Graduate Colloquium Fall 2012

Thursdays 4 PM
McHenry Library Room 4130
Refreshments served at 3:30
For further information please contact Corey Shanbrom

October 11, 2012

Burnside and double Burnside groups and rings

Philipp Perepelitsky 

In this talk, I shall introduce the notions of Burnside and double Burnside groups and rings. I shall present some classical results concerning these objects as well as some recent results obtained in joint work by Robert Boltje and myself.

November 1, 2012

Quantum Dimensions and Quantum Galois Theory

Xiangyu Jiao, Mathematics Graduate Student 

I will talk about "dimensions" of modules of a vertex operator algebra.

Quantum Galois theory,which is an analogue of classic Galois theory in VOA theory, will also be presented.

November 8, 2012

Z-Graded Weak Modules and Regularity

Nina Yu 

Rationality, C_{2}-cofiniteness and regularity are probably the three most important concepts in represenation theory of vertex operator algebras. In my talk I am going to prove that if any \mathbb{Z}-graded weak module for vertex operator algebra V is completely reducible, then V is regular. This gives a natural characterization of regular verex operator algebras.

November 15, 2012

Floer Homology and the Arnold Conjecture

Gabriel Martins, UCSC Graduate Student, Mathematics 

On this talk I'll discuss a bit of the history of the Arnold Conjecture and illustrate the construction of the Floer complex which was the major technique used to establish it in the general case.

November 22, 2012

No Colloquium - Happy Holidays!!!

December 6, 2012

Psuedo VOAs: Complex, But Still Semi-Simple

Robert Laber 

A vertex operator algebra (VOA) is a certain kind of non-associative, non-commutative "algebra," together with a distinguished element omega, called the conformal vector. Associated to this element is a linear operator L(0) that is required to be semisimple with integral spectrum. A psuedo vertex operator algebra (PVOA) generalizes the notion of VOA by relaxing these requirements on L(0). For a suitably "nice" VOA V, there is a finite dimensional, semisimple associative algebra A(V) associated to V with the property that the simple A(V)-modules are in bijective correspondence with the simple admissible V-modules. In this talk, I will (briefly) present the formal definitions of VOAs and PVOAs, and I will show how one can obtain a family of PVOAs from a given VOA by "shifting" the conformal vector. I will also discuss my current project, which is to find an analog of the associative algebra A(V) for a PVOA.