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Now showing items 1-16 of 16

    • Nahms Equations and Nilpotent Orbits 

      Krüger, Christoff (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 

      Deng, Jialong (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 

      Luckhardt, Daniel (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 

      Raymond, Robin (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 

      Nitsche, Martin (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 

      Sageman-Furnas, Andrew O'Shea (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 

      Maslovaric, Marcel (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 

      Merz, Georg (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 

      Tergiakidis, Ilias (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 

      Callies, Martin (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 

      Reede, Fabian (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. 

      Garfias-Macedo, Tania (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 

      Szawlowski, Adrian (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 

      Alekseev, Vadim (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 

      Miesener, Michael (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 

      Eickhoff-Schachtebeck, Annika (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 ...