Department of

# Mathematics

Seminar Calendar
for events the day of Friday, October 27, 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, October 27, 2017

12:00 pm in 243 Altgeld Hall,Friday, October 27, 2017

#### Universal Taylor series

###### Maria Siskaki

Abstract: A series of the form $Σa_n z^n, z \in \mathbb{C}$, with radius of convergence $R=1$, is called a Universal Taylor series if for each compact set $K$ which is disjoint from the unit disc and has connected complement, and each function $h$ in $A(K)$, there exists a subsequence of the sequence of partial sums of the series that approximates $h$ uniformly on $K$. In other words, the series diverges so badly outside the unit disc, that it approximates any reasonably good function defined on any reasonably good set. In this talk I will prove the existence of Universal Taylor series and discuss some of their properties.

3:00 pm in 341 Altgeld Hall,Friday, October 27, 2017

#### Affine Growth Diagrams

###### Tair Akhmejanov (Cornell University)

Abstract: We introduce a new type of growth diagram, arising from the geometry of the affine Grassmannian for $GL_m$. These affine growth diagrams are in bijection with the $c_{\vec\lambda}$ many components of the polygon space Poly($\vec\lambda$) for $\vec\lambda$ a sequence of minuscule weights and $c_{\vec\lambda}$ the Littlewood--Richardson coefficient. Unlike Fomin growth diagrams, they are infinite periodic on a staircase shape, and each vertex is labeled by a dominant weight of $GL_m$. Letting $m$ go to infinity, a dominant weight can be viewed as a pair of partitions, and we recover the RSK correspondence and Fomin growth diagrams within affine growth diagrams. The main combinatorial tool used in the proofs is the $n$-hive of Knutson--Tao--Woodward. The local growth rule satisfied by the diagrams previously appeared in van Leeuwen's work on Littelmann paths, so our results can be viewed as a geometric interpretation of this combinatorial rule.

4:00 pm in 345 Altgeld Hall,Friday, October 27, 2017

#### On "Universal-homogeneous structures are generic" by Kabluchko and Tent (Part 1)

###### Erik Walsberg (Illinois Math)

Abstract: I will 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. It is rather surprising that this result, which provides a natural connected between model theory and descriptive set theory, was only proven recently.

4:00 pm in 241 Altgeld Hall,Friday, October 27, 2017