Colloquia 2012-2013: Difference between revisions
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|[http://www.math.sunysb.edu/~alexk/ Alex Kontorovich] (Yale) | |||
|''On Zaremba's Conjecture'' | |||
|Shamgar | |||
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|'''oct 19, Wed''' | |'''oct 19, Wed''' | ||
Revision as of 00:25, 18 July 2011
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 |
| 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.