| 1. |
- Xia, Jiacheng, 1991
(författare)
-
Vector-valued Eisenstein series of congruence types and their products
- 2019
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Historically, Kohnen and Zagier connected modular forms with period polynomials, and as a consequence of this association concluded that the products of at most two Eisenstein series span all spaces of classical modular forms of level 1. Later Borisov and Gunnells among other authors extended the result to higher levels. We consider this problem for vector-valued modular forms, establish the framework of congruence types and obtain the structure of the space of vector-valued Eisenstein series using tools from representation theory. Based on this development and historic results, we show that the space of vector-valued modular forms of certain weights and any congruence type can be spanned by the invariant vectors of that type tensor at most two Eisenstein series.
|
|
| 2. |
- Berman, Robert, 1976
(författare)
-
On the strict convexity of the K-energy
- 2019
-
Ingår i: Pure and Applied Mathematics Quarterly. - 1558-8599 .- 1558-8602. ; 15:4, s. 983-999
-
Tidskriftsartikel (refereegranskat)abstract
- Let (X, L) be a polarized projective complex manifold. We show, by a simple toric one-dimensional example, that Mabuchi's K-energy functional on the geodesically complete space of bounded positive (1, 1)-forms in c(1)(L), endowed with the Mabuchi-Donaldson-Semmes metric, is not strictly convex modulo automorphisms. However, under some further assumptions the strict convexity in question does hold in the toric case. This leads to a uniqueness result saying that a finite energy minimizer of the K-energy (which exists on any toric polarized manifold (X, L) which is uniformly K-stable) is uniquely determined modulo automorphisms under the assumption that there exists some minimizer with strictly positive curvature current.
|
|
| 3. |
- Almquist, Martin, et al.
(författare)
-
Order-preserving interpolation for summation-by-parts operators at nonconforming grid interfaces
- 2019
-
Ingår i: SIAM Journal of Scientific Computing. - : Society for Industrial and Applied Mathematics Publications. - 1064-8275 .- 1095-7197. ; 41:2, s. A1201-A1227
-
Tidskriftsartikel (refereegranskat)abstract
- We study nonconforming grid interfaces for summation-by-parts finite difference methods applied to partial differential equations with second derivatives in space. To maintain energy stability, previous efforts have been forced to accept a reduction of the global convergence rate by one order, due to large truncation errors at the nonconforming interface. We avoid the order reduction by generalizing the interface treatment and introducing order-preserving interpolation operators. We prove that, given two diagonal-norm summation-by-parts schemes, order-preserving interpolation operators with the necessary properties are guaranteed to exist, regardless of the grid-point distributions along the interface. The new methods retain the stability and global accuracy properties of the underlying schemes for conforming interfaces.
|
|
| 4. |
- Bandara, Lashi, et al.
(författare)
-
Riesz continuity of the Atiyah–Singer Dirac operator under perturbations of local boundary conditions
- 2019
-
Ingår i: Communications in Partial Differential Equations. - : Informa UK Limited. - 0360-5302 .- 1532-4133. ; 44:12, s. 1253-1284
-
Tidskriftsartikel (refereegranskat)abstract
- On a smooth complete Riemannian spin manifold with smooth compact boundary, we demonstrate that Atiyah–Singer Dirac operator /DB in L2 depends Riesz continuously on L∞ perturbations of local boundary conditions B. The Lipschitz bound for the map B→/DB(1+/D2B)−12 depends on Lipschitz smoothness and ellipticity of B and bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius away from a compact neighbourhood of the boundary. More generally, we prove perturbation estimates for functional calculi of elliptic operators on manifolds with local boundary conditions.
|
|
| 5. |
- Rowlett, Julie, 1978, et al.
(författare)
-
How to hear the corners of a drum
- 2019
-
Ingår i: Matrix Annals. - Cham : Springer International Publishing. ; 2017, s. 243-278, s. 243-278
-
Konferensbidrag (refereegranskat)abstract
- We prove that the existence of corners in a class of planar domain, which includes all simply connected polygonal domains and all smoothly bounded domains, is a spectral invariant of the Laplacian with both Neumann and Robin boundary conditions. The main ingredient in the proof is a locality principle in the spirit of Kac’s “principle of not feeling the boundary,” but which holds uniformly up to the boundary. Albeit previously known for Dirichlet boundary condition, this appears to be new for Robin and Neumann boundary conditions, in the geometric generality presented here. For the case of curvilinear polygons, we describe how the same arguments using the locality principle are insufficient to obtain the analogous result. However, we describe how one may be able to harness powerful microlocal methods and combine these with the locality principles demonstrated here to show that corners are a spectral invariant; this is current work-in-progress (Nursultanov et al., Preprint).
|
|
| 6. |
- Goffeng, Magnus C H T, 1987, et al.
