Department of

# Mathematics

Seminar Calendar
for Topology Seminar events the week of Tuesday, September 18, 2018.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     August 2018           September 2018          October 2018
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1  2  3  4                      1       1  2  3  4  5  6
5  6  7  8  9 10 11    2  3  4  5  6  7  8    7  8  9 10 11 12 13
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Tuesday, September 18, 2018

11:00 am in 345 Altgeld Hall,Tuesday, September 18, 2018

#### Unstable $v_1$-periodic Homotopy Groups through Goodwillie Calculus

###### Jens Kjær (Notre Dame Math)

Abstract: It is a classical result that the rational homotopy groups, $\pi_*(X)\otimes \mathbb{Q}$, as a Lie-algebra can be computed in terms of indecomposable elements of the rational cochains on $X$. The closest we can get to a similar statement for general homotopy groups is the Goodwillie spectral sequence, which computes the homotopy group of a space from its "spectral Lie algebra". Unfortunately both input and differentials are hard to get at. We therefore simplify the homotopy groups by taking the unstable $\nu_h$-periodic homotopy groups, $\nu_h^{-1}\pi_*(\ )$ (note $h=0$ recovers rational homotopy groups). For $h=1$ we are able to compute the $K$-theory based $\nu_1$-periodic Goodwillie spectral sequence in terms of derived indecomposables. This allows us to compute $\nu_1^{-1}\pi_*SU(d)$ in a very different way from the original computation by Davis.

Friday, September 21, 2018

4:00 pm in 241 Altgeld Hall,Friday, September 21, 2018

#### The geometry of some low dimensional Lie groups

###### Ningchuan Zhang (UIUC)

Abstract: In this talk, I'll give explicit geometric descriptions of some low dimensional matrix groups. The goal is to show $\mathrm{SU}(2)\simeq S^3$ is a double cover of $\mathrm{SO}(3)$ and $\mathrm{SL}_2(\mathbb{C})$ is a double cover of the Lorentz group $\mathrm{SO}^+(1,3)$. Only basic knowledge of linear algebra and topology is assumed.