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First Bourbaki seminar of 2015 (II): Carron's talk

For the second installment of this series of posts (which started here) on the first Bourbaki seminar of 2015, we will discuss Gilles Carron… 2,384 more words


Khot, Osher, Griffiths

In addition to the Fields medallists mentioned in the previous post, the IMU also awarded the Nevanlinna prize to Subhash Khot, the Gauss prize… 1,142 more words


Dynamics of the Weil-Petersson flow: proof of Burns-Masur-Wilkinson ergodicity criterion II

Last time, we showed the first part of Burns-Masur-Wilkinson ergodicity criterion:

Theorem 1 (Burns-Masur-Wilkinson) Let be the quotient of a contractible, negatively curved, possibly incomplete, Riemannian manifold by a subgroup of isometries of acting freely and properly discontinuously.

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Dynamics of the Weil-Petersson flow: proof of Burns-Masur-Wilkinson ergodicity criterion I

Last time, we reduced the proof of Burns-Masur-Wilkinson theorem on the ergodicity (and mixing) of the Weil-Petersson geodesic flow to a certain estimate for the first derivative of a geodesic flow on negatively curved manifolds (cf. 4,041 more words


The Cayley-Salmon theorem via classical differential geometry

Let be an irreducible polynomial in three variables. As is not algebraically closed, the zero set can split into various components of dimension between and . 1,278 more words


Dynamics of the Weil-Petersson flow: basic geometry of the Weil-Petersson metric I

Today we will define the Weil-Petersson (WP) metric on the cotangent bundle of the moduli spaces of curves and, after that, we will see that the WP metric satisfies the first three items of the… 5,688 more words


Energy of links and Freedman-He-Wang's conjecture after Ian Agol, Fernando Coda Marques and Andre Neves

The solution of a long-standing conjecture normally provokes a lot of excitement in the mathematical community because it usually brings a considerable amount of new ideas… 2,418 more words