Department of

Mathematics


Seminar Calendar
for events the day of Monday, February 12, 2018.

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Monday, February 12, 2018

3:00 pm in Altgeld Hall 345,Monday, February 12, 2018

Thom Spectra

William Balderrama (UIUC Math)

Abstract: Thom spectra are suspension spectra with a twist, in the same way fiber bundles are products with a twist. Following this idea, I will introduce these objects and talk about some of the structure they can support.

4:00 pm in 245 Altgeld Hall,Monday, February 12, 2018

Symplectic toric rigidity

Susan Tolman   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: Given any integral polytope $\Delta$ in ${\mathbb R}^n$, we can construct a toric variety, which is an $n$ dimensional algebraic variety $X$ with an $n$ dimensional torus action. If this variety is smooth, it has a natural symplectic form $\omega$, that is, a natural closed, non-degenerate two-form. In this case, we call $(X,\omega)$ a symplectic toric manifold. Clearly, if two symplectic toric manifolds $(X,\omega)$ and $(X',\omega')$ are diffeomorphic, then their cohomology rings are isomorphic. Moreover, if they are symplectomorphic, this isomorphism must take $[\omega]$ to $[\omega']$. The rigidity conjecture, which is still open in general, postulates that these conditions are both necessary and sufficient. I will discuss recent progress on proving this in certain special cases. Based on joint work with Milena Pabiniak.

5:00 pm in 241 Altgeld Hall,Monday, February 12, 2018

More on W*-modules

Marius Junge (UIUC)

Abstract: We study the von Neumann version of Hilbert C*-modules and their dimension.