Mathematics

Harmonic balls are domains that satisfy the mean-value property for harmonic functions. We establish the existence and uniqueness of harmonic balls on Liouville quantum g [...]

We consider the analysis of singular waveguides separating insulating phases in two-space dimensions. The insulating domains are modeled by a massive Schrödinger equatio [...]

In a Mean Field Game (MFG) each decision maker cares about the cross sectional distribution of the state and the dynamics of the distribution is generated by the agents [...]

We derive the variational formula of the Loewner driving function of a simple chord under infinitesimal quasiconformal deformations with Beltrami coefficients supported a [...]

Background: Determining the composition of artifact residues is a central problem in ancient residue metabolomics. This is done by comparing mass spectral features in [...]

Let p ≥ 3 be a prime and suppose G is a form of a reductive group, that is compact at infinity and splits at p. Under these assumptions, we can est [...]

This thesis is a compilation of two papers that are essentially independent. In Chapter One, we first introduce the development of Anderson localization and its relevance [...]

We study the ramification on the cohomology of a smooth proper surface $X$ in mixed characteristic, when $X$ degenerates to a surface over $\overline{\mathbb{F}}_p$ with [...]

This thesis studies various problems that arise in the study of Mean Field Games and Mean Field Control. First we prove that a hypoelliptic MFG system with local-coupling [...]

This thesis details recent results concerning the regularity, well-posedness, and long-time behavior of the first-order mean field games system with a local coupling. Fir [...]

Let 𝜉 be an analytic bracket-generating distribution. We show that the subspace of germs that are singular (in the sense of control theory) has infinite codimension [...]

Let $G$ be a (split) reductive group over $F_q$, $T$ a maximal torus, $T' \subset T$ a subtorus, and $M = Z_G(T')$ -- a reductive subgroup of $G$. Let $P$ denote a parabo [...]

This thesis consists of two chapters: The first and primary component is dedicated to the Hitchin morphism for symmetric spaces, which is joint work with B. Morrissey. W [...]

This thesis studies the existence of smooth models for fibered partially hyperbolic systems. Fibered partially hyperbolic systems are partially hyperbolic diffeomorphisms [...]

Fix a prime number $p>2.$ Let $\bar{r} : Gal(\overline{Q}_p/Q_p)\to GL_2(\overline{F}_p)$ be an absolutely irreducible residual representation. In this paper, we descr [...]

In this thesis, we develop a scattering theory for the asymmetric transport observed at interfaces separating two-dimensional topological insulators. Starting from the sp [...]

The structure of the Galois group of the maximal unramified extension of a number field has been an object of interest for more than a century now. This thesis is partial [...]

In this thesis, we prove existence of global solutions and scattering for systems of quadratic nonlinear Schr\"odinger equations in the critical three-dimensional ca [...]

Given a p-complete, animated ring S, we define a filtration on the Nygaard-complete, absolute prismatic cohomology, which we call the r-Nygaard filtration. This is obtain [...]

In this thesis, we study the differences between smooth and topological manifolds in the equivariant setting. The central topic will be on smooth structures. Kirby-Sieben [...]

This thesis comprises one chapter (plus this introduction) and two appendices. Chapter $\ref{computability theory of ec groups}$ appears, with minor modifications, as a st [...]

This thesis consists of four parts. In the first part, we introduce the results, and sketch the ideas behind the proofs. In the second part, we construct genus one singul [...]

Radiotherapy is a cancer treatment that uses high-energy X-rays to kill cancer cells. A major challenge in treating cancer is the heterogeneity of the disease. Preclinica [...]

Our article is motivated by the vanishing condition of minimal volume of closed smooth manifolds $M$ that admit locally homogeneous Riemannian metric.We give a complete c [...]

Networks of neurons produce diverse patterns of oscillations, arising from the network's global properties, the propensity of individual neurons to oscillate, or a mix [...]