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Mathematical Physics

Theses

Bachelor and master theses at Chair X are usually connected with specific problems from mathematical physics and use techniques from differential geometry, functional analysis and algebra. In the following some details about prerequisites as well as a list of previous theses can be found.

Bachelor theses at Chair X

A bachelor thesis in mathematics or in mathematical physics is not yet an independent scientific work. Instead, the main purpose is to understand a known result, formulate it properly and illustrate it with some, perhaps new examples.

At Chair X, we supervise bachelor theses on various topics. On the physical side we are interested in classical and quantum mechanics including in particular the transition between these two dominant theories in physics. On the mathematical side this results in topics with focus in differential geometry, functional analysis or algebra and their applications. If you are interested you should have visited at least some of the relevant lectures and participated in corresponding bachelor seminars.

Generally, a certain interest in the physical motivation of the questions and tasks in a bachelor thesis are not strictly needed but helpful to a large extend. Students of mathematical physics will have participated in typical lectures on theoretical mechanics and quantum mechanics anyway. For students of bachelor programs in mathematics this needs not to be the case. Nevertheless, also for them a bachelor thesis at Chair X is definitely possible.

The precise topic of a bachelor thesis is then determined individually depending on the interests and previously taken courses. A bachelor thesis can be written either in German or in English.

List of the Bachelor Theses

Name Title Date Supervisor
Kaja Alina Jurak Die universell Einhüllende und das Gutt-Sternprodukt 8 / 2019 Stefan Waldmann
Nadja Egner Satz von Morita 9 / 2018 Stefan Waldmann
Carolin Bothe Magnetic Monopoles 8 / 2018 Knut Hüper
Andreas Schüßler Lineare Dirac-Strukturen und ihre Morphismen 8 / 2018 Stefan Waldmann
Thomas Wagner Integralformeln für Sternprodukte auf dem Schwartz-Raum 8 / 2018 Stefan Waldmann
Kevin Ruck Der Bargmann-Fock-Raum 7 / 2018 Stefan Waldmann
Max Steinlein Uniforme Räume und ihre Vervollständigung 7 / 2018 Stefan Waldmann
Michael Heins Paley-Wiener-Schwartz Theorems 7 / 2018 Stefan Waldmann
Felix Menke Das affine Non-Squeezing-Theorem und die lineare symplektische Breite 7 / 2018 Stefan Waldmann
Jonas Kleineisel Die Fundamentalgruppe topologischer Mannigfaltigkeiten 5 / 2018 Stefan Waldmann
Andreas Drotloff Die freie lokal multiplikativ konvexe Algebra 8 / 2017 Stefan Waldmann
Eva Horlebein Lokal Konvexe Topologien auf der Tensoralgebra 8 / 2017 Stefan Waldmann
Marisa Schult The Gel'fand-Naimark-Segal Construction for a ∗-Algebra and two major Examples 3 / 2017 Stefan Waldmann
Andreas Kraft Kofreie zusammenhängende Koalgebren 1 / 2017 Stefan Waldmann
Thomas Bendokat Deformation und Starrheit der kanonischen Poisson-Klammer 5 / 2016 Stefan Waldmann
Felix Endres Die Lorentz-Gruppe als Matrix-Lie-Gruppe 11 / 2015 Stefan Waldmann
Florian Ulrich Paralleltransport und affine Zusammenhänge auf S2 und SO(3) 5 / 2015 Knut Hüper
Marvin Dippell Poisson-Strukturen im R^n 3 / 2015 Stefan Waldmann
Timo Fuller Das Noether-Theorem in der geometrischen Mechanik 10 / 2014 Stefan Waldmann
Thomas Weber G-invariante de-Rham-Kohomologie 1 / 2014 Stefan Waldmann
Dominik Zoar Die Poincaré-Scheibe als reduzierter Phasenraum 10 / 2013 Stefan Waldmann

Master Theses at Chair X

Master theses at Chair X are offered and supervised for the master programs in mathematics, mathematics international and mathematical physics.

