Colloquia 2012-2013
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.