Department of

# Mathematics

Seminar Calendar
for events the day of Monday, September 23, 2019.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, September 23, 2019

3:00 pm in 243 Altgeld Hall,Monday, September 23, 2019

#### Moment maps in quantum mechanics

###### Eugene Lerman (Illinois)

Abstract: I will try to explain how Atiyah-Guillemin-Sternberg-Kirwan convexity theorem shows up in quantum mechanics. The talk is expository. I claim no originality.

3:00 pm in 441 Altgeld Hall,Monday, September 23, 2019

#### Splitting $BP\langle 1\rangle \wedge BP\langle 1\rangle$ at odd primes

###### Liz Tatum (UIUC Math)

Abstract: The Adams Spectral Sequence is a tool for approximating $\pi_{*}X$, where $X$ is a connective spectrum. If $E$ is a ring spectrum satisfying certain properties, then we can define an $E$-based Adams spectral sequence converging to $\pi_{*}\hat{X}$, where $\hat{X}$ is the $E$-completion of $X$. When $E_{*}E$ is flat over $E_{*}$, the $E^{2}$-page of the spectral sequence can be described as $Ext_{E_{*}E}(E_{*}, E_{*}X)$. But if $E_{*}E$ is not flat over $E_{*}$, then there is no such description. Instead, we must study $E\wedge E$ to understand the spectral sequence. The Brown-Peterson spectra $BP\langle n \rangle$ are an example of such spectra. One approach is to split the product $E \wedge E$ into more manageable pieces. When $n=1$, we can construct a splitting $BP\langle 1 \rangle \wedge BP\langle 1 \rangle$ as $\vee_{k=0}^{\infty}\Sigma^{2k(p-1)} BP\langle 1 \rangle 1 \wedge B(k)$, where $B(k)$ is the $k^{th}$ integral Brown-Gitler spectrum. We give a sketch of Kane's construction of this splitting for odd primes.

5:00 pm in 241 Altgeld Hall,Monday, September 23, 2019

#### Boundary Representations

###### Chris Linden (UIUC)

Abstract: We will continue the discussion of boundary of previously considered operator algebras, and launch into Arveson’s general general.