Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, November 21, 2013.

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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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Thursday, November 21, 2013

11:00 am in 241 Altgeld Hall,Thursday, November 21, 2013

#### Congruences between modular forms and consequences for automorphic Galois representations

###### Martin Luu (Stanford)

Abstract: In 1954, Martin Eichler did something very interesting: Attach group representations to certain modular forms. The local properties of these representations are linked to the level of the modular form, amongst other things. I will explain how one can use congruences between modular forms (or more generally, automorphic forms) together with the powerful tools of modularity lifting theorems and eigenvarieties to simplify the local study of these representations at the "difficult primes", namely those dividing the level.

1:00 pm in Altgeld Hall 347,Thursday, November 21, 2013

#### Fixed currents for hyperbolic automorphisms of free groups

###### Martin Lustig (Marseille)

Abstract: It is known that for an irreducible hyperbolic automorphisms \phi of a finitely generated non-abelian free group F_n there are precisely two currents \mu_+ and \mu_- which are projectively fixed, i.e. \phi(\mu_+) = \lambda_+ \mu_+ and \phi(\mu_-) = \lambda_- \mu_-, for some positive "stretching factors" \lambda_+ > 1 and \lambda_- < 1. In this talk we will explain how to generalize this result to general hyperbolic automorphisms \psi of F_n, and exhibit a natural bijection from the set of projectively fixed currents to the set of non-negative (row) eigenvectors for the transition matrix of a train track representative of \psi or of \psi^{-1}. We will also apply this result to exhibit the first known example of any R-tree T in compactified Outer space which is not "diagonally equalizable". This talk is based on joint work with N. Bedaride and A. Hilion.

2:00 pm in 345 Altgeld Hall,Thursday, November 21, 2013

#### Rigid and Weakly Mixing Cutting and Stacking Constructions

###### Kelly Yancey (Maryland)

Abstract: In the setting of infinite ergodic theory, measure-preserving transformations that are rigid and spectrally weakly mixing are generic in the sense of Baire category. During this talk we will discuss rigid verses various types of weakly mixing in infinite ergodic theory. We will also construct examples of transformations that have these desired properties. Our examples will be via the method of cutting and stacking. This is joint work with Rachel Bayless. (Note special time and date.)

2:00 pm in 243 Altgeld Hall,Thursday, November 21, 2013

#### Coarse differentiability of Lipschitz functions

###### Sean Li (University of Chicago)

Abstract: Bates, Johnson, Lindenstrauss, Preiss, and Schechtman introduced a large scale notion of differentiability for Lipschitz maps between normed linear spaces. We review a recent extension of this result to the nonabelian setting of Carnot groups and discuss its application to quantitative nonembeddability problems.

2:00 pm in 149 Henry Administration Building,Thursday, November 21, 2013

#### The proportion of zeros of the Riemann zeta-function on the critical line

###### Nicolas Robles (University of Zurich, Switzerland)

Abstract: We aim to give an overview of the results concerning the percentage of non-trivial zeros of the Riemann zeta-function which are located on the critical line Re(s)=12. In particular, we explain the tools by which Levinson (1974) managed to show that the proportion is at least 13. Finally, we introduce the tools used by Conrey (1989) to increase this to 25.

3:00 pm in 241 Altgeld Hall,Thursday, November 21, 2013

#### Morse Theory with Melinda

###### Melinda Lanius (UIUC Math)

Abstract: Morse theory is a powerful computational tool of differential topology. The plan for this talk is to introduce the basic ideas of Morse theory with plenty of examples. The main results will be stated and proofs may be briefly discussed. Use in applications will be stressed.

4:00 pm in 245 Altgeld Hall,Thursday, November 21, 2013

#### Dispersive Quantization -- the Talbot Effect

###### Peter Olver (University of Minnesota)

Abstract: The evolution, through linear dispersion, of piecewise constant periodic initial data leads to surprising quantized structures at rational times, and fractal, non-differentiable profiles at irrational times. Similar phenomena have been observed in optics and quantum mechanics, where it is known as the Talbot effect after an optical experiment by one of the founders of photography, and lead to intriguing connections with exponential sums arising in number theory. Ramifications of these observations for numerics and nonlinear wave models will be discussed.