Brandt Matrices And Theta Series Over Global Function Fields
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| Author | : Chih-Yun Chuang |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 76 |
| Release | : 2015-08-21 |
| Genre | : Mathematics |
| ISBN | : 1470414198 |
The aim of this article is to give a complete account of the Eichler-Brandt theory over function fields and the basis problem for Drinfeld type automorphic forms. Given arbitrary function field k together with a fixed place ∞, the authors construct a family of theta series from the norm forms of "definite" quaternion algebras, and establish an explicit Hecke-module homomorphism from the Picard group of an associated definite Shimura curve to a space of Drinfeld type automorphic forms. The "compatibility" of these homomorphisms with different square-free levels is also examined. These Hecke-equivariant maps lead to a nice description of the subspace generated by the authors' theta series, and thereby contributes to the so-called basis problem. Restricting the norm forms to pure quaternions, the authors obtain another family of theta series which are automorphic functions on the metaplectic group, and this results in a Shintani-type correspondence between Drinfeld type forms and metaplectic forms.
| Author | : Martin Luu |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 116 |
| Release | : 2015-10-27 |
| Genre | : Mathematics |
| ISBN | : 1470414228 |
The deformation theory of automorphic representations is used to study local properties of Galois representations associated to automorphic representations of general linear groups and symplectic groups. In some cases this allows to identify the local Galois representations with representations predicted by a local Langlands correspondence.
| Author | : Genni Fragnelli |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 96 |
| Release | : 2016-06-21 |
| Genre | : Mathematics |
| ISBN | : 1470419548 |
The authors consider a parabolic problem with degeneracy in the interior of the spatial domain, and they focus on observability results through Carleman estimates for the associated adjoint problem. The novelties of the present paper are two. First, the coefficient of the leading operator only belongs to a Sobolev space. Second, the degeneracy point is allowed to lie even in the interior of the control region, so that no previous result can be adapted to this situation; however, different cases can be handled, and new controllability results are established as a consequence.
| Author | : Wen Huang |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 98 |
| Release | : 2016-04-26 |
| Genre | : Mathematics |
| ISBN | : 147041872X |
Two closely related topics, higher order Bohr sets and higher order almost automorphy, are investigated in this paper. Both of them are related to nilsystems. In the first part, the problem which can be viewed as the higher order version of an old question concerning Bohr sets is studied: for any d∈N does the collection of {n∈Z:S∩(S−n)∩…∩(S−dn)≠∅} with S syndetic coincide with that of Nild Bohr0 -sets? In the second part, the notion of d -step almost automorphic systems with d∈N∪{∞} is introduced and investigated, which is the generalization of the classical almost automorphic ones.
| Author | : Bob Oliver |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 112 |
| Release | : 2016-01-25 |
| Genre | : Mathematics |
| ISBN | : 1470415488 |
The author classifies all reduced, indecomposable fusion systems over finite -groups of sectional rank at most . The resulting list is very similar to that by Gorenstein and Harada of all simple groups of sectional -rank at most . But this method of proof is very different from theirs, and is based on an analysis of the essential subgroups which can occur in the fusion systems.
| Author | : U. Meierfrankenfeld |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 356 |
| Release | : 2016-06-21 |
| Genre | : Mathematics |
| ISBN | : 1470418770 |
Let p be a prime, G a finite Kp-group S a Sylow p-subgroup of G and Q a large subgroup of G in S (i.e., CG(Q)≤Q and NG(U)≤NG(Q) for 1≠U≤CG(Q)). Let L be any subgroup of G with S≤L, Op(L)≠1 and Q⋬L. In this paper the authors determine the action of L on the largest elementary abelian normal p-reduced p-subgroup YL of L.
| Author | : Georgios Daskalopoulos |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 102 |
| Release | : 2016-01-25 |
| Genre | : Mathematics |
| ISBN | : 1470414600 |
The authors prove that the singular set of a harmonic map from a smooth Riemammian domain to a Riemannian DM-complex is of Hausdorff codimension at least two. They also explore monotonicity formulas and an order gap theorem for approximately harmonic maps. These regularity results have applications to rigidity problems examined in subsequent articles.
| Author | : M. Escobedo |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 120 |
| Release | : 2015-10-27 |
| Genre | : Mathematics |
| ISBN | : 1470414341 |
The authors study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrödinger equation. They define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. The authors also prove the existence of a family of solutions that exhibit pulsating behavior.
| Author | : Weiwei Ao |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 100 |
| Release | : 2016-01-25 |
| Genre | : Mathematics |
| ISBN | : 1470415437 |
Click here to view the abstract. IntroductionProof of Theorem 1.1 in the caseProof of Theorem 1.1 in the caseAppendixBibliography
| Author | : Kieran G. O'Grady |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 188 |
| Release | : 2016-03-10 |
| Genre | : Mathematics |
| ISBN | : 1470416964 |
The author studies the GIT quotient of the symplectic grassmannian parametrizing lagrangian subspaces of ⋀3C6 modulo the natural action of SL6, call it M. This is a compactification of the moduli space of smooth double EPW-sextics and hence birational to the moduli space of HK 4-folds of Type K3[2] polarized by a divisor of square 2 for the Beauville-Bogomolov quadratic form. The author will determine the stable points. His work bears a strong analogy with the work of Voisin, Laza and Looijenga on moduli and periods of cubic 4-folds.
