Browsing Scholarly Works  Pure Mathematics and Mathematical Statistics by Title
Now showing items 120 of 250

The 12 model
(American Mathematical Society, 2016)The current paper is a short review of rigorous results for the 12 model. The 12 model on the hexagonal lattice is a model of statistical mechanics in which each vertex is constrained to have degree either 1 or 2. It was ... 
A 2adic automorphy lifting theorem for unitary groups over CM fields
(Springer, 2016)We prove a ‘minimal’ type automorphy lifting theorem for 2adic Galois representations of unitary type, over imaginary CM fields. We use this to improve an automorphy lifting theorem of Kisin for GL_2. 
A 3manifold group which is not four dimensional linear
(Elsevier, 20140128)We give examples of closed orientable graph 3manifolds having a fundamental group which is not a subgroup of GL(4, F) for any field F. This answers a question in the Kirby problem list from 1977 which is credited to the ... 
3manifolds everywhere
A random group contains many subgroups which are isomorphic to the fundamental group of a compact hyperbolic 3manifold with totally geodesic boundary. These subgroups can be taken to be quasiisometrically embedded. This ... 
Abelian quotients of mapping class groups of highly connected manifolds
(Springer, 20151012)We compute the abelianisations of the mapping class groups of the manifolds W²ⁿ_g = g(Sⁿ × Sⁿ) for n ≥ 3 and g ≥ 5. The answer is a direct sum of two parts. The first part arises from the action of the mapping class group ... 
About Kac's Program in Kinetic Theory
In this Note we present the main results from the recent work arxiv:1107.3251, which answers several conjectures raised fifty years ago by Kac. There Kac introduced a manyparticle stochastic process (now denoted as Kac's ... 
Active spanning trees with bending energy on planar maps and SLEdecorated Liouville quantum gravity for $\kappa > 8$
We consider the Peano curve separating a spanning tree from its dual spanning tree on an embedded planar graph, where the tree and dual tree are weighted by $y$ to the number of active edges, and "active" is in the sense ... 
Acylindrical Hyperbolicity, nonsimplicity and SQuniversality of groups splitting over $\mathbb{Z}$
(De Gruyter, 20160915)We show, using acylindrical hyperbolicity, that a finitely generated group splitting over $\mathbb{Z}$ cannot be simple. We also obtain SQuniversality in most cases, for instance a balanced group (one where if two powers ... 
Adaptation in logconcave density estimation
The logconcave maximum likelihood estimator of a density on the real line based on a sample of size n is known to attain the minimax optimal rate of convergence of O(n −4/5 ) with respect to, e.g., squared Hellinger ... 
The algebra of bounded linear operators on ℓp ⊕ ℓq has infinitely many closed ideals
We prove that in the reflexive range 1 < p < q < ∞, the algebra ℒ(ℓp⊕ℓq) of all bounded linear operators on ℓp⊕ℓq has infinitely many closed ideals. This solves a problem raised by A. Pietsch [Operator ideals, Math. Monogr. ... 
Algebraic boundaries of Hilbert's SOS cones
(Cambridge University Press, 20121015)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 ... 
Almost sure multifractal spectrum of SLE
Suppose that $\eta$ is a SchrammLoewner evolution (SLE$_\kappa$) in a smoothly bounded simply connected domain $D \subset {\mathbb C}$ and that $\phi$ is a conformal map from ${\mathbb D}$ to a connected component of $D ... 
Alperin–McKay natural correspondences in solvable and symmetric groups for the prime p=2
(Nicola Zanichelli, 20171029)Let G be a finite solvable or symmetric group and let B be a 2block of G. We construct a canonical correspondence between the irreducible characters of height zero in B and those in its Brauer first main correspondent. ... 
Alpha invariants and coercivity of the Mabuchi functional on Fano manifolds
(Université Paul Sabatier, 2016)We give a criterion for the coercivity of the Mabuchi functional for general Kàhler classes on Fano manifolds in terms of Tian's alpha invariant. This generalises a result of Tian in the anticanonical case implying the ... 
Alpha Invariants and KStability for General Polarizations of Fano Varieties
(Oxford University Press, 20140926)We provide a sufficient condition for polarisations of Fano varieties to be Kstable in terms of Tian’s alpha invariant, which uses the log canonical threshold to measure singularities of divisors in the linear system ... 
Ample subvarieties and qample divisors
(Elsevier, 20120320)We introduce a notion of ampleness for subschemes of any codimension using the theory of qample line bundles. We also investigate certain geometric properties satisfied by ample subvarieties, e.g. the Lefschetz ... 
Arithmetic invariant theory and 2descent for plane quartic curves
(Mathematical Sciences Publishers, 20160927)Given a smooth plane quartic curve C over a field $\textit{k}$ of characteristic 0, with Jacobian variety $\textit{J}$, and a marked rational point P $\in$ C($\textit{k}$), we construct a reductive group $\textit{G}$ and ... 
Asymptotics of Partial Density Functions for Divisors
(Springer, 20160919)We study the asymptotic behaviour of the partial density function associated to sections of a positive hermitian line bundle that vanish to a particular order along a fixed divisor $Y$ . Assuming the data in question is ...