Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, July 5, 2016.

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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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Tuesday, July 5, 2016

11:00 am in 343 Altgeld Hall,Tuesday, July 5, 2016

#### Asymptotic distribution of Beurling's generalized prime numbers

###### Jasson Vindas (Ghent University, Belgium)

Abstract: This talk is a survey of classical and recent results on the asymptotic distribution of generalized prime numbers. The goal of Beurling's generalized prime number theory is to replace the ordinary prime numbers by a rather arbitrary non-decreasing sequence of positive real numbers (generalized primes), consider then the multiplicative semigroup generated by it (generalized integers), and then establish relations between asymptotic properties of the counting functions of the generalized primes and integers. We will discuss various conditions that ensure the validity of the prime number theorem in this context.

12:00 pm in 345 Altgeld Hall,Tuesday, July 5, 2016

#### Invitation to Convex Geometries

Abstract: Convex geometries are interesting combinatorial objects which generalize a notion of convexity on the Euclidean plane. In 2005, Kashiwabara, Nakamura and Okamoto showed that every convex geometry can be represented by convex sets relative to some finite point configuration in n-dimensional space, for suitable n. In this talk we will see that not all finite convex geometries can be represented by a finite configuration of circles on the plane. We also present some interesting questions for future investigation.

1:00 pm in 345 Altgeld Hall,Tuesday, July 5, 2016

#### The most important equation in financial mathematics: Introduction to the Black-Scholes equation

###### Laila Zhexembay (Nazarbayev University)

Abstract: An option is a bet on a future price of a stock. Options are of enormous importance in the financial world, so it is equally important to determine their prices correctly. The standard way to do so is by the famous Black-Scholes equation, for which Myron Scholes received the Nobel prize in Economics in 1997. We introduce the mathematical and financial sides of this equation and discuss numerical solution methods.

2:00 pm in 343 Altgeld Hall,Tuesday, July 5, 2016

#### Exact Wiener-Ikehara theorems

###### Wen-Bin Zhang (University of the West Indies, Kingston, Jamaica and UIUC)

Abstract: The famous tauberian theorem of Wiener and Ikehara gives a sufficient condition for deducing the asymptotic behavior of a function from information about its Laplace transform. In this talk, we show that the "nondecreasing" condition can be replaced by a weaker one, and this set of conditions is necessary as well as sufficient.

4:00 pm in 245 Altgeld Hall,Tuesday, July 5, 2016