Organizers: Emily Peters, Peter Tingley
January  
No talks (please attend special colloquia!  
February  
6 
No talk 

13 
No talk 

20 
Organizational meeting 

27 
Peter Tingley 
Quiver varieties and root multiplicities for symmetric KacMoody algebras 
March  
6  No talk (spring break)  
13 
Nicolas Mayers (Lehigh University) 
Calculating the Index of Poset Algebras 
20 
Marius Radulescu 
Vector Bundles on Elliptic Curves 
27 


April  
3 
Daniele Rosso (Indiana University Northwest) 

10 
Aaron Lauve 

17 
Christopher Drupieski 

24 
Peter or Tony? 

Directions 

IES (the institute for environmental sustainability) is located at the corner of W. Sheridan and N. Kenmore Avenues, Chicago, IL (map)
Parking is available oncampus for $7 in the Parking Garage (building P1 on the Lake shore campus map). To get to the Parking Garage, enter campus at the corner of West Sheridan Road and North Kenmore Avenue.
Abstracts 

February 27: Peter tingley. Quiver varieties and root multiplicities for symmetric KacMoody algebras
We discuss combinatorial upper bounds on dimensions of certain imaginary root spaces for symmetric KacMoody algebras. These come from a realization of the infinity crystal using quiver varieties. The framework is quite general, but we only work out specifics for one special case. We conjecture that our bound is quite tight, and give both computational evidence and heuristic justification for this conjecture, but unfortunately not a proof.
March 13: Nicholas Mayers. Calculating the Index of Poset Algebras
The index of a Lie algebra is an important algebraic invariant which is usually quite difficult to compute. Recently, there has been a push to find closedform formulas for the index of families of Lie algebras which are combinatorially defined. Much of this work is related to what are known as Seaweed algebras which are subalgebras of sl(n) which can be parametrized by a pair of compositions of n. In this talk I will discuss some recent work related to finding combinatorial formulas for the index of a different family of Lie algebras which are defined via posets.
March 20: Marius Radulescu. Vector Bundles on Elliptic Curves
In his paper "Vector bundles over an elliptic curve," Michael Atiyah classified indecomposable vector bundles of arbitrary rank and degree on elliptic curves. The set of isomorphic classes of indecomposable vector bundles of fixed rank and degree is isomorphic with the Jacobian of the elliptic curve, which in turn is isomorphic with the curve itself. Based on Atiyah's paper, I will provide a detailed description of rank 2, 3 and 4 vector bundles on an elliptic curve.