Department of

Mathematics

Seminar Calendar
for events the day of Thursday, July 7, 2016.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, July 7, 2016

11:00 am in 343 Altgeld Hall,Thursday, July 7, 2016

PNT equivalences for Beurling numbers

Gregory Debruyne (Ghent University, Belgium)

Abstract: In classical prime number theory several asymptotic relations are considered to be "equivalent" with the prime number theorem, meaning that they could be deduced by simple real variable arguments. In the context of Beurling numbers, however, this is no longer the case: sometimes extra hypotheses have to be imposed to show the equivalence between different asymptotic relations. We will present some recent results on the subject. In contrast to the earlier work of Diamond and Zhang, who used strictly elementary methods, our approach will make extensive use of the zeta function of the prime number system and can thus no longer be regarded as elementary. The talk is based on collaborative work with Jasson Vindas.

12:00 pm in 345 Altgeld Hall,Thursday, July 7, 2016

Applications of Homology

Nicholas Kosar (University of Illinois at Urbana-Champaign)

Abstract: Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study spaces and how to distinguish them. One such tool is homology. In this talk, I will give a brief introduction to homology and explain why it is useful. I will then discuss how homology can be used in applications to sensor networks. If time permits, I will also discuss how homology can be used to help determine the shape of data.

1:00 pm in 345 Altgeld Hall,Thursday, July 7, 2016

Introduction to the Hyperbolic Plane

Qingci An (University of Illinois at Urbana-Champaign)

Abstract: Hyperbolic geometry is a non-Euclidean geometry in which the parallel postulate does not hold. In this talk, we will introduce the basic properties of hyperbolic geometry using the hyperbolic plane as our main example. We will construct an invariant notion of distance on the hyperbolic plane and explore some of its properties. In particular, we will show that the group of Möbius transformations on the hyperbolic plane is the set of isometries of the hyperbolic plane.