Department of

Mathematics


Seminar Calendar
for events the day of Monday, November 13, 2017.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, November 13, 2017

3:00 pm in 141 Altgeld Hall,Monday, November 13, 2017

Miller’s Proof of the Height 1 Telescope Conjecture

Dominic Culver   [email] (UIUC)

Abstract: In their attempt to find a better qualitative understanding of the stable homotopy groups of spheres, Morava and Miller-Ravenel-Wilson found that there are pervasive periodic phenomena in the Adams-Novikov E_2-term. These phenomena were originally understood only algebraically, but in 1984, Doug Ravenel attempted to provide topological origins for these algebraic periodicities. He asked, the now famous, telescope conjecture, which in essence, asks to what degree the topological periodic phenomena is controlled by the geometry of formal groups. In this talk, I will give a precise formulation of the telescope conjecture and sketch Miller’s proof of the height 1 telescope conjecture at odd primes. I will also sketch the basic ideas of chromatic homotopy theory along the way.

3:00 pm in 243 Altgeld Hall,Monday, November 13, 2017

Symplectic groupoids up to homotopy

Cristian Ortiz (University of Sao Paulo)

Abstract: Symplectic groupoids correspond to the global counterpart of Poisson manifolds and play a role in generalized notions of moment maps. In this seminar, we will introduce symplectic groupoids "up to homotopy" and we will show the relation between these objects and symplectic stacks. We will also describe Lagrangian morphisms in this context and we will present examples arising in connection with moment maps in Dirac geometry.

4:00 pm in 343 Altgeld Hall,Monday, November 13, 2017

Stability in the homology of configuration spaces

Jenny Wilson (Stanford)

Abstract: This talk will illustrate some patterns in the homology of the space F_k(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena – relationships between unstable homology classes in different degrees – established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius–Kupers–Randal-Williams.

4:00 pm in 245 Altgeld Hall,Monday, November 13, 2017

Signed Laplacians, What Are They Good For?

Lee DeVille   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: We will present results on the eigenvalues of the Laplacians of graphs that have (possibly) negatively-weighted edges, and motivate these results using models of opinion formation on social networks.

5:00 pm in 445 Altgeld Hall,Monday, November 13, 2017

Concentration and hypercontractivity for quantum systems

Marius Junge (UIUC )

Abstract: We will focus on L_p regularity and how to derive hupercontractivity from ultracontractivity-follwing papers by Temme and his coauthors.