Let G be a finite group and p a prime. The Brauer graph of G encodes information regarding the connection between the representations of G over the complex numbers and the representations of G over an algebraically closed field of characteristic p. It is surprising that other than the classical case of cyclic defect groups, not much is known about the structure of Brauer graphs. This talk will begin with the basics of representation theory of finite groups and blocks. We will then discuss some recent developments about Brauer graphs in solvable groups and certain “useful” blocks of symmetric groups, and discuss some conjectures for more general results.
This seminar is joint with the Lie Theory/Algebraic Combinatorics Seminar.
Brauer graphs of finite groups Sponsored by the Meyer Fund
Apr. 16, 2015 12pm (MATH 350)
Lie Theory
JP Cossey (University of Akron)
X
Let G be a finite group and p a prime. The Brauer graph of G encodes information regarding the connection between the representations of G over the complex numbers and the representations of G over an algebraically closed field of characteristic p. It is surprising that other than the classical case of cyclic defect groups, not much is known about the structure of Brauer graphs. This talk will begin with the basics of representation theory of finite groups and blocks. We will then discuss some recent developments about Brauer graphs in solvable groups and certain “useful” blocks of symmetric groups, and discuss some conjectures for more general results.
The dual complex of a degeneration records how the components of the special fiber intersect. It appears in tropical geometry as a parameterizing object for the tropicalization. While any graph appears as the dual complex of a degeneration of curves, the same is not true in higher dimensions. I will discuss some obstructions to realizing specified dual complexes.
We study the asymptotics for sparse exponential random graph models where the parameters may depend on the number of vertices of the graph. We obtain exact estimates for the mean and variance of the limiting probability distribution and the limiting log partition function of the edge-(single)-star model. They are in sharp contrast to the corresponding asymptotics in dense exponential random graph models. Time permitting, similar analysis will be done for directed sparse exponential random graph models parametrized by edges and multiple outward stars. Part of this talk is based on joint work with Lingjiong Zhu.
Asymptotics for sparse exponential random graph models
Apr. 16, 2015 4pm (Webber 20…
Algebraic Geometry
Anna Kazanova (UGA)
X
Anna Kasanova
Conformal block vector bundles are vector bundles on the moduli space of stable curves with marked points defined using certain Lie theoretic data. Over smooth curves, these vector bundles can be identified with generalized theta functions. In this talk we discuss extension of this identification over the stable curves. This is joint work with P. Belkale and A. Gibney
Brauer graphs of finite groups