Department of

Mathematics


Seminar Calendar
for events the day of Monday, March 2, 2015.

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Monday, March 2, 2015

12:00 pm in 341 AH,Monday, March 2, 2015

Non-Hamiltonian actions with isolated fixed points

Susan Tolman (UIUC Math)

Abstract: Let a circle act symplectically on a closed symplectic manifold $M$. If the action is Hamiltonian, we can pass to the reduced space; moreover, the fixed set largely determines the cohomology and Chern classes of $M$. In particular, symplectic circle actions with no fixed points are never Hamiltonian. This leads to the following important question: What conditions force a symplectic action with fixed points to be Hamiltonian? Frankel proved that Kahler circle actions with fixed points on Kahler manifolds are always Hamiltonian. In contrast, McDuff constructed a non-Hamiltonian symplectic circle action with fixed tori. Despite significant additional research, the following question is still open: Does there exists a non-Hamiltonian symplectic circle action with isolated fixed points? The main goal of this talk is to answer this question by constructing a non-Hamiltonian symplectic circle action with exactly 32 fixed points on a closed six-dimensional symplectic manifold. Based in part on joint work with J. Watts.

5:00 pm in 241 Altgeld Hall,Monday, March 2, 2015

Khintchine/Tensor products of group $C^*$-algebras admitting a continuum of $C^*$-norms

Li Gao/Mathew Wiersma:

Abstract: The first half of the talk will finish the Khintchine p<1 business. Second talk: It is known that $C^*$-algebras admit unique $C^*$-norms, but this is not true in general for dense $*$-subalgebras of $C^*$-algebras. For example, the algebraic tensor product $A\otimes B$ of $C^*$-algebras $A$ and $B$ may admit multiple $C^*$-norms. We will show that if $\Gamma$ is a discrete group containing a copy of a noncommutative free group, then $C^*_r(\Gamma)\otimes C^*_r(\Gamma)$ and $C^*(\Gamma)\otimes C^*_r(\Gamma)$ admit a continuum of $C^*$-norms.