Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Referee "Pidstrygach, Viktor Prof. Dr."
Now showing items 118 of 18

Divisors on K3 surfaces and Hilbert schemes
(20240627)This thesis consists of three chapters. In the first chapter we study rational curves on K3 surfaces and show that on elliptic K3s there are rational curves whose arithmetic genus tends to infinity. In the second chapter ... 
Invariants of Kähler manifolds and Generalized SeibergWitten Equations
(20240306)The thesis explores the generalized SeibergWitten equations, a gauge theoretic differential equation arising in physics by coupling a nonlinear spinor to a connection. The study involves an analysis of the solution space ... 
Nahms Equations and Nilpotent Orbits
(20220531)P. Kronheimer has identified certain space of solutions to Nahms equations with a coadjoint orbit of a nilpotent element in a complex, semisimple Lie algebra and that way equipped the orbit with an hyperkähler structure ... 
Foliated Positive Scalar Curvature
(20211111)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 ... 
BenjaminiSchramm Convergence of Normalized Characteristic Numbers of Riemannian Manifolds
(20200430)We study a weak form of GromovHausdorff convergence of Riemannian manifolds, also known as BenjaminiSchramm convergence. This concept is also applicable to other areas and has widely been studied in the context of ... 
Generalized SeibergWitten and the Nahm Transform
(20190111)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 ... 
New topological and index theoretical methods to study the geometry of manifolds
(20180731)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 ... 
A theory of discrete parametrized surfaces in R^3
(20180727)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 ... 
Variational Geometric Invariant Theory and Moduli of Quiver Sheaves
(20180626)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 ... 
On NewtonOkounkov bodies, linear series and positivity
(20180404)This thesis consists of four independent articles all connected to the theory of NewtonOkounkov bodies. It contains result about toric degenerations of Del Pezzo surfaces/BottSamelson varieties as well as an extension ... 
Local invariants of fourdimensional Riemannian manifolds and their application to the Ricci flow
(20171215)In this thesis, we study the fourdimensional 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 oneparameter family of curves, ... 
Permuting actions, moment maps and the generalized SeibergWitten equations
(20160421)In this thesis, we study properties and the geometry related to the generalization of the SeibergWitten equations introduced by Taubes and Pidstrygach. A crucial ingrediant to these equations is a hyperkähler manifold M ... 
Moduli spaces of bundles over twodimensional orders
(20130515)We study modules over maximal orders on smooth projective surfaces and their moduli spaces. We investigate zero and twodimensional moduli spaces on K3 and abelian surfaces for unramified orders, so called Azumaya algebras. ... 
Approximation of Baker domains and convergence of Julia sets.
(20130514)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 ... 
The Geometry of the Milnor Number
(20120612)In the first part of this thesis we derive a volumepreserving 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 ... 
Noncommutative manifolds and SeibergWittenequations
(20111017)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 the action of the group of automorphisms of the affine plane on instantons
(20110209)We define an action of the group of automorphism of the affine plane on SU(2)instantons ans investgate the orbits of this action. 
Thetafunktionen und konjugationsinvariante Funktionen auf Paaren von Matrizen
(20090116)We express conjugationinvariant functions on the space of equivalence classes of pairs of kxk matrices via theta functions. Our approach is based on the wellknown interplay between algebraic ...