(författare)
-
Constructing KMS states from infinite-dimensional spectral triples
- 2019
-
Ingår i: Journal of Geometry and Physics. - : Elsevier BV. - 0393-0440. ; 143, s. 107-149
-
Tidskriftsartikel (refereegranskat)abstract
- We construct KMS-states from Li1-summable semifinite spectral triples and show that in several important examples the construction coincides with well-known direct constructions of KMS-states for naturally defined flows. Under further summability assumptions the constructed KMS-state can be computed in terms of Dixmier traces. For closed manifolds, we recover the ordinary Lebesgue integral. For Cuntz–Pimsner algebras with their gauge flow, the construction produces KMS-states from traces on the coefficient algebra and recovers the Laca–Neshveyev correspondence. For a discrete group acting on its Stone–Čech boundary, we recover the Patterson–Sullivan measures on the Stone-Čech boundary for a flow defined from the Radon–Nikodym cocycle.
|
|
| 7. |
- Andersson, Mats, 1957, et al.
(författare)
-
On a Monge-Ampere Operator for Plurisubharmonic Functions with Analytic Singularities
- 2019
-
Ingår i: Indiana University Mathematics Journal. - : Indiana University Mathematics Journal. - 0022-2518. ; 68:4, s. 1217-1231
-
Tidskriftsartikel (refereegranskat)abstract
- We study continuity properties of generalized Monge-Ampere operators for plurisubharmonic functions with analytic singularities. In particular, we prove continuity for a natural class of decreasing approximating sequences. We also prove a formula for the total mass of the Monge-Ampere measure of such a function on a compact Kahler manifold.
|
|
| 8. |
- Bershtein, O., et al.
(författare)
-
Maximum modulus principle for "holomorphic functions" on the quantum matrix ball
- 2019
-
Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 276:5, s. 1479-1509
-
Tidskriftsartikel (refereegranskat)abstract
- We describe the Shilov boundary ideal for a q-analog of the algebra of holomorphic functions on the unit ball in the space of n x n matrices and show that its C*-envelope is isomorphic to the C*-algebra of continuous functions on the quantum unitary group U-q(n). (C) 2018 Elsevier Inc. All rights reserved.
|
|
| 9. |
- Billig, Y., et al.
(författare)
-
Representations of the Lie algebra of vector fields on a sphere
- 2019
-
Ingår i: Journal of Pure and Applied Algebra. - : Elsevier BV. - 0022-4049. ; 223:8, s. 3581-3593
-
Tidskriftsartikel (refereegranskat)abstract
- For an affine algebraic variety X we study a category of modules that admit compatible actions of both the algebra A of functions on X and the Lie algebra of vector fields on X. In particular, for the case when X is the sphere S-2, we construct a set of simple modules that are finitely generated over A. In addition, we prove that the monoidal category that these modules generate is equivalent to the category of finite-dimensional rational GL(2)-modules. (C) 2018 Elsevier B.V. All rights reserved.
|
|
| 10. |
- Deeley, Robin J., et al.
(författare)
-
Relative geometric assembly and mapping cones Part II: Chern characters and the Novikov property
- 2019
-
Ingår i: Münster Journal of Mathematics. - 1867-5778 .- 1867-5786. ; 12:1, s. 57-92
-
Tidskriftsartikel (refereegranskat)abstract
- We study Chern characters and the assembly mapping for free actions using the framework of geometric K-homology. The focus is on the relative groups associated with a group homomorphism phi: Gamma(1) -> Gamma(2) along with applications to Novikov type properties. In particular, we prove a relative strong Novikov property for homomorphisms of hyperbolic groups and a relative strong l(1)-Novikov property for polynomially bounded homomorphisms of groups with polynomially bounded cohomology in C. As a corollary, relative higher signatures on a manifold with boundary W, with pi(1)(partial derivative W) -> pi(1) (W) belonging to the class above, are homotopy invariant.
|
|
