We give results on when a finitely generated torsion free group does or does not embed in SL(2, C). For instance if we glue two copies of the figure 8 knot along its torus boundary then the fundamental group of the resulting ...

We establish the automorphy of some families of 2-dimensional representations of the absolute Galois group of a totally real field, which do not satisfy the so-called ‘Taylor–Wiles hypothesis’. We apply this to the problem ...

In the recent articles [PSU13, PSU14c], a number of tensor tomography results were proved on two-dimensional manifolds. The purpose of this paper is to extend some of these methods to manifolds of any dimension. A central ...

Mandarin Chinese is characterized by being a tonal language; the pitch (or F0) of its utterances carries considerable linguistic information. However, speech samples from different individuals are subject to changes in ...

We prove that there is no algorithm that can determine whether or not a finitely presented group has a non-trivial finite quotient; indeed, this property remains undecidable among the fundamental groups of compact, ...

We study the problem of variation of Frobenius eigenvalues on the cohomology of families of local systems of algebraic curves over finite fields.

We show that if a closed orientable 2k-manifold K, k > 2, with Euler characteristic χ(K) ≠ -2 admits an exact Lagrangian immersion into C2k with one transverse double point and no other self intersections, then K is ...

This thesis presents methods for the inference of system state and the learning of model structure for a number of hidden-state time series models, within a Bayesian probabilistic framework. Motivating examples are taken ...

The use of trading stops is a common practice in financial markets for a variety of reasons: it reduces the frequency of trading and thereby transaction costs; it provides a simple way to control losses on a given trade, ...

We embed triangulated categories defined by quivers with potential arising from ideal triangulations of marked bordered surfaces into Fukaya categories of quasiprojective 3–folds associated to meromorphic quadratic ...

This work investigates the dynamics of magnetic flows on closed orientable Riemannian surfaces. These flows are determined by triples (M, g, σ), where M is the surface, g is the metric and σ is a 2-form on M . Such dynamical ...

The present thesis deals with the mathematical treatment of kinetic theory and focuses more precisely on the Boltzmann equation. We investigate several properties of the solutions to the latter equation: their positivity ...

We study the geometry underlying the difference between nonnegative polynomials and sums of squares. The hypersurfaces that discriminate these two cones for ternary sextics and quaternary quartics are shown to be ...

We introduce a notion of ampleness for subschemes of any codimension using the theory of q-ample line bundles. We also investigate certain geometric properties satisfied by ample subvarieties, e.g. the Lefschetz ...

This thesis is devoted to the study of excitations in atomic and polariton Bose-Einstein condensates (BEC). These two specimens are prime examples for equilibrium and non equilibrium BEC. The corresponding condensate wave ...

In the econometrics of financial time series, it is customary to take some parametric model for the data, and then estimate the parameters from historical data. This approach suffers from several problems. Firstly, how is ...

High-dimensional optimal investment/consumption problems are hard to deal with, not least because of the difficulty in characterizing the value function. This paper tries to offer ways to determine an approximately optimal ...

In this paper we solve the hedge fund manager’s optimization problem in a model that allows for investors to enter and leave the fund over time depending on its performance. The manager’s payoff at the end of the year will ...

Helfgott proved that there exists a δ > 0 such that if S is a symmetric generating subset of SL(2, p)containing 1 then either S^3=SL(2, p)or |S^3| ≥|S|^1+ δ. It is known that δ ≥ 1/3024. Here we show that δ ≤ (log_2 (7) ...

We prove that moduli spaces of meromorphic quadratic differentials with simple zeroes on compact Riemann surfaces can be identified with spaces of stability conditions on a class of CY3 triangulated categories defined using ...