Talks

Dwarf galaxies are the most know dark matter dominated luminous objects in Universe. Observing the line of sight velocity and position of stars in Milky way satellites, and assuming the dark matter potential and a specific configuration of stellar orbits, one can obtain the mass profile of dark matter in galaxies. In this talk I will show that by considering a generic case of  phase-space density as a function of energy and angular momentum and by relaxing the specific choice of orbital configuration (which is assumed in literature), we can find  the dark matter potential and mass profile in this general case and restudy the challenges of Cold Dark Matter(CDM) paradigm like core-cusp or missing satellite problem.

We study the problem of reconstructing an unknown matrix M, of rank r and dimension d, using O(rd poly log d) Pauli measurements. This has applications to compressed sensing methods for quantum state tomography.  We give a solution to this problem based on the restricted isometry property (RIP), which improves on previous results using dual certificates. In particular, we show that almost all sets of O(rd log^6 d) Pauli measurements satisfy the rank-r RIP. This implies that M can be recovered from a fixed ("universal") set of Pauli measurements, using nuclear-norm minimization (e.g., the matrix Lasso), with nearly-optimal bounds on the error. Our proof uses Dudley's inequality for Gaussian processes, together with bounds on covering numbers obtained via entropy duality.