Every smooth p-adic Lie group admits a compatible analytic structure

We show that every finite-dimensional p-adic Lie group of class C^k admits a C^k-compatible analytic Lie group structure.Comment: LaTeX, 37 page

Log Hodge groups on a toric Calabi-Yau degeneration

We give a spectral sequence to compute the logarithmic Hodge groups on a hypersurface type toric log Calabi-Yau space, compute its E_1 term explicitly in terms of tropical degeneration data and Jacobian rings and prove its degeneration at E_2 under mild assumptions. We prove the basechange of the affine Hodge groups and deduce it for the logarithmic Hodge groups in low dimensions. As an application, we prove a mirror symmetry duality in dimension two and four involving the usual Hodge numbers, the stringy Hodge numbers and the affine Hodge numbers.Comment: 49 pages, 3 figure

Localization for random operators with non-monotone potentials with exponentially decaying correlations

I consider random Schr\"odinger operators with exponentially decaying single site potential, which is allowed to change sign. For this model, I prove Anderson localization both in the sense of exponentially decaying eigenfunctions and dynamical localization. Furthermore, the results imply a Wegner-type estimate strong enough to use in classical forms of multi-scale analysis