For m in the natural numbers, let \(S_m\) be the Suzuki curve defined over the finite field of size \(2^{2m+1}\). Because of the large number of rational points relative to their genus, the Suzuki curves provide good examples of Goppa codes. The automorphism group of \(S_m\) is the Suzuki group \(Sz(2m+1)\). However, the structure of the Jacobian of \(S_m\) has not been determined. The a-number is a finer invariant than the p-rank of the isomorphism class of the 2-torsion group scheme. The a-number also places constraints on the decomposition of the Jacobian into indecomposable varieties. In this talk, I will discuss joint work with Holley Friedlander, Derek Garton, Rachel Pries, and Colin Weir in which which we computed a closed formula for the a-number of \(S_m\) using the action of the Cartier operator on \(H_0\), and continuing work with Pries and Weir to determine the full Eckdahl-Oort type of the curves.
The a-numbers and Eckdahl-Oort types of Jacobians of Suzuki Curves
Oct. 29, 2013 1pm (MATH 220)
Grad Algebra/Logic
Clifford Bridges (CU Boulder) A Method to Realize Groups as Galois Groups: Rigidity in An, Part 2
Oct. 29, 2013 2pm (MATH 350)
Lie Theory
Richard Green (CU)
X
The numbers game , due to Mozes, is something close to a type of chip-firing game on a graph. It arises naturally in the context of Coxeter groups. I will discuss some of the combinatorial features of this game, as well as its points of contact with heaps and minuscule representations.
Some Combinatorial Aspects of the Numbers Game
Oct. 29, 2013 3pm (MATH 350)
PDE/Analysis
Boramey Chhay
X
We will discuss certain geometric properties such as curvature (sectional, scalar, Ricci), which lead to the characterization of unimodular 3 dimensional Lie groups. Then we will move on to the group of diffeomorphisms on the circle and hopefully will be able to do some computations and talk about the Virasoro-Bott group.
The a-numbers and Eckdahl-Oort types of Jacobians of Suzuki Curves