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We establish p-adic versions of the Manin-Mumford conjecture, which states that an irreducible subvariety of an abelian variety with dense torsion has to be the translate of a subgroup by a torsion point. We do so in the context of certain rigid analytic s ...
We propose a computational approach to approximate the value function and control poli- cies for a finite horizon stochastic reach-avoid problem as follows. First, we formulate an infinite dimensional linear program whose solution characterizes the optimal ...
We consider the infinite dimensional linear programming (inf-LP) approach for solving stochastic control problems. The inf-LP corresponding to problems with uncountable state and input spaces is in general computationally intractable. By focusing on linear ...
In this thesis we consider the problem of estimating the correlation of Hecke eigenvalues of GL2 automorphic forms with a class of functions of algebraic origin defined over finite fields called trace functions. The class of trace functions is vast and inc ...
We investigate generalizations along the lines of the Mordell-Lang conjecture of the author's p-adic formal Manin-Mumford results for n-dimensional p-divisible formal groups F. In particular, given a finitely generated subgroup (sic) of F(Q(p)) and a close ...
One of the most fundamental problems in Markov decision processes is analysis and control synthesis for safety and reachability specifications. We consider the stochastic reach-avoid problem, in which the objective is to synthesize a control policy to max ...
Inspired by recent experiments using synthetic microswimmers to manipulate droplets, we investigate the low-Reynolds-number locomotion of a model swimmer (a spherical squirmer) encapsulated inside a droplet of a comparable size in another viscous fluid. Me ...
A bipartite graph G is semi-algebraic in R-d if its vertices are represented by point sets P,Q subset of R-d and its edges are defined as pairs of points (p,q) epsilon P x Q that satisfy a Boolean combination of a fixed number of polynomial equations and i ...
A non-reciprocal acoustic device that accomplishes non-reciprocity via linear or angular-momentum bias. The non-reciprocal acoustic device includes an azimuthally symmetric or planar acoustical cavity (e.g., ring cavity), where the cavity is biased by impo ...
