Computational Mathematics Seminar

Posted September 3, 2015

3:30 pm - 4:30 pm 1034 Digital Media Center
Christopher Davis, Tennessee Tech University

A Two Level Additive Schwarz Preconditioner for a Partition of Unity Method

Abstract: The partition of unity finite element method is a type of finite element method that enables one to construct smooth approximation functions at low cost. Investigation into the conditioning of partition of unity methods is an active field or research. In this talk, we discuss the use of two level additive Schwarz preconditioners for a partition of unity method. The numerical algorithm will be presented and analyzed. Numerical examples will be given to demonstrate the effectiveness of the method. This is joint work with Susanne C. Brenner and Li-yeng Sung.

Student Algebra Seminar
Graduate Student Algebra and Number Theory Seminar

Posted October 12, 2015

3:15 pm - 4:15 pm Lockett 233
Bach Nguyen, LSU

A New Look into the Center of the Quantized Enveloping Algebra of a Complex Semi-simple Lie Algebra

Abstract: In the paper \textit{``Local Finiteness of the Adjoint Action for Quantized Enveloping Algebras''} by Anthony Joseph and Gail Letzter, they show that the center of $U_{q}(\mathfrak{g})$ ($\mathfrak{g}$ is the Kac-Moody algbra) is isomorphic to the $W$-invariants in the ring $k(q)[T^0]$, where $W$, the Weyl group, acting by traslation, and $T^{0}=T_{<}^{-1}T_{<}$, where $T_<=-R^+$, and $R^+$ is the intersection of four times the dominant weight with the extended root lattice. Recently, in \textit{``Generalized Joseph's Decompositions,''} Arkady Berenstein and Jacob Greenstein give a new construction for the basis of $\mathcal{Z}(U_q)$ which allows us to identify the center with the ring of symmetric functions. In this talk, we'll be discussing the construction that lead to this new basis of $\mathcal{Z}(U_q)$.