Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Referee "Pidstrygach, Viktor Prof. Dr."
Now showing items 1-18 of 18
-
Divisors on K3 surfaces and Hilbert schemes
(2024-06-27)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 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 ... -
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 ... -
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 ... -
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 ... -
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 ... -
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 ... -
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 ... -
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 ... -
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 ... -
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, ... -
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 ... -
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. ... -
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 ... -
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 ... -
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 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. -
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 ...