Seminar Calendar
for events the day of Wednesday, April 6, 2011.

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Wednesday, April 6, 2011

Algebra, Geometry and Combinatorics Seminar
3:00 pm   in 7 Illini Hall,  Wednesday, April 6, 2011
 Del Edit Copy
Submitted by ecsima.
 Jeb Willenbring (University of Wisconsin - Milwaukee )Graph Coverings, Quantum Entanglement, and Invariant Theory Abstract: We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical state space of a multi-particle system in which each particle has finitely many outcomes upon observation. Moreover, these invariant functions separate the entangled and unentangled states, and are therefore viewed as measurements of quantum entanglement. When the ranks of the unitary groups are large, we provide a graph theoretic interpretation for the dimension of the invariants of a fixed degree. We also exhibit a bijection between isomorphism classes of finite coverings of connected simple graphs and a basis for the space of invariants. The graph coverings are related to branched coverings of surfaces. This work is joint with Michael W. Hero and Lauren Kelly Williams.

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, April 6, 2011
 Del Edit Copy
Submitted by seminar.
 Hal Schenck (Department of Mathematics, University of Illinois)Combinatorics and Commutative Algebra

Graduate Analysis Seminar
4:00 pm   in Altgeld Hall,  Wednesday, April 6, 2011
 Del Edit Copy
Submitted by savsec2.
 Kelly Funk (UIUC Math)Ergodic Theory meets Topological DynamicsAbstract: I will review the notions of weakly mixing in ergodic theory and uniform rigidity in topological dynamics. I will then show that there exists a large family of homeomorphisms that are weakly mixing, uniformly rigid, and strictly ergodic on the two torus by giving a category argument. This talk is practice for my preliminary examination. Snacks will be provided.