Department of

Mathematics

Seminar Calendar
for events the day of Friday, October 23, 2015.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, October 23, 2015

2:00 pm in 447 Altgeld Hall,Friday, October 23, 2015

A Friendly Introduction to Mean Curvature Flow

Abstract: A surface evolves by a geometric flow if some geometric quantity (shape, curvature, metric, etc.) changes accrording to a partial differential equation. The study of such geometric flows combines geometry and analysis to gain further insight into the underlying geometry and topology of a surface. In this talk we’ll discuss flow by mean curvature of a surface: one of the first such geometric flows investigated. We’ll also discuss how this PDE can be re-interpreted as a gradient flow of surface area, where each point moves in such a direction that the surface area is minimized. We’ll also discuss how easily this PDE becomes singular, and some current questions relating to singularity analysis of the flow."

2:00 pm in Altgeld Hall,Friday, October 23, 2015

Contact invariants via Hamiltonian Floer theory

Ely Kerman   [email] (UIUC Math)

Abstract: In this talk I will describe a work in progress to construct invariants for contact manifolds by considering certain sequences of Hamiltonian flows and symplectic structures on their symplectizations.

4:00 pm in 243 Altgeld Hall,Friday, October 23, 2015

Discrete Homotopy Theory and Finite Topological Spaces

Joseph Rennie (UIUC Math)

Abstract: I will use a simply phrased problem as a guide through the basics of Topology (General and Algebraic) for finite spaces, and how it connects to familiar spaces. I will then use a problem from Complexity Theory to motivate a discrete analogue to Homotopy Theory which coincides with the homotopy theory of finite spaces. If time permits, I will discuss some applications of algebraic Topology of finite spaces to the study of Sylow Subgroups of finite groups. Much of "Discrete Homotopy Theory" has some surprisingly nontrivial (haha) open problems, new ways of looking at old unsolved problems, and some unexpected results. My overall goal is to leave you with a sense of astonishment with an area which is too often neglected.

4:00 pm in 345 Altgeld Hall,Friday, October 23, 2015

On "Reducibility and nonreducibility of between $\ell^p$ equivalence relations" by R. Dougherty and G. Hjorth [pdf]

Aristotelis Panagiotopoulos (UIUC Math)

Abstract: For $1 \le p < \infty$, we call two sequences of reals $\ell^p$-equivalent if their difference is in $\ell^p$. In the paper mentioned in the title, the authors prove that for $p < q$, the $\ell^p$-equivalence is strictly below the $\ell^q$-equivalence in the Borel reducibility hierarchy of equivalence relations. In this talk, we will prove the strictness, i.e. the nonreducibility of the $\ell^q$-equivalence to the $\ell^p$-equivalence.