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On the Geometry of the Nodal Lines of Eigenfunctions of the Two-Dimensional Torus
Geometry of the Nodal Lines of Eigenfunctions Two-Dimensional Torus
2011/2/22
The width of a convex curve in the plane is the minimal distance between a pair of parallel supporting lines of the curve. In this paper we study the width of nodal lines of eigenfunctions of the Lapl...
The paper is an informal report on joint work with Stefan Haller on Dynamics in relation with Topology and Spectral Geometry. By dynamics one means a smooth vector field on a closed smooth manifold; t...
The Convex Geometry of Linear Inverse Problems
Convex optimization semidefinite programming atomic norms
2011/1/17
In applications throughout science and engineering one is often faced with the challenge of
solving an ill-posed inverse problem, where the number of available measurements is smaller
than the dimen...
Diophantine Geometry over Groups X: The Elementary Theory of Free Products of Groups
Diophantine Geometry Groups X Elementary Theory of Free Products of Groups
2011/1/14
This paper is the 10th in a sequence on the structure of sets of solutions to systems of equations over groups, projections of such sets (Diophantine sets), and the structure of definable sets over fe...
Exceptional collections on toric Fano threefolds and birational geometry
Exceptional collections toric Fano threefolds birational geometry
2011/2/22
Bernardi and Tirabassi show the existence of a full strong excep-tional collection consisting of line bundles on smooth toric Fano 3-folds under assuming Bondal’s conjecture, which states that the Fro...
In a holomorphic family (Xb)b∈B of non-K¨ahlerian compact manifolds,the holomorphic curves representing a fixed 2-homology class do not form a proper family in general.
Gauge fixing in (2+1)-gravity: Dirac bracket and spacetime geometry
Gauge fixing (2+1)-gravity: Dirac bracket spacetime geometry
2011/3/2
We consider (2+1)-gravity with vanishing cosmological constant as a constrained dynamical system. By applying Dirac’s gauge fixing procedure, we implement the constraints and determine the Dirac brack...
Geometry of CR submanifolds of maximal CR dimension in complex space forms
Complex space form CR submanifold of maximal CR dimension
2011/2/24
On real hypersurfaces in complex space forms many results are proven.In this paper we generalize some results concerning extrinsic geometry of real hypersurfaces, to CR submanifolds of maximal CR dime...
Line bundles and the Thom construction in noncommutative geometry
Line bundles Thom construction noncommutative geometry
2011/1/19
The idea of a line bundle in classical geometry is transferred to noncommutative geometry by the idea of a Morita context. From this we can construct Z and N graded algebras, the Z graded algebra bein...
Geometry of free cyclic submodules over ternions
Geometry of free cyclic submodules ternions
2011/1/19
Given the algebra T of ternions (upper triangular 2 ×2 matrices)over a commutative field F we consider as set of points of a projective line over T the set of all free cyclic submodules of T2. This se...
Universal Hyperbolic Geometry II: A pictorial overview
Universal Hyperbolic Geometry II pictorial overview
2011/1/18
This article provides a simple pictorial introduction to universal hyperbolic geometry. We explain how to understand the subject using only elementary projective geometry, augmented by a distinguished...
We study pure Yang–Mills theory on × S2, where is a compact Riemann surface, and invariance is assumed under rotations of S2. It is well known that the self-duality equations in this set-up reduce...
Geometry of maximum likelihood estimation in Gaussian graphical models
Geometry of maximum likelihood estimation Gaussian graphical models
2011/1/21
We study maximum likelihood estimation in Gaussian graphical models from a geometric point of view. An algebraic elimination criterion allows us to nd exact lower bounds on the number of observations...
Quantum Gravity coupled to Matter via Noncommutative Geometry
Quantum Gravity Matter Noncommutative Geometry
2011/3/2
We show that the principal part of the Dirac Hamiltonian in 3+1 dimensions emerges in a semi-classical approximation from a construc-tion which encodes the kinematics of quantum gravity.
Classical integral geometry takes place in Rn equipped with the Euclidean metric. We begin to develop integral geometry for Rn equipped with the taxicab metric (induced by the 1-norm).