-
作者：Jiang, Dihua; Zhang, Lei
摘要：The endoscopic classification via the stable trace formula comparison provides certain character relations between irreducible cuspidal automorphic representations of classical groups and their global Arthur parameters, which are certain automorphic representations of general linear groups. It is a question of J. Arthur and W. Schmid that asks how to construct concrete modules for irreducible cuspidal automorphic representations of classical groups in term of their global Arthur parameters? In...
-
作者：Blum, Harold; Xu, Chenyang
摘要：We prove that K-polystable degenerations of Q-Fano varieties are unique. Furthermore, we show that the moduli stack of K-stable Q-Fano varieties is separated. Together with recently proven boundedness and openness statements, the latter result yields a separated Deligne-Mumford stack parametrizing all uniformly K-stable Q-Fano varieties of fixed dimension and volume. The result also implies that the automorphism group of a K-stable Q-Fano variety is finite.
-
作者：Gao, Ziyang; Habegger, Philipp
摘要：On an abelian scheme over a smooth curve over (Q) over bar a symmetric relatively ample line bundle defines a fiberwise Neron-Tate height. If the base curve is inside a projective space, we also have a height on its (Q) over bar -points that serves as a measure of each fiber, an abelian variety. Silverman proved an asymptotic equality between these two heights on a curve in the abelian scheme. In this paper we prove an inequality between these heights on a subvariety of any dimension of the ab...
-
作者：Rondigs, Oliver; Spitzweck, Markus; Ostvaer, Paul Arne
摘要：We compute the 1-line of stable homotopy groups of motivic spheres over fields of characteristic not two in terms of hermitian and Milnor K-groups. This is achieved by solving questions about convergence and differentials in the slice spectral sequence.
-
作者：Zemke, Ian
摘要：We prove that the map on knot Floer homology induced by a ribbon concordance is injective. As a consequence, we prove that the Seifert genus is monotonic under ribbon concordance. Generalizing theorems of Gabai and Scharlemann, we also prove that the Seifert genus is super-additive under band connected sums of arbitrarily many knots. Our results give evidence for a conjecture of Gordon that ribbon concordance is a partial order on the set of knots.
-
作者：Du, Xiumin; Zhang, Ruixiang
摘要：We show that, for n >= 3, limt(t -> 0) e(it Delta) f (x) = f (x) holds almost everywhere for all f is an element of H-s (R-n) provided that s > n/2(n+1). Due to a counterexample by Bourgain, up to the endpoint, this result is sharp and fully resolves a problem raised by Carleson. Our main theorem is a fractal L-2 restriction estimate, which also gives improved results on the size of the divergence set of the Schrodinger solutions, the Falconer distance set problem and the spherical average Fou...
-
作者：Prywes, Eden
摘要：We show that a closed, connected and orientable Riemannian manifold M of dimension d that admits a nonconstant quasiregular mapping from R-d must have bounded dimension of the cohomology independent of the distortion of the map. The dimension of the degree l de Rham cohomology of M is bounded above by ((d)(l)). This is a sharp upper bound that proves the Bonk-Heinonen conjecture. A corollary of this theorem answers an open problem posed by Gromov in 1981. He asked whether there exists a d-dime...
-
作者：Schneiderman, Rob; Teichner, Peter
摘要：We compute the group LM2,24 of link homotopy classes of link maps of two 2-spheres into 4-space. It turns out to be free abelian, generated by geometric constructions applied to the Fenn-Rolfsen link map and detected by two self-intersection invariants introduced by Kirk in this setting. As a corollary, we show that any link map with one topologically embedded component is link homotopic to the unlink. Our proof introduces a new basic link homotopy, which we call a Whitney homotopy, that shrin...
-
作者：Anantharaman, Nalini; Sabri, Mostafa
摘要：We prove a quantum-ergodicity theorem on large graphs, for eigenfunctions of Schrodinger operators in a very general setting. We consider a sequence of finite graphs endowed with discrete Schrodinger operators, assumed to have a local weak limit. We assume that our graphs have few short loops, in other words that the limit model is a random rooted tree endowed with a random discrete Schrodinger operator. We show that an absolutely continuous spectrum for the infinite model, reinforced by a goo...
-
作者：Gamburd, Alex; Magee, Michael; Ronan, Ryan
摘要：We establish an asymptotic formula for the number of integer solutions to the Markoff-Hurwitz equation x(1)(2) + x(2)(2) + ... +x(n)(2) = ax(1)x(2) ... x(n) + k. When n >= 4, the previous best result is by Baragar (1998) that gives an exponential rate of growth with exponent beta that is not in general an integer when n >= 4. We give a new interpretation of this exponent of growth in terms of the unique parameter for which there exists a certain conformal measure on projective space.
