-
作者：Losert, Viktor
摘要：If G is a locally compact group, then for each derivation D from L-1 (G) into L-1 (G) there is a bounded measure mu is an element of M(G) with D (a) = a * mu - mu * a for a is an element of L-1 (G) (derivation problem of B. E. Johnson).
-
作者：Keith, Stephen; Zhong, Xiao
摘要：Let p > 1 and let (X, d, mu) be a complete metric measure space with mu Borel and doubling that admits a (1, p)-Poincare inequality. Then there exists epsilon > 0 such that (X, d, mu) admits a, (1, q)-Poincare inequality for every q > p - epsilon, quantitatively.
-
作者：Boupgain, Jean; Gamburd, Alex
摘要：We prove that Cayley graphs of SL2(F-p) are expanders with respect to the projection of any fixed elements in SL(2,Z) generating a non-elementary subgroup, and with respect to generators chosen at random in SL2(F-p).
-
作者：Green, Ben; Tao, Terence
摘要：We prove that there are arbitrarily long arithmetic progressions of primes. There are three major ingredients. The first is Szemeredi's theorem, which asserts that any subset of the integers of positive density contains progressions of arbitrary length. The second, which is the main new ingredient, of this paper, is a, certain transference principle. This allows us to deduce from Szemeredi's theorem that any subset of a sufficiently pseudorandom set (or measure) of positive relative density co...
-
作者：Chuang, Joseph; Rouquier, Raphael
摘要：We define and study sl(2)-categorifications on abelian categories. We show in particular that there is a self-derived (even homotopy) equivalence categorifying the adjoint action of the simple reflection. We construct categorifications for blocks of symmetric groups and deduce that two blocks are splendidly Rickard equivalent whenever they have isomorphic defect groups and we show that this implies Broue's abelian defect group conjecture for symmetric groups. We give similar results for genera...
-
作者：Colding, Tobias H.; Minicozzi, William P., II
-
作者：Green, Ben; Sanders, Tom
摘要：Suppose that G is a locally compact abelian group, and write M(G) for the algebra of bounded, regular, complex-valued measures under convolution. A mea-sure p E M(G) is said to be idempotent if mu * mu = mu, or alternatively if (mu) over cap takes only the values 0 and 1. The Cohen-Helson-Rudin idempotent theorem states that a measure mu is idempotent if and only if the set {gamma is an element of (G) over cap : (mu) over cap(gamma) = 1} belongs to the coset ring of (G) over cap, that is to sa...
-
作者：Krushkal, Vyacheslav S.
摘要：A long-standing conjecture due to Michael Freedman asserts that the 4-dimensional topological surgery conjecture fails for non-abelian free groups, or equivalently that a family of canonical examples of links (the generalized Borromean rings) are not A - B slice. A stronger version of the conjecture, that the Borromean rings are not even weakly A - B slice, where one drops the equivariant aspect of the problem, has been the main focus in the search for an obstruction to surgery. We show that t...
-
作者：Anantharaman, Nalini
摘要：We study the large eigenvalue limit for the eigenfunctions of the Laplacian, on a compact manifold of negative curvature - in fact, we only assume that the geodesic flow has the Anosov property. In the semi-classical limit, we prove that the Wigner measures associated to eigenfunctions have positive metric entropy. In particular, they cannot concentrate entirely on closed geodesics.
-
作者：Constantin, P.; Kiselev, A.; Ryzhik, L.; Zlatos, A.
摘要：We study enhancement of diffusive mixing on a compact Riemannian manifold by a fast incompressible flow. Our main result is a sharp description of the class of flows that make the deviation of the solution from its average arbitrarily small in an arbitrarily short time, provided that the flow amplitude is large enough. The necessary and sufficient condition on such flows is expressed naturally in terms of the spectral properties of the dynamical system associated with the flow. In particular, ...
