Department of

# Mathematics

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

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    February 2015            March 2015             April 2015
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5  6  7    1  2  3  4  5  6  7             1  2  3  4
8  9 10 11 12 13 14    8  9 10 11 12 13 14    5  6  7  8  9 10 11
15 16 17 18 19 20 21   15 16 17 18 19 20 21   12 13 14 15 16 17 18
22 23 24 25 26 27 28   22 23 24 25 26 27 28   19 20 21 22 23 24 25
29 30 31               26 27 28 29 30



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.