Now showing items 1-20 of 250

• The 1-2 model ﻿

(American Mathematical Society, 2016)
The current paper is a short review of rigorous results for the 1-2 model. The 1-2 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 2-adic automorphy lifting theorem for unitary groups over CM fields ﻿

(Springer, 2016)
We prove a ‘minimal’ type automorphy lifting theorem for 2-adic Galois representations of unitary type, over imaginary CM fields. We use this to improve an automorphy lifting theorem of Kisin for GL_2.
• A 3-manifold group which is not four dimensional linear ﻿

(Elsevier, 2014-01-28)
We give examples of closed orientable graph 3-manifolds 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 ...
• 3-manifolds everywhere ﻿

A random group contains many subgroups which are isomorphic to the fundamental group of a compact hyperbolic 3-manifold with totally geodesic boundary. These subgroups can be taken to be quasi-isometrically embedded. This ...
• Abelian quotients of mapping class groups of highly connected manifolds ﻿

(Springer, 2015-10-12)
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 many-particle stochastic process (now denoted as Kac's ...

(2005)
• Active spanning trees with bending energy on planar maps and SLE-decorated 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, non-simplicity and SQ-universality of groups splitting over $\mathbb{Z}$ ﻿

(De Gruyter, 2016-09-15)
We show, using acylindrical hyperbolicity, that a finitely generated group splitting over $\mathbb{Z}$ cannot be simple. We also obtain SQ-universality in most cases, for instance a balanced group (one where if two powers ...
• Adaptation in log-concave density estimation ﻿

The log-concave 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, 2012-10-15)
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 ...