Department of

Mathematics


Seminar Calendar
for events the day of Monday, April 16, 2018.

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Monday, April 16, 2018

3:00 pm in 243 Altgeld Hall,Monday, April 16, 2018

The globalization of the Poisson sigma model in the BV-BFV formalism

Nima Moshayedi (University of Zurich)

Abstract: One of the central problems of mathematical physics is understanding how to pass from classical to quantum physics. One procedure that implements that passage, called deformation quantization, achieves quantization by deforming the Poisson algebra of classical observables into a non-commutative algebra of quantum observables. The algebraic structure of the quantum observables is determined by the star product, which is a formal deformation of the algebraic structure on the classical observables. Kontsevich showed that any Poisson manifold admits a star product and gave an explicit formula for it. The Poisson Sigma Model (PSM) is an AKSZ-theory closely related to deformation quantization. We will give a short introduction to the BV-BFV formalism, the PSM and discuss briefly how we can construct a globalized version of Kontsevich's star product using this formalism by extending a condition called the modi fied Quantum Master Equation to a differential version of it.

3:00 pm in Altgeld Hall 345,Monday, April 16, 2018

Tale of an Exotic Sphere

Venkata Sai Narayana Bavisetty (UIUC Math)

Abstract: I will start out by explaining how trying to classify manifolds naturally leads to the discovery of exotic spheres and then construct an exotic sphere in dimension 7.

4:00 pm in 245 Altgeld Hall,Monday, April 16, 2018

Geometry without points?

Marius Junge   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: Recently a big effort has been made to translate versions of the isoperimetric inequality to matrix algebras. The motivation for this problem is the aim to built large quantum networks which eventually lead to a `large' quantum computer. Be this as it may, the mathematics behind these efforts is beautiful and reveals interesting ways to use geometric insight even if topologically this enterprise is pointless.

5:00 pm in 241 Altgeld Hall,Monday, April 16, 2018

An $\ell_2$-proof of Gaboriau's theorem II

Anton Bernshteyn (Illinois Math)

Abstract: Last time, we defined Hilbert $E$-modules and their von Neumann dimension. In this talk, we will apply this theory to prove that treeings realize cost.