Colloquium
Questions or comments?

Posted August 31, 2015

3:30 pm - 4:20 pm Lockett 277
Pramod Achar, Mathematics Department, LSU

TBA

Student Algebra Seminar
Graduate Student Algebra and Number Theory Seminar

Posted August 27, 2015

3:15 pm - 4:15 pm Lockett 233
Kyle Istvan, LSU

Quantum Invariant Theory

This informal discussion will focus on motivating the use of quantum groups to creating topological invariants, following the perspective of Manin. We will begin with a brief discussion of SL(2,C), its action on C^2, and why this particular group is of interest in geometry, topology, (and vaguely, number theory.) We will then define a new "geometric" object, the quantum complex plane C_q^{2}, and proceed to derive the necessary deformation of SL(2,C) in order to have a useful action on the quantum plane. If time permits, we will see the Kauffman relations (from the study of links and 3-manifolds) appear very naturally in this setting as the quantum analogue of the Cayley-Hamilton Identity, and hopefully motivate the further study of deformations of classical groups. This talk is based on a series of lectures given by Roland van der Veen at Gazi University in August 2015.