UIUC Dept. of Mathematics Seminar Calendar

      March 2012             April 2012              May 2012      
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Thursday, April 26, 2012

Number Theory Seminar
11:00 am in 243Altgeld Hall, Thursday, April 26, 2012

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Submitted by ford.

Youness Lamzouri (Department of Mathematics, University of Illinois at Urbana-Champaign)
Discrepancy bounds for the distribution of the Riemann zeta function
Abstract: In 1930 Bohr and Jessen proved that for any $1/2<\sigma\leq 1$, $\log \zeta(\sigma+it)$ has a continuous limiting distribution in the complex plane. As a consequence they deduced that the set of values of $\log \zeta(\sigma+it)$ is everywhere dense in $\mathbb{C}$. Harman and Matsumoto obtained a quantitative version of the Bohr-Jessen Theorem using Fourier analysis on a multidimensional torus. In this talk we shall present a different approach which leads to uniform discrepancy bounds for the distribution of $\log \zeta(\sigma+it)$ that improve the Matsumoto-Harman estimates.

NetMath Lunch Seminar
12:05 pm in 102 Altget Hall, Thursday, April 26, 2012

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Submitted by gfrancis.

Peter Glaze (Department of Mathematics, University of Illinois at Urbana-Champaign)
Peer-led Learning and the Student Experience in NetMath
Abstract: One of the most innovative aspects of the NetMath approach to online education is our integral student mentoring system. Qualified undergraduate students assist NetMath instructors, and develop a personal, tutorial relationship with their students. We will discuss how this mentoring system is intimately tied to the learning experience of our students, the pedagogical principles it implements, and our plans for its renovation, improved recruitment and supervision in the future.

Harmonic Analysis and Differential Equations
1:00 pm in 345 Altgeld Hall, Thursday, April 26, 2012

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Submitted by bronski.

Florian Dorfler (UCSB Engineering)
Synchronization in Power Networks and Coupled Oscillators
Abstract: We discuss the synchronization and transient stability problem in power networks. We exploit the relationship between the power network model considered in transient stability analysis and the well-known Kuramoto model of coupled phase oscillators. A tight connection between these two models can be rigorously established by means of topological conjugacy arguments. In particular, we show the equivalence of local synchronization conditions in both models. Furthermore, we present novel algebraic conditions for synchronization of coupled Kuramoto oscillators. Our synchronization conditions are necessary and sufficient for particular interconnection topologies and network parameters, they are sufficient in the general case, and they improve upon previously-available tests for the Kuramoto model. In the end, we are able to state concise and purely algebraic conditions that relate synchronization in a power network to certain graph-theoretical properties of the underlying electric network. The results reveal elegant connections between the transient stability problem in power networks and the theory of coupled oscillators and multi-agent dynamical systems.

Group Theory Seminar
1:00 pm in Altgeld Hall 347, Thursday, April 26, 2012

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Submitted by kapovich.

Pekka Pankka (University of Helsinki)
From Picard's theorem to quasiregular ellipticity
Abstract: In the quasiconformal geometry of Riemannian manifolds the classical Picard theorem from complex analysis turns into an existence question for non-constant quasiregular mappings from Euclidean spaces into Riemannian manifolds. In this talk, I will discuss the role of the fundamental group in these questions and a class of metrics, introduced by Semmes, that connect these quesiregular ellipticity questions to questions on quasiconformal geometry of decomposition spaces. This talk is based on joint works with Kai Rajala and Jang-Mei Wu.

Graduate Analysis Seminar
5:00 pm in 147 Altgeld Hall, Thursday, April 26, 2012

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Submitted by funk3.

Rami Luisto (University of Helsinki)
On the non-existence of BLD-mappings between manifolds
Abstract: I will give my talk about the main result of my Master's thesis [1]. The result can be seen to be a metric version of the Varopoulos theorem, which states that if N is a compact n-dimensional Riemannian manifold whose fundamental group has hyperbolic growth rate, then there exists no quasiregular mapping from the Euclidean n-space to N. In my thesis I translate this result to the metric setting by talking about path-metric manifolds and Bounded Length Distortion (BLD) mappings between them. A BLD mapping, in short, is an open, discrete and continuous mapping that preserves the lengths of rectifiable paths up to a fixed multiplicative constant. In my talk I will introduce the concepts of the growth rate of a finitely generated group, path-length structure of a manifold and the basic properties of Bounded Length Distortion mappings. If we have time left, I will talk about some results of my Licentiate's thesis which embetter the results given in my Master's thesis. There might be chocolate available during the presentation.

[1] Luisto, Rami. ``On the non-existence of BLD-mappings between manifolds.'' Master's thesis, available at http://helsinki.fi/~luisto/ProGradu.pdf