Department of

Mathematics


Seminar Calendar
for events the day of Friday, November 15, 2013.

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Friday, November 15, 2013

11:00 am in 140 Henry,Friday, November 15, 2013

Schematic Homotopy Types of Operads

Marcy Robertson (U. of Western Ontario)

Abstract: The rational homotopy type $X_{\mathbb{Q}}$of an arbitrary space $X$ has pro-nilpotent homotopy type. As a consequence, pro-algebraic homotopy invariants of the space $X$ are not accessible through the space $X_{\mathbb{Q}}$. In order to develop a substitute of rational homotopy theory for non-nilpotent spaces Toen introduced the notion of a pointed schematic homotopy type over a field $\mathbb{k}$, $(X\times k)^{sch}.$

In his recent study of the pro-nilpotent Grothendieck-Teichmuller group via operads, Fresse makes use of the rational homotopy type of the little $2$-disks operad $E_2$. As a first step in the extension of Fresse's program to the pro-algebraic case we discuss the existence of a schematization of the little $2$-disks operad.

4:00 pm in 241 Altgeld Hall,Friday, November 15, 2013

An Introduction to Discrete Morse Theory

Anna Weigandt (UIUC Math)

Abstract: Discrete Morse Theory is a generalization of the idea of a Morse function to simplicial complexes and CW complexes. Many of the main theorems of Morse theory can be adapted to the discrete setting. We will give an introduction to discrete Morse theory. We will then discuss some applications of discrete Morse theory.