Department of

Mathematics


Seminar Calendar
for Graduate Student Homotopy Seminar events the year of Thursday, October 12, 2017.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
    September 2017          October 2017          November 2017    
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Monday, September 11, 2017

3:00 pm in 141 Altgeld Hall,Monday, September 11, 2017

What is tmf

Ningchuan Zhang   [email] (UIUC)

Abstract: In short, Topological Modular Forms (tmf) is a “universal elliptic cohomology theory”. More precisely, it is the global section of a sheaf of $E_\infty$-ring spectra over the moduli stack of (generalized) elliptic curves. In this talk, I’ll introduce tmf and sketch the construction of it (or really this sheaf of $E_\infty$ ring spectra). If time allows, I’ll also explain its relationship to classical modular forms.

Monday, September 18, 2017

3:00 pm in 141 Altgeld Hall,Monday, September 18, 2017

Framed Cobordism and Stable Homotopy Groups

Brian Shin   [email] (UIUC)

Abstract: I will introduce the notion of framed cobordism describe its connection to the homotopy groups of spheres. Using this connection, I will calculate several of these groups using geometry.

Monday, September 25, 2017

3:00 pm in 141 Altgeld Hall,Monday, September 25, 2017

An Invitation to Motivic Homotopy Theory

Daniel Carmody   [email] (UIUC)

Abstract: In this talk I’ll introduce some of the basic constructions in motivic homotopy theory while trying to give motivations for some of the more complex definitions. This will be largely based on Dan Dugger’s $Universal$ $Homotopy$ $Theories$ paper.

Monday, October 2, 2017

3:00 pm in 141 Altgeld Hall,Monday, October 2, 2017

Why Higher Categories come into Topological Field Theories

Nima Rasekh   [email] (UIUC)

Abstract: In this talk we introduce topological field theories and give various examples. The eventual goal of the talk is to see why it makes sense to use higher categories when studying topological field theories. No knowledge of any of these subjects is assumed.

Monday, October 9, 2017

3:00 pm in 141 Altgeld Hall,Monday, October 9, 2017

Cohomology operations for Landweber exact spectra

William Balderrama   [email] (UIUC)

Abstract: If $E$ is a complex-oriented spectrum, then we can obtain a formal group law on $\pi_\ast E$ from the map $\mathbb{CP}^\infty\times\mathbb{CP}^\infty\rightarrow\mathbb{CP}^\infty$ classifying the tensor product of line bundles. If $E$ is Landweber exact, this formal group law completely controls the structure of stable operations in $E$-cohomology. There are, however, many useful unstable cohomology operations. In this talk, I will try to say something about structures related to these.

Monday, October 16, 2017

3:00 pm in 141 Altgeld Hall,Monday, October 16, 2017

Motivating Higher Topos Theory

Joseph Rennie   [email] (UIUC)

Abstract: In this talk I will try to argue for the necessity of higher topos theory without using the word “derived” once. I will very briefly discuss the various demonstrations of possibility, but will mostly focus on two aspects which make them interesting: object classifiers, and descent. If time permits, I will give a Weil’ld outline of a connection to physics.