Colloquia 2012-2013

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Revision as of 10:40, 26 July 2011 by Maxim (talk | contribs) (Fall 2011)
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Mathematics Colloquium

All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.

Fall 2011

date speaker title host(s)
Sep 9 Tentatively Scheduled TBA Fish
Sep 16 Rimanyi (UNC-Chapel Hill) TBA Maxim
Oct 7 Hala Ghousseini (University of Wisconsin-Madison) TBA Lempp
Oct 14 Alex Kontorovich (Yale) On Zaremba's Conjecture Shamgar
oct 19, Wed Bernd Sturmfels (UC Berkeley) TBA distinguished lecturer
oct 20, Thu Bernd Sturmfels (UC Berkeley) TBA distinguished lecturer
oct 21 Bernd Sturmfels (UC Berkeley) TBA distinguished lecturer
oct 28 Peter Constantin (University of Chicago) TBA distinguished lecturer
oct 31, Mon Peter Constantin (University of Chicago) TBA distinguished lecturer
Nov 4 Sijue Wu (U Michigan) TBA Qin Li
Nov 11 Henri Berestycki (EHESS and University of Chicago) TBA Wasow lecture
Dec 2 Robert Dudley (University of California, Berkeley) From Gliding Ants to Andean Hummingbirds: The Evolution of Animal Flight Performance Jean-Luc
dec 9 Xinwen Zhu (Harvard University) TBA Tonghai

Spring 2012

date speaker title host(s)
Feb 24 Malabika Pramanik (University of British Columbia) TBA Benguria


Abstracts

Alex Kontorovich (Yale)

On Zaremba's Conjecture

It is folklore that modular multiplication is "random". This concept is useful for many applications, such as generating pseudorandom sequences, or in quasi-Monte Carlo methods for multi-dimensional numerical integration. Zaremba's theorem quantifies the quality of this "randomness" in terms of certain Diophantine properties involving continued fractions. His 40-year old conjecture predicts the ubiquity of moduli for which this Diophantine property is uniform. It is connected to Markoff and Lagrange spectra, as well as to families of "low-lying" divergent geodesics on the modular surface. We prove that a density one set satisfies Zaremba's conjecture, using recent advances such as the circle method and estimates for bilinear forms in the Affine Sieve, as well as a "congruence" analog of the renewal method in the thermodynamical formalism. This is joint work with Jean Bourgain.