The Hausdorff and dynamical dimensions of self-affine sponges: a dimension gap result [0.03%]
自仿射海绵的豪斯多夫维数和拓扑维数：一个维度差距结论
Tushar Das,David Simmons
Tushar Das
We construct a self-affine sponge in R 3 whose dynamical dimension, i.e. the supremum of the Hausdorff dimensions of its invariant measures, is strictly less than its Hausdorff dimension. This resolves a long-standing open problem in the ...
Dan Ciubotaru
Dan Ciubotaru
We prove that for every Bushnell-Kutzko type that satisfies a certain rigidity assumption, the equivalence of categories between the corresponding Bernstein component and the category of modules for the Hecke algebra of the type induces a b...
Converse theorems and the local Langlands correspondence in families [0.03%]
converse定理与带有族的局部Langlands对应关系
David Helm,Gilbert Moss
David Helm
We prove a descent criterion for certain families of smooth representations of GL n ( F ) (F a p-adic field) in terms of the γ -factors of pairs constructed in Moss (Int Math Res Not 2016(16):4903-4936, 2016). We then use this desce...
Tropical refined curve counting from higher genera and lambda classes [0.03%]
从更高亏格和lambda类出发的热带精化曲线计数问题
Pierrick Bousseau
Pierrick Bousseau
Block and Göttsche have defined a q-number refinement of counts of tropical curves in R 2 . Under the change of variables q = e iu , we show that the result is a generating series of higher genus log Gromov-Witten invariants with inse...
Valentin Blomer
Valentin Blomer
We develop a fairly explicit Kuznetsov formula on GL(3) and discuss the analytic behavior of the test functions on both sides. Applications to Weyl's law, exceptional eigenvalues, a large sieve and L-functions are given. ...