Department of

# Mathematics

Seminar Calendar
for events the day of Friday, November 10, 2017.

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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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Friday, November 10, 2017

8:00 am in Alice Campbell Alumni Center,Friday, November 10, 2017

#### MDAB Annual Meeting

12:00 pm in 243 Altgeld Hall,Friday, November 10, 2017

#### Lipschitz Algebras

###### Chris Gartland (UIUC)

Abstract: Through the theory of Gelfand duality, a compact Hausdorff space $X$ may be recovered purely from its commutative C*-algebra of continuous $\mathbb{C}$-valued functions, $C(X)$. In the case where $X$ carries a metric $d$, $C(X)$ alone is not sufficient to determine $d$, as a generic metrizable space carries many mutually inequivalent metrics. However, the commutative Banach *-algebra of $\mathbb{C}$-valued Lipschitz functions, Lip$(X,d)$, is sufficient to recover $d$ up to biLipschitz equivalence, and we'll outline the proof of this fact. We will also discuss possible abstract characterizations of the commutative Banach *-algebras isomorphic to Lip$(X,d)$ for some $(X,d)$.

4:00 pm in 345 Altgeld Hall,Friday, November 10, 2017

#### On "Universal-homogeneous structures are generic" by Kabluchko and Tent (Part 2)

###### Minh Chieu Tran (Illinois Math)

Abstract: I will continue to discuss the recent paper "Universal-homogeneous structures are generic" by Zakhar Kabluchko and Katrin Tent [arXiv]. They show that the set of structures isomorphic to a Fraisse limit is comeager in a certain space of structures.

4:00 pm in 241 Altgeld Hall,Friday, November 10, 2017

#### Manifolds of Mappings

###### Timothy Drake (UIUC)

Abstract: This talk will introduce the notion of manifolds locally modeled on arbitrary (possibly infinite-dimensional) topological vector spaces, focusing on Banach and Fréchet manifolds. We will discuss the manifold structure on the space of $C^k$ mappings between finite-dimensional manifolds and give applications of infinite-dimensional manifold theory to finite-dimensional geometry and topology.