Colloquia 2012-2013

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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 30 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 18 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 2011

date speaker title host(s)
jan 21 Emanuele Macri (University of Bonn) Stability conditions and Bogomolov-type inequalities in higher dimension Andrei Caldararu
jan 28 Marcus Roper (Berkeley) Modeling microbial cooperation Paul Milewski
jan 31, 2:30pm, room 901 Ana-Maria Castravet (Arizona) Hypertrees and moduli spaces of stable rational curves Andrei
feb 4 Xinyi Yuan (Columbia University) Equidistribution in algebraic dynamics Tonghai
feb 11 Christian Schnell (U. Illinois at Chicago) On the locus of Hodge classes and its generalizations Andrei
feb 25 Omri Sarig (Penn State and Weizmann Institute) Measure rigidity for dynamical systems on (very) non-compact spaces Shamgar
mar 4 Jeff Weiss (Colorado) Nonequilibrium Statistical Mechanics and Climate Variability Jean-Luc
mar 11 Roger Howe (Yale) Hibi Rings in Invariant Theory Shamgar
mar 22, Tue Sylvain Cappell (Courant, NYU) Compact aspherical manifolds whose fundamental groups have center Laurentiu
mar 25 Pham Huu Tiep (Arizona) Representations of finite simple groups and applications Martin Isaacs
apr 1 Amy Ellis (Madison) Do algebra students need a reality check? How quantitative reasoning can support function understanding. Steffen
apr 8 Alan Weinstein (Berkeley) Symplectic and Quantum Categories Yong-Geun
apr 15 Max Gunzburger (Florida State) A nonlocal vector calculus and finite element methods for nonlocal diffusion and mechanics James Rossmanith
apr 21, Thu Jane Hawkins (U. North Carolina) Dynamical properties and parameter space of elliptic functions WIMAW (Diane Holcomb)
apr 29 Jaroslaw Wlodarczyk (Purdue) Algebraic Morse Theory and factorization of birational maps Laurentiu
may 2, Mon Olga Holtz (Berkeley) On complexity of linear problems LAA Lecture (Shamgar)
may 6 Rami Aizenbud (MIT) Gelfand pairs and Invariant distributions Shamgar

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.