In contrast to a bachelor thesis there is a certain scientific level expected, requiring more independence from the student but also allowing her to work in close proximity of current research. Although it is not required, a master thesis can often lead to new scientific results. On the one side, intensive supervision during the master thesis will be offered, on the other side active participation in the life at Chair X and in particular the Oberseminar Deformation Quantization is expected. Here all members present their own work and guests give talks about different topics.

As prerequisites a certain familiarity with methods from differential geometry will be necessary. But interest in techniques from algebra and/or functional analysis can also be useful. General interest in the motivation provided by physics is helpful, which requires some knowledge about the physical origins of the problems. In addition, the participation of at least one Research in Groups is presumed, from which possible topics for the thesis might emerge. A different Research in Groups in the area of differential geometry, functional analysis or algebra will be offered every semester.

The exact topic of the master thesis will be individually discussed according to the interests and prior knowledge of the student. A master thesis can be written either in German or in English.

List of previous master theses

Name Title Date Supervisor
Marisa Christin Schult Kähler Reduction for Arbitrary Regular Moment Map Values and the Shifting Trick 11 / 2019 Stefan Waldmann
Katia Winklmaier-Peran Convergent Star Products on Cotangent Bundles of Lie Groups 9 / 2019 Stefan Waldmann
David Kern Unimodular Extension of Lie Algebroids and Quantization of their Morphisms 9 / 2019 Stefan Waldmann
Tobias Schmude The Idempotent Completion of Categories 8 / 2019 Stefan Waldmann
Mahdi Hamdan Morita Theory for Locally Convex Algebras 7 / 2019 Stefan Waldmann
Marvin Dippell Morita Theory for Generalized Coisotropic Reduction 9 / 2018 Stefan Waldmann
Thomas Bendokat Differential Geometry of the Essential Manifold 9 / 2018 Knut Hüper
Andreas Kraft BRST Reduction of Quantum Algebras with *-Involution 8 / 2018 Stefan Waldmann
Lukas Miaskiwskyi Invariant Hochschild Cohomology 1 / 2018 Stefan Waldmann
Florian Ullrich Rolling Maps for Real Stiefel Manifolds 7 / 2017 Knut Hüper
Philipp Schmitt Convergent Star Products on Coadjoint Orbits 7 / 2017 Stefan Waldmann
Julian Keller Mathematische Aspekte des Todagitters 9 / 2016 Knut Hüper
Jonas Schnitzer A simple algebraic construction of Drinfel'd twists 8 / 2016 Stefan Waldmann
Thomas Weber Star Products that can not be induced by Drinfel'd Twists 6 / 2016 Stefan Waldmann
Paul Stapor Convergence of the Gutt Star Product 10 / 2015 Stefan Waldmann
Bastian Seifert Morita theory with Hopf algebra symmetries 7 / 2015 Stefan Waldmann
Philipp Wolf Zur Rollabbildung von Kleinscher Flasche und Möbiusband 5 / 2015 Knut Hüper
Benedikt Hurle Generalizations of the Hochschild-Kostant-Rosenberg-Theorem in deformation quantization 12 / 2014 Stefan Waldmann
Matthias Schötz Konvergente Sternprodukte auf Hilberträumen 10 / 2014 Stefan Waldmann

Ph.D. at chair X

A Ph.D. at our chair at first requires a significantly higher than average academic performance. Only then new scientific results can  be expected in the wide offer of the chair X. For a PhD it is necessary to get involved both in finding the relevant question and, of course, in the subsequent solution. In most cases, there is no precise problem but a suggestion or an idea. It is then the task of the doctoral candidate to formulate an exact and meaningful question, which then allows a solution. Methodically, a greater familiarity with techniques of differential geometry, functional analysis or algebra is expected as well as a certain interest in the physical motivations of the questions.

Previous Ph.D. Students

Name Title Date Supervision
Bastian Seifert Multivariate Chebyshev Polynomials and FFT-like Algorithms 2019 Knut Hüper
Matthias Schötz Convergent Star Products and Abstract O*-Algebras 9 / 2018 Stefan Waldmann
Thorsten Reichert Classification and Reduction of Equivariant Star Products on Symplectic Manifolds 9 / 2017 Stefan Waldmann