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Ahlfors Lecture series
October 15-16, 2012, Organizers: H-T Yau and S-T Yau
Harvard University, Science Center, Hall A
Speaker and Program
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Elon Lindenstrauss (Hebrew University)
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October 15, 2012:
Lecture I
4:15-5:15 PM
in SC Hall A
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Homogeneous dynamics and diagonalizable actions
Algebraic actions on quotient spaces of algebraic (or Lie) groups
G/Gamma give highly interesting dynamical systems that are in many
cases intimately linked with number theory. Already
in the 1950's Cassels and Swinnerton Dyer observed implicitly (in a dual
language) that higher rank diagonal groups have interesting rigidity
properties; this was explicitly brought to the fore by Furstenberg in 1967.
These delicate rigidity properties are still far from being
understood; I will survey some of
the progress made in this direction, particularly regarding the
classification of invariant measures.
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October 16, 2012:
Lecture II
4:15-5:15 PM
in SC Hall A
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Effective theorems in homogeneous dynamics
Ergodic theory gives an extremely powerful set of tools to prove
equidistribution when there is a group action in sight (as well as
when the symmetry related to the group action is hidden and requires
an imaginative eye to become visible!)
However, most of the traditional ergodic theoretic arguments do not
give a rate of convergence to equidistribution or even for density.
This is slowly changing, and I will survey some of the progress as
well as connections to spectral gap and arithmetic combinatorics.
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