Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, October 9, 2014.

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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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30


Thursday, October 9, 2014

11:00 am in 241 Altgeld Hall,Thursday, October 9, 2014

#### The distribution of quadratic Weyl sums

###### Francesco Cellarosi   [email] (UIUC Math)

Abstract: I will present some recent progress on the distribution of quadratic Weyl sums. For example, the exact asymptotic in the tail distribution is related to counting integer solutions on Vinogradov's quadric. This result also comes with an explicit power saving. Our method uses the modularity of the Jacobi theta function and equidistribution of long closed horocycles. Joint work with J. Marklof (Bristol)

1:00 pm in 243 Altgeld Hall,Thursday, October 9, 2014

#### Arithmetic quotients of the mapping class group from covers

###### Justin Malestein (Universitat Bonn)

Abstract: In this talk, I will discuss a procedure using the action on homology of covers for obtaining infinitely many “virtual” arithmetic quotients of mapping class groups of closed surfaces, (surjective maps up to finite index). Specifically, for any irreducible rational representation of a finite group of rank less than g, we produce a corresponding virtual arithmetic quotient of the genus g mapping class group. Particular choices of irreducible representations of finite groups yield arithmetic quotients of type Sp(2m), SO(2m, 2m), and SU(m, m) for arbitrarily large m in every genus. Joint with F. Grunewald, M. Larsen, and A. Lubotzky. View talk at http://youtu.be/GHTjiQp0fQI

2:00 pm in 007 Illini Hall,Thursday, October 9, 2014

#### Non-Periodic continued fractions for quadratic irrationalities

###### Michael Oyengo (UIUC Math)

Abstract: A well known theorem of Lagrange states that the simple continued fraction of a real number x is periodic if and only if x is a quadratic irrational. We examine non-periodic and non-simple continued fractions formed by two interlacing geometric series and show that in certain cases they converge to quadratic irrationalities. This phenomenon is connected with a certain sequence of polynomials whose properties we examine further.

4:00 pm in 245 Altgeld Hall,Thursday, October 9, 2014

#### Dendroidal topology

###### Ieke Moerdijk (Radboud University Nijmegen)

Abstract: Simplicial topology is an effective theory for approximating topological spaces by spaces built up out of simplices, and since its early development the theory has played a dominant role in algebraic topology and its applications. In this lecture, I will try to sketch how a similar theory can be developed in which one replaces simplices by tree-like objects. This new theory strictly contains the older simplicial one, and forms an effective tool for the approximation of operads (mathematical objects used to encode algebraic structures on spaces) and of infinite loop spaces.