract:
The quiver mutations used to define some cluster algebras can be classified as red or green with respect to an initial seed. Some combinatorial aspects of the resulting maximal green sequences (MGS) will be described. One surprising application is a relationship between MGS and (quantum) dilogarithm identities.

April 23

Alex Nowak: to be announced.

April 16

Shuvra Gupta: to be announced.

April 9

Josh Zelinsky: to be announced.

April 2

Christian Roettger: to be announced.

March 26

Joanna Meinel (Max Planck Institute for Mathematics): to be announced.

March 19

Gerrit Smith: Maximal green sequences of quiver mutations.
Abstract:
The quiver mutations used to define some cluster algebras can be classified as red or green with respect to an initial seed. Some combinatorial aspects of the resulting maximal green sequences (MGS) will be described. One surprising application is a relationship between MGS and (quantum) dilogarithm identities.

March 12

Spring break: no seminar.

March 5

Gene B. Kim (University of Southern California): A central limit theorem for descents in conjugacy classes of S_{n}.
Abstract:
The distribution of descents in certain conjugacy classes of S_{n} has been studied previously, and it is shown that its moments have interesting properties. This talk provides a bijective proof of the symmetry of the descents and major indices of matchings and uses a generating function approach to prove a central limit theorem for the number of descents in matchings. We extend this result to all conjugacy classes of S_{n}.

February 26

Jonathan Smith: Sylow theory for quasigroups.
Abstract:
We extend Wielandt's treatment of Sylow theory from finite groups to quasigroups. Because of the nonassociativity inherent to general quasigroups, the quasigroup version comes in two flavors, based either on the action of the full group generated by the set of left multiplications, or just based on the actions of the left multiplications themselves. The theory offers powerful and readily computed isomorphism invariants, capable, for example, of distinguishing all eighty Steiner triple systems of order fifteen. Part of this work is joint with Michael Kinyon and Petr Vojtechovsky.

January 22, 29; February 5, 12, 19

Candidate talks: no seminar.

January 15

King Day: no seminar.

January 8

Jorge ChavezSalas: Fuzzy logic fundamentals.
Abstract:
The fundamental concepts and results of fuzzy logic theory will be
introduced from an algebraic and logical point of view, and a very simple but original application to human behavior (mathematical psychology or cognitive science in this case) will be presented.
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