Dokumente Fakultät für Mathematik und Informatik (inkl. GAUSS) nach Gutachter "Pidstrygach, Viktor Prof. Dr."
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A theory of discrete parametrized surfaces in R^3
(2018-07-27)In discrete differential geometry (DDG) one considers objects from discrete geometry from a differential geometric perspective. Rather than focusing on approximations of the smooth theory, with error vanishing in the ... -
Approximation of Baker domains and convergence of Julia sets.
(2013-05-14)The goal of this thesis is to prove the Hausdorff convergence of Julia sets as we approximate a family of transcendental entire functions featuring a unique Baker domain. At first, we give a dynamical description of the ... -
Benjamini-Schramm Convergence of Normalized Characteristic Numbers of Riemannian Manifolds
(2020-04-30)We study a weak form of Gromov-Hausdorff convergence of Riemannian manifolds, also known as Benjamini-Schramm convergence. This concept is also applicable to other areas and has widely been studied in the context of ... -
Foliated Positive Scalar Curvature
(2021-11-11)In this thesis we study different questions on scalar curvatures. The first part is devoted to obstructions against existence of a (Riemannian) metric with positive scalar curvature on a closed manifold. The second ... -
Generalized Seiberg-Witten and the Nahm Transform
(2019-01-11)Using the viewpoint of principal bundles on hyperk¨ ahler reductions, we recover the results of Gocho and Nakajima [GN92] and give insights into the role that the quater- nions play. We define a framework for dimensional ... -
Invariants of Kähler manifolds and Generalized Seiberg-Witten Equations
(2024-03-06)The thesis explores the generalized Seiberg-Witten equations, a gauge theoretic differential equation arising in physics by coupling a non-linear spinor to a connection. The study involves an analysis of the solution space ... -
Local invariants of four-dimensional Riemannian manifolds and their application to the Ricci flow
(2017-12-15)In this thesis, we study the four-dimensional Ricci flow with the help of local invariants.If $(M^4, g(t))$ is a solution to the Ricci flow and $x \in M$, we can associate to the point $x$ a one-parameter family of curves, ... -
Moduli spaces of bundles over two-dimensional orders
(2013-05-15)We study modules over maximal orders on smooth projective surfaces and their moduli spaces. We investigate zero- and two-dimensional moduli spaces on K3 and abelian surfaces for unramified orders, so called Azumaya algebras. ... -
Nahms Equations and Nilpotent Orbits
(2022-05-31)P. Kronheimer has identified certain space of solutions to Nahms equations with a coadjoint orbit of a nilpotent element in a complex, semi-simple Lie algebra and that way equipped the orbit with an hyperkähler structure ... -
New topological and index theoretical methods to study the geometry of manifolds
(2018-07-31)For a $\mathit{Spin}$ manifold $M$ the Rosenberg index $\alpha([M])$ is an obstruction against positive scalar curvature metrics. When $M$ is non-$\mathit{Spin}$ but $\mathit{Spin}^c$, Bolotov and Dranishnikov suggested ... -
Noncommutative manifolds and Seiberg-Witten-equations
(2011-10-17)In this thesis we study differential geometry of noncommutative manifolds. We introduce a general framework of noncommutative manifolds based on Poincaré duality and study the notions of differential forms and Sobolev ... -
On Newton-Okounkov bodies, linear series and positivity
(2018-04-04)This thesis consists of four independent articles all connected to the theory of Newton-Okounkov bodies. It contains result about toric degenerations of Del Pezzo surfaces/Bott-Samelson varieties as well as an extension ... -
On the action of the group of automorphisms of the affine plane on instantons
(2011-02-09)We define an action of the group of automorphism of the affine plane on SU(2)-instantons ans investgate the orbits of this action. -
Permuting actions, moment maps and the generalized Seiberg-Witten equations
(2016-04-21)In this thesis, we study properties and the geometry related to the generalization of the Seiberg-Witten equations introduced by Taubes and Pidstrygach. A crucial ingrediant to these equations is a hyperkähler manifold M ... -
The Geometry of the Milnor Number
(2012-06-12)In the first part of this thesis we derive a volume-preserving normal form for function germs in n complex variables which are right equivalent to the product of all coordinates. In the second part of the thesis we discuss ... -
Thetafunktionen und konjugationsinvariante Funktionen auf Paaren von Matrizen
(2009-01-16)We express conjugation-invariant functions on the space of equivalence classes of pairs of kxk matrices via theta functions. Our approach is based on the well-known interplay between algebraic ... -
Variational Geometric Invariant Theory and Moduli of Quiver Sheaves
(2018-06-26)We are concerned with two applications of GIT. First, we prove that a geometric GIT quotient of an a ne variety X = Spec(A) by a reductive group G, where A is an almost factorial domain, is a Mori dream space, regardless ...