Department of

Mathematics


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

     .
events for the
events containing  

(Requires a password.)
More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
     January 2014          February 2014            March 2014     
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
           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
 12 13 14 15 16 17 18    9 10 11 12 13 14 15    9 10 11 12 13 14 15
 19 20 21 22 23 24 25   16 17 18 19 20 21 22   16 17 18 19 20 21 22
 26 27 28 29 30 31      23 24 25 26 27 28      23 24 25 26 27 28 29
                                               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.