This paper shows that every totally-geodesic isometry from the unit disk to a finite-dimensional Teichmüller space for the intrinsic Kobayashi metric is either holomorphic or anti-holomorphic; in particular, it is a ...

Let f=\sum a_nq^n be a normalised eigen-newform of weight k\ge2 and p an odd prime which does not divide the level of f. We study a reformulation of Kato's main conjecture for f over the Zp-cyclotomic extension of Q. In ...

We formulate a notion of K-stability for Kähler manifolds, and prove one direction of the Yau–Tian–Donaldson conjecture in this setting. More precisely, we prove that the Mabuchi functional being bounded below (resp. ...

The statistical analysis of data belonging to Riemannian manifolds is becoming increasingly important in many applications, such as shape analysis, diffusion tensor imaging and the analysis of covariance matrices. In many ...

We present a graph manifold analog of the Jankins–Neumann classification of Seifert fibered spaces over $S^2$ admitting taut foliations, providing a finite recursive formula to compute the L-space Dehn-filling interval for ...

We study the level lines of a Gaussian free field in a planar domain with general boundary data F. We show that the level lines exist as continuous curves under the assumption that F is regulated (i.e., admits finite left ...

The simplest case of the Langlands functoriality principle asserts the existence of the symmetric powers Symn of a cuspidal representation of GL.2/ over the adèles of F , where F is a number field. In 1978, Gelbart and ...

I study linear waves on higher dimensional Schwarzschild black holes and Schwarzschild de Sitter spacetimes. In the first part of this thesis two decay results are proven for general finite energy solutions to the linear ...

In this paper, we deal with the problem of marginalization over and conditioning on two disjoint subsets of the node set of chain graphs (CGs) with the LWF Markov property. For this purpose, we define the class of chain ...

In response to the 2015 Royal Statistical Society's statistical analytics challenge, we propose to model the fixation locations of the human eye when observing a still image by a Markov point process in R$_{2}$. Our approach ...

We study Lagrangian embeddings of a class of two-dimensional cell complexes L_p,q into the complex projective plane. These cell complexes, which we call pinwheels, arise naturally in algebraic geometry as vanishing cycles ...

In this work we let Φ be an irreducible root system, with Coxeter group W. We consider subsets of Φ which are abelian, meaning that no two roots in the set have sum in Φ∪{0}. We classify all maximal abelian sets (i.e., ...

Density estimation is a fundamental statistical problem. Many methods are either sensitive to model misspecification (parametric models) or difficult to calibrate, especially for multivariate data (nonparametric smoothing ...

Time series models are used to characterise uncertainty in many real-world dynamical phenomena. A time series model typically contains a static variable, called parameter, which parametrizes the joint law of the random ...

We present a novel method for detecting some structural characteristics of multidimensional functions. We consider the multidimensional Gaussian white noise model with an anisotropic estimand. Using the relation between ...

We study the problem of high-dimensional regression when there may be interacting variables. Approaches using sparsity-inducing penalty functions such as the Lasso (Tibshirani, 1996) can be useful for producing interpretable ...

This thesis was motivated by data from the Emerging Risk Factors Collaboration (ERFC), a large individual participant data (IPD) meta-analysis of risk factors for coronary heart disease(CHD). Cardiovascular disease is the ...

In this thesis we give insight into the minimisation problem of genus one curves defined by equations other than Weierstrass equations. We are interested in genus one curves given as double covers of P1, plane cubics, or ...

This work constructs and compares different kinds of categorified cohomology of a locally contractible topological space X. Fix a commutative ring k of characteristic 0 and also denote by k the differential graded category ...

In quantitative finance, we often model asset prices as semimartingales, with drift, diffusion and jump components. The jump activity index measures the strength of the jumps at high frequencies, and is of interest both ...