We prove that for generic geometry, the curl-eigenfield solutions to the steady Euler equations on R 3 /Z 3 are all hydrodynamically unstable (linear, L norm). The proof involves amarriage of contact topological methods with the instability criterion of Friedlander-Vishik. An application of contact homology is the crucial step.

We prove that if R is a Hensel local ring with infinite residue field k, the natural map Hi(GLn(R),Z/p) → Hi(GLn(k), Z/p) is an isomorphism for i ≤ 3, p 6= char k. This implies rigidity for Hi(GLn), i ≤ 3, which in turn implies the Friedlander–Milnor conjecture in positive characteristic in degrees ≤ 3. A fundamental question in the homology of linear groups is that of rigidity: given a smooth ...

Abstract In 1998 Friedlander and Iwaniec proved that there are infinitely many primes of the form $$a^2+b^4$$ a 2 + b 4 . To show this they used Jacobi symbol to define spin Gaussian integers, one...

M. A. Vogelsong, E. Staroswiecki, B. A. Hargreaves, E. Han, J. A. Fattor, A. L. Friedlander, O. Shah, J. M. Beaubien, and G. E. Gold Radiology, Stanford University, Stanford, CA, United States, Electrical Engineering, Stanford University, Stanford, CA, Radiology, Stanford University, Stanford, CA, GE Healthcare Global Applied Sciences Laboratory, Menlo Park, CA, Stanford Center on Longevity, St...

1358 NOTICES OF THE AMS VOLUME 46, NUMBER 11 O ur everyday life is full of examples of fluid motion, from the drama of tornadoes and hurricanes, the turbulent cascading flows in rivers, and the breaking of massive ocean waves to the undramatic familiarity of stirring a cup of tea. Inspired by observation, scientists have sought for centuries to understand and predict fluid behavior. Over two hu...

We prove interlacing inequalities between spectral minimal energies of metric graphs built on Dirichlet and standard Laplacian eigenvalues, as recently introduced in [Kennedy et al, arXiv:2005.01126]. These inequalities, which involve the first Betti number degree one vertices graph, recall both other for eigenvalues whole well estimates difference nodal Neumann domains graph eigenfunctions. To...

We prove quantitative nonvanishing theorems for central values and central derivatives of L–series associated to canonical Hecke characters of imaginary quadratic fields. These results have applications to the study of Chow groups of Kuga-Sato varieties. Some key ingredients in the proofs are bounds for `-torsion in class groups obtained recently by Ellenberg and Venkatesh [EV], and subconvexit...