Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Advisor "Pidstrygach, Viktor Prof. Dr."
Now showing items 1-10 of 10
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Conformal Properties of Generalized Dirac Operator
(2013-07-24)In this thesis we study the non-linear Dirac operator in dimension four and the associated generalization of the Seiberg-Witten equations in dimension four. The central object of this generalization is a hyperK ahler ... -
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 ... -
Generalized Seiberg-Witten equations and hyperKähler geometry
(2006-09-18)In this thesis we study a certain generalization of the gauge-theoretical Seiberg-Witten equations over a source 4-manifold X. The generalization involves a hyperKähler manifold M with ... -
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, ... -
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 ... -
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 ...