-
作者：Brunat, Olivier; Dudas, Olivier; Taylor, Jay
摘要：We show that the decomposition matrix of unipotent l-blocks of a finite reductive group G(F-q) has a unitriangular shape, assuming q is a power of a good prime and l is very good for G. This was conjectured by Geck in 1990 as part of his PhD thesis. We establish this result by constructing projective modules using a modification of generalised Gelfand-Graev characters introduced by Kawanaka. We prove that each such character has at most one unipotent constituent which occurs with multiplicity ...
-
作者：Balister, Paul; Bollobas, Bela; Morris, Robert; Sahasrabudhe, Julian; Tiba, Marius
摘要：We show that there exist absolute constants Delta > delta > 0 such that, for all n >= 2, there exists a polynomial P of degree n, with coefficients in { -1, 1}, such that delta root n <= vertical bar P(z)vertical bar <= Delta root n for all z is an element of C with vertical bar z vertical bar = 1. This confirms a conjecture of Littlewood from 1966.
-
作者：Schafhauser, Christopher
摘要：It is shown that if A is a separable, exact C*-algebra which satisfies the Universal Coefficient Theorem (UCT) and has a faithful, amenable trace, then A admits a trace-preserving embedding into a simple, unital AF algebra with a unique trace. Modulo the UCT, this provides an abstract characterization of C*-subalgebras of simple, unital AF-algebras. As a consequence, for a countable, discrete, amenable group G acting on a second countable, locally compact, Hausdorff space X, C-o(X) infinity(r)...
-
作者：Chodosh, Otis; Mantoulidis, Christos
摘要：The Allen-Cahn equation is a semilinear PDE which is deeply linked to the theory of minimal hypersurfaces via a singular limit. We prove curvature estimates and strong sheet separation estimates for stable solutions (building on recent work of Wang-Wei) of the Allen-Cahn equation on a 3-manifold. Using these, we are able to show that for generic metrics on a 3-manifold, minimal surfaces arising from Allen-Cahn solutions with bounded energy and bounded Morse index are two-sided and occur with m...
-
作者：Browning, Tim; Sawin, Will
摘要：We develop a geometric version of the circle method and use it to compute the compactly supported cohomology of the space of rational curves through a point on a smooth affine hypersurface of sufficiently low degree.
-
作者：McLean, Mark
摘要：We show that any two birational projective Calabi-Yau manifolds have isomorphic small quantum cohomology algebras after a certain change of Novikov rings. The key tool used is a version of an algebra called symplectic cohomology, which is constructed using Hamiltonian Floer cohomology. Morally, the idea of the proof is to show that both small quantum products are identical deformations of symplectic cohomology of some common open affine subspace.
-
作者：Tikhomirov, Konstantin
摘要：For each n, let M-n, be an n x n random matrix with independent +/- 1 entries. We show that P{M-n is singular} = (1/2 + o(n)(1))(n), which settles an old problem. Some generalizations are considered.
-
作者：Kupiainen, Antti; Rhodes, Remi; Vargas, Vincent
摘要：Dorn and Otto (1994) and independently Zamolodchikov and Zamolodchikov (1996) proposed a remarkable explicit expression, the so-called DOZZ formula, for the three point structure constants of Liouville Conformal Field Theory (LCFT), which is expected to describe the scaling limit of large planar maps properly embedded into the Riemann sphere. In this paper we give a proof of the DOZZ formula based on a rigorous probabilistic construction of LCFT in terms of Gaussian Multiplicative Chaos given ...
-
作者：Fournais, Soren; Solovej, Jan Philip
摘要：For a dilute system of non-relativistic bosons interacting through a positive, compactly supported, L-1-potential v with scattering length a we prove that the ground state energy density satisfies the bound e(rho) >= 4 pi a rho(2)(1 + 128/15 root pi root rho a(3) + o(root rho a(3))), thereby proving the Lee-Huang-Yang formula for the energy density.
-
作者：Ivanisvili, Paata; van Handel, Ramon; Volberg, Alexander
摘要：A nonlinear analogue of the Rademacher type of a Banach space was introduced in classical work of Enflo. The key feature of Enflo type is that its definition uses only the metric structure of the Banach space, while the definition of Rademacher type relies on its linear structure. We prove that Rademacher type and Enflo type coincide, settling a long-standing open problem in Banach space theory. The proof is based on a novel dimension-free analogue of Pisier's inequality on the discrete cube.
