Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, February 21, 2019.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, February 21, 2019

11:00 am in 241 Altgeld Hall,Thursday, February 21, 2019

#### Prime number models, large gaps, prime tuples and the square-root sieve

###### Kevin Ford (Illinois Math)

Abstract: We introduce a new probabilistic model for primes, which we believe is a better predictor for large gaps than the models of Cramer and Granville. We also make strong connections between our model, prime k-tuple counts, large gaps and the "square-root sieve". In particular, our model makes a prediction about large prime gaps that may contradict the models of Cramer and Granville, depending on the tightness of a certain sieve estimate. This is joint work with Bill Banks and Terence Tao.

12:00 pm in 243 Altgeld Hall,Thursday, February 21, 2019

#### Taut foliations and left-orderability of 3 manifold groups

###### Ying Hu (University of Nebraska-Omaha)

Abstract: A group G is called left-orderable if there exists a strict total order on G which is invariant under the left-multiplication. Given an irreducible 3-manifold M, it is conjectured that the fundamental group of the 3-manifold is left-orderable if and only if M admits a co-orientable taut foliation. In this talk, we will discuss the left-orderability of the fundamental groups of 3-manifolds that admit co-orientable taut foliations.

2:00 pm in 241 Altgeld Hall,Thursday, February 21, 2019

#### A note on the Liouville function in short intervals

Abstract: We will begin discussing a note of Kaisa Matomaki and Maksym Radziwill on the Liouville function in short intervals. Come prepared to discuss and participate. You can find the note here: https://arxiv.org/abs/1502.02374

2:00 pm in 243 Altgeld Hall,Thursday, February 21, 2019

#### Lipschitz free spaces on finite metric spaces

###### Denka Kutzarova-Ford (UIUC Math)

Abstract: We prove that the Lipschitz free space on any finite metric space contains a large well-complemented subspace which is close to $\ell_1^n$. We show that Lipschitz free spaces on large classes of recursively defined sequences of graphs are not uniformly isomorphic to $\ell_1^n$ of the corresponding dimension. These classes contain well-known families of diamond graphs and Laakso graphs. The paper is joint with S. J. Dilworth and M. Ostrovskii.