Topics for students

Completed student projects and theses in the Algebra and Number Theory group

PhD thesis

Laia Amorós Carafí: Images of Galois Representations and p-adic Models of Shimura Curves, 16/12/2016, University of Luxembourg, co-tutelle with University of Barcelona
Adam Mohamed: Some explicit aspects of modular forms over imaginary quadratic fields, 13/09/2011, Universität Duisburg-Essen.

MSc theses/Diplomarbeiten

Zeros of Eisenstein Series, MSc thesis, Université du Luxembourg, June 2015.
Remarkable index calculus algorithms for discrete logarithm problems in small characteristic finite fields, MSc thesis, Université du Luxembourg, June 2015.
The Golod-Shafarevich Inequality, MSc thesis, Université du Luxembourg, June 2014.
On primitive roots and permutations, MSc thesis, Université du Luxembourg, June 2014.
Density of arithmetic functions, MSc thesis, Université du Luxembourg, June 2013.
On the radical of a perfect number and the ABC-Conjecture, MSc thesis, Université du Luxembourg, January 2013.
Kongruenzen der Partitionsfunktion (nach Scott Ahlgren und Ken Ono), Diplomarbeit, Universität Duisburg-Essen, September 2011.
Edwardskurven, Diplomarbeit, Universität Duisburg-Essen, September 2011.
Differents for mod p Galois representations, MSc thesis, Universität Duisburg-Essen, September 2010.
Der AKS- und der Lucas-Lehmer-Primzahltest, Diplomarbeit, Universität Duisburg-Essen, April 2010.
On computing coefficient fields of eigenforms and applications, Diplomarbeit, Universität Duisburg-Essen, September 2009.

BSc theses/Staatsarbeiten

Verallgemeinerung der Fibonacci Zahlen und des goldenen Schnittes, BSc thesis, Université du Luxembourg, August 2016.
Profinite Galois Theory, BSc thesis, Université du Luxembourg, June 2016.
L'arbre modulaire de Pythagore, BSc thesis, Université du Luxembourg, June 2016.
Primes in P, BSc thesis, Université du Luxembourg, June 2015.
Elliptic curve cryptography and the Weil pairing, BSc thesis, Université du Luxembourg, June 2015.
Lucas sequences and primality tests, BSc thesis, Université du Luxembourg, June 2013.
Continued fractions and the Pell equation, BSc thesis, Université du Luxembourg, June 2013.
Mathematische Theorie des Origami, Staatsarbeit, Universität Duisburg-Essen, August 2011.
Auflösbarkeit von Gleichungen, Staatsarbeit, Universität Duisburg-Essen, March 2011.
Die Pellsche Gleichung, Catalans Vermutung und Fermats letzter Satz - Einige Diophantische Gleichungen, Staatsarbeit, Universität Duisburg-Essen, September 2010.

Student projects, Master in Mathematics

An Introduction to Fibonacci and Lucas Numbers, Student project in Master of Mathematics, Université du Luxembourg, December 2016.
The Collatz Conjecture, Student project in Master of Mathematics, Université du Luxembourg, December 2016.
Factorisation of polynomials over Z/p n Z[x], Student project in Master of Mathematics, Université du Luxembourg, December 2014.
Computing Galois Group via Chebotarev Density, Student project in Master of Mathematics, Université du Luxembourg, December 2014.
Galois groups in generalisation of Maeda's conjecture, Student project in Master of Mathematics, Université du Luxembourg, December 2014.
Modular forms and Maeda's conjecture, Student project in Master of Mathematics, Université du Luxembourg, December 2014.
Prime producing polynomials, Student project in Master of Mathematics, Université du Luxembourg, December 2013.
Visualisation of modular forms, Student project in Master of Mathematics, Université du Luxembourg, December 2013.
Invariant theory of finite groups, Student project in Master of Mathematics, Université du Luxembourg, December 2012.
Shidoku and Gröbner Bases, Student project in Master of Mathematics, Université du Luxembourg, December 2012.
Modular forms - A congruence of Ramanujan, Student project in Master of Mathematics, Université du Luxembourg, December 2011.

Projects in the Experimental Mathematics Lab

Harmonic partitions (EM 1, ST 2016)
Magic squares (EM 1, ST 2016)
Visualising modular forms (EM 3, ST 2016)
Rational Points on Algebraic Curves (EM 2, WT 2015)
Galois groups in generalisations of Maeda's conjecture (Master Student Project, WT 2015)
Computing Galois groups via Chebotarev density (Master Student Project, WT 2015)
Factorisation of polynomials modulo p^n (Master Student Project, WT 2015)
Visualisation of p-adic integers (EM 1, ST 2015)
Testing conjectures on primes (EM 1, ST 2015)
Visualising the distribution of primes (EM 3, ST 2015)
Primes is in P (Bachelor Thesis, ST 2015)
Elliptic Curve Cryptography and the Weil pairing (Bachelor Thesis, ST 2015)