Billiards in quadrilaterals, Hurwitz spaces, and real multiplication of Hecke type

Alexander Wright
Stanford University; Member, School of Mathematics
November 30, 2015

After a brief introduction to the dynamics of the $\mathrm{GL}(2,\mathbb R)$ action on the Hodge bundle (the space of translations surfaces), we will give a construction of six new orbit closures and explain why they are interesting. Joint work with Alex Eskin, Curtis McMullen, and Ronen Mukamel.

Rigidity of random Toeplitz matrices with an application to depth three circuits

Avishay Tal
Member, School of Mathematics
December 1, 2015
Joint work with Oded Goldreich. We prove that random $n$-by-$n$ Toeplitz matrices over $GF(2)$ have rigidity $\Omega(n^3/(r^2 \log n))$ for rank $r > \sqrt{n}$, with high probability. This improves, for $r = o(n / \log n \log\log n)$, over the $\Omega( (n^2 / r) \cdot \log(n/r) )$ bound that is known for many explicit matrices.

Volume and homology for hyperbolic 3-orbifolds, and the enumeration of arithmetic groups I & II

Peter Shalen
December 1, 2015
A theorem of Borel's asserts that for any positive real number $V$, there are at most finitely many arithmetic lattices in ${\rm PSL}_2({\mathbb C})$ of covolume at most $V$, or equivalently at most finitely many arithmetic hyperbolid $3$-orbifolds of volume at most $V$. Determining all of these for a given $V$ is algorithmically possible for a given $V$ thanks to work by Chinburg and Friedman, but appears to be impractical except for very small values of $V$, say $V=0.41$.

Joshua Lederberg - John von Neumann Symposium: Towards Quantitative Biology

December 2, 2015
2015 Joshua Lederberg - John von Neumann Symposium
Towards Quantitative Biology

Hosted by: The Rockefeller University and The Simons Center for Systems Biology, Institute for Advanced Study

Wednesday, December 2, 2015
Wolfensohn Hall, Institute for Advanced Study

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Speakers Include:

Uri Alon
Weizmann Institute of Science, Rehovot
Evolutionary tradeoffs and the geometry of phenotype space