PIMS Geometry, Algebra and Physics Seminar
Organized by Alex Weekes, Steve Rayan and Curtis Wendlandt
Schedule (2023-2024)
Talks are normally held on Thursdays at 4:00-5:30pm CST, and each can be attended virtually via Zoom (including those talks held in-person at the University of Saskatchewan) using the following information:
Meeting ID | Passcode | Link |
---|---|---|
936 6357 4827 | qUSaskGAP | Here |
The seminar is intended to be informal and accessible to graduate students studying algebra, geometry, or mathematical physics. Speakers typically prepare an hour-long talk, with the remaining half hour dedicated to discussion and questions.
Date/Location |
Speaker |
Title and Abstract |
---|---|---|
Thursday, October 12th 4:30-6:00PM CST (Hybrid) THORV 124 |
Abid Ali |
Strong Integrality of Inversion Subgroups of Kac-Moody Groups The question of integrality for semi-simple algebraic groups over the field of rational numbers was esablished by Chevalley in the 1950s as part of his work on associating affine group schemes with groups over integers. For infinite-dimensional Kac-Moody groups, it remains an open problem. To state this problem more precisely, let \(\mathfrak{g}\) be a symmetrizable Kac-Moody algebra over \(\mathbb{Q}\), \(V\) be an integral highest weight \(\mathfrak{g}\)-module and \(V_{\mathbb{Z}}\) be a \(\mathbb{Z}\)-form of \(V\). Let \(G=G(\mathbb{Q})\) be an associated minimal representation-theoretic Kac-Moody group and let \(G(\mathbb{Z})\) be its integral subgroup. Suppose \(\Gamma(\mathbb{Z})\) is the Chevalley subgroup of \(G\), that is, the the subgroup that stabilizes the lattice \(V_{\mathbb{Z}}\) in \(V\). The integrality for \(G\) is to determine if \(G(\mathbb{Z})=\Gamma(Z)\). We will discuss some progress on this problem, which we made in a joint work with Lisa Carbone, Dongwen Liu, and Scott H. Murray. Our results have various applications, including the integrality of subgroups of the unipotent subgroup \(U\) of \(G\) that are generated by commuting real root groups. |
Wednesday, November 22nd 4-5:30pm CST (Hybrid) PHYSICS 128 |
Casey Blacker |
Geometric and Algebraic Reduction of Multisymplectic Manifolds A symplectic Hamiltonian manifold consists of a Lie group action on a symplectic manifold, together with the additional structure of a moment map, which encodes the group action in terms of the assignment of Hamiltonian vector fields. In special cases, the moment map determines a smooth submanifold to which the Lie group action restricts and the resulting quotient inherits the structure of symplectic manifold. In every case, it is possible to construct a reduced Poisson algebra that plays the role of the space of smooth functions on the reduced symplectic manifold. |