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.
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.
|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 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.
|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|
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.
|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|