We construct algebras of endomorphisms in the derived category of the cohomology of arithmetic manifolds, which are generated by Hecke operators. We construct Galois representations with coefficients in these Hecke algebras ...

We discuss properties of distributions that are multivariate totally positive of order two (MTP$_{2}$) related to conditional independence. In particular, we show that any independence model generated by an MTP$_{2}$ ...

Model comparison for the purposes of selection, averaging and validation is a problem found throughout statistics. Within the Bayesian paradigm, these problems all require the calculation of the posterior probabilities of ...

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 explore transversals of finite index subgroups of finitely generated groups. We show that when H is a subgroup of a rank n group G and H has index at least n in G then we can construct a left transversal for H which ...

We investigate the rate of convergence to equilibrium for subcritical solutions to the Becker–Döring equations with physically relevant coagulation and fragmentation coefficients and mild assumptions on the given initial ...

Those who value quantitative and scientific evidence are faced with claims both of a reproducibility crisis in scientific publication, and of a post-truth society abounding in fake news and alternative facts. Both issues ...

We identify when a tubular group (the fundamental group of a finite graph of groups with $\mathbb{Z}$$^{2}$ vertex and $\mathbb{Z}$ edge groups) is free by cyclic and show, using Wise's equitable sets criterion, that every ...

We consider an h-partite version of Dilworth's theorem with multiple partial orders. Let P be a fi nite set, and let <₁, ..., <ᵣ be partial orders on P. Let G(P, <₁, ..., <ᵣ) be the graph whose vertices are the elements ...

Financial Mathematics is often presented as being composed of two main branches: one dealing with investment and consumption, with the aim of answering the now ancient question of how people should invest and spend their ...

This thesis presents a characterization of those categories with weak factorization systems that can interpret the theory of intensional dependent type theory with Σ, Π, and identity types. We use display map categories ...

A $\textit{permutoid}$ is a set of partial permutations that contains the identity and is such that partial compositions, when defined, have at most one extension in the set. In 2004 Peter Cameron conjectured that there ...

In this note, Black--Scholes implied volatility is expressed in terms of various optimization problems. From these representations, upper and lower bounds are derived which hold uniformly across moneyness and call price. ...

We introduce a norm on the space of test configurations, called the minimum norm. We conjecture that uniform K-stability is equivalent to the existence of a constant scalar curvature Kähler metric. This uniformity is ...

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 ...

This thesis is concerned with three distinct, but closely related, research topics focusing on the unipotent elements of a connected reductive algebraic group G, over an algebraically closed field k, and nilpotent elements ...

For any cosmological constant Λ = −3/$l^2$ < 0 and any $\alpha$ < 9/4, we find a Kerr-AdS spacetime ($M$, $g_{KAdS}$), in which the Klein-Gordon equation $\square g_{KAdS}$ ψ+$\alpha$/$l^2$ψ = 0 has an exponentially growing ...

We introduce a notion of stability for sheaves with respect to several polarisations that generalises the usual notion of Gieseker-stability. We prove, under a boundedness assumption, which we show to hold on threefolds ...

The thesis Witt Groups of Complex Varieties studies and compares two related cohomology theories that arise in the areas of algebraic geometry and topology: the algebraic theory of Witt groups, and real topological K-theory. ...