Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, February 13, 2014.

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Questions regarding events or the calendar should be directed to Tori Corkery.
January 2014          February 2014            March 2014
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1  2  3  4                      1                      1
5  6  7  8  9 10 11    2  3  4  5  6  7  8    2  3  4  5  6  7  8
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30 31

Thursday, February 13, 2014

11:00 am in 241 Altgeld Hall,Thursday, February 13, 2014

#### Small gaps between primes

###### James Maynard (Univ. Montreal)

Abstract: It is believed that there should be infinitely many pairs of primes which differ by 2; this is the famous twin prime conjecture. More generally, it is believed that for every positive integer $m$ there should be infinitely many sets of $m$ primes, with each set contained in an interval of size roughly $m\log{m}$. Although proving these conjectures seems to be beyond our current techniques, recent progress has enabled us to obtain some partial results. We will introduce a refinement of the `GPY sieve method' for studying these problems. This refinement will allow us to show (amongst other things) that $\liminf_n(p_{n+m}-p_n)<\infty$ for any integer $m$, and so there are infinitely many bounded length intervals containing $m$ primes.

1:00 pm in Altgeld Hall 347,Thursday, February 13, 2014

#### Moduli spaces of constant curvature spacetimes

###### Jeff Danciger (University of Texas - Austin)

Abstract: A Margulis spacetime is the quotient of three-dimensional space by a free group of affine transformations acting properly discontinuously. Each of these manifolds is equipped with a flat Lorentzian metric compatible with the affine structure. I will survey some recent results, joint with Francois Gueritaud and Fanny Kassel, about the geometry, topology, and deformation theory of these flat spacetimes. In particular, we give a parameterization of the moduli space in the same spirit as Penner's cell decomposition of the decorated Teichmuller space of a punctured surface. I will also discuss connections with the negative curvature (anti de Sitter) setting.

2:00 pm in 140 Henry Administration Building,Thursday, February 13, 2014

#### Some proofs of quadratic reciprocity

###### Dane Skabelund (UIUC Math)

Abstract: The law of quadratic reciprocity, first completely proven by Gauss in 1801, is perhaps the most proved theorem in number theory. I will present several proofs of this theorem which I find interesting, some of which I hope not everyone will have seen before.

4:00 pm in 245 Altgeld Hall,Thursday, February 13, 2014

#### Complex dynamics in several variables

###### Eric Bedford (Indiana University)

Abstract: The study of the dynamics of polynomial and rational maps of C has developed into a beautiful theory. The analogous results in higher dimension are still in the early stages of development. We will give a general survey of the behavior of polynomial and rational maps in higher dimensions. Our focus is on self-mappings of complex Euclidean space.