For my project proposals for undergraduate student projects / Master thesis projects at University of Luxembourg, please find them on the Experimental Mathematics Lab page.

Ongoing and past scientific supervision of student projects:

Currently, supervising the PhD thesis of Phan Phuong Dung (her first name is Dung):
Cohomology of semi-direct product groups structuring Oeljeklaus-Toma manifolds (jointly supervised with Dr. Bui Anh Tuan) at the GAATI Mathematics Laboratory of Université de la Polynésie Française.

Currently, supervising the PhD thesis of Cu Minh Khuong (his first name is Khuong):
Cell complexes for crystallographic groups (jointly supervised with Dr. Bui Anh Tuan) at Ho Chi Minh City University of Science, Vietnam.

Summer semester 2020, supervised the Master studies' final project of Déborah Amani Faraja:
The geometry and topology of Bianchi orbifolds, at Institut Fourier, Grenoble, in remote supervision.

2016-2019, supervised the PhD thesis of Nghia Thi Hieu Tran:
Hochschild (co)homology of two families of complete intersections (jointly supervised with Dr. Emil Sköldberg) at NUI Galway.

2018/2019, supervised the Master thesis of Kelly Jost:
Visualization of fundamental polyhedra in hyperbolic space, didactical Master thesis project at University of Luxembourg (Experimental Mathematics Lab), the project description is linked here.

Summer semester 2019, supervised the Bachelor thesis of Arno Geimer and the EML1 project of Marie Baroni and Darina Zakharova:
Experimental tests on the abc conjecture, in the Experimental Mathematics Lab of University of Luxembourg.

Winter semester 2018/2019, supervised the Master 1 project of Tara Trauthwein:
Approximation of Cantor rational cardinalities by primitive words in the Experimental Mathematics Lab

Summer 2018, supervised the research internship of Atin Modi:
An interactive surface for Bianchi orbifolds at University of Luxembourg (see his software on the web page).

Summer Semester 2018, supervised the Bachelor thesis of Robert François Contignon:
Expériences numériques sur les rationnels de Cantor at University of Luxembourg.

September 2014 to June 2018, supervised the PhD thesis of Daher Waly Freh Al-Baydli:
Computation Of Cohomology Operations For Finite Groups (jointly supervised with Dr. Emil Sköldberg) at NUI Galway, thesis submitted in April 2018, defended June 21st 2018.

Winter semester 2017/2018, supervised the Experimental Mathematics Lab project of Fabio Marcelo Carvalho dos Santos:
Convex hulls of finite packs of spheres. The project report is here.

Academic year 2014/2015, supervised the Master Thesis of Katherine Wilkie:
A SAGE surface for Bianchi fundamental polyhedra at NUI Galway.

Academic year 2013/2014, supervised the Final Year thesis of Sarah Morahan:
Credit risk models and CDS valuation at NUI Galway.

Academic year 2013/2014, examined the Final Year thesis of Damien Hurney:
Adaptive Bayesian modelling at NUI Galway.

Diplom thesis of Hendrik Demmer (defended 2011, Universität Göttingen),
jointly supervised with Prof. Dr. Horst S. Holdgrün:

Stern-Brocot-Brüche, Graphen und die Modulgruppe

The full text of Hendrik Demmer's Diplom thesis is here.

English translation of below German description:

In his Diplom thesis, Hendrik Demmer studied the modular group: the quotient of the group SL2 (Z) by its centre. He constructed a cellular model for the action of the modular group, as a bridge between the classical geometrical model - the modular tree of Serre - and Kulkarni's arithmetic model. The latter admits the advantage that for every subgroup of finite index in the modular group, a Farey symbol can be computed in an efficient way, containing the essential information about the group structure. Demmer's model is a graph, constituting the 1-skeleton of a two-dimensional cell complex dual to the modular tree. Its set of edges is the set of elements of the modular group itself; and its 0-skeleton is the projective line over the rational numbers, to which Hendrik Demmer lends additional arithmetic structure as the set of "Stern-Brocot fractions".
This enables Demmer to compute the Farey symbol of a subgroup from a fundamental domain for it in the modular tree. To arrive there, he shows that he can choose fundamental domains in the modular tree particularly appropriately. Demmer's fundamental domains incorporate the bifurcation points into their interior and hence avoid that a bifurcation in the quotient graph becomes visible only after carrying out the identifications. Also, bifurcations of the modular tree are either incorporated entirely into Demmer's fundamental domain, or as a single edge in the case that the orbit of the latter contains the whole bifurcation. By the strictness concerning the edges, it is achieved that the number of edges of such a fundamental domain equals the index of the concerned subgroup. The information attached to the corners in terms of Stern-Brocot fractions now allows to compute the identifications among the endpoints of the fundamental domain as matrices, via an algorithm conceived by Hendrik Demmer.
Furthermore, Hendrik Demmer has elaborated algorithms for the conversion between matrices of the modular group and words in the free product (isomorphic to the latter group) of the two finite groups of orders 2 and 3.

Stern-Brocot-Brüche, Graphen und die Modulgruppe
Hendrik Demmer studierte in seiner Diplomarbeit die Modulgruppe: den Quotienten der Gruppe SL2(Z) nach ihrem Zentrum. Er konstruierte ein zellulares Modell für die Wirkung der Modulgruppe, als eine Brücke zwischen dem klassischen geometrischen Modell - dem Serre'schen modularen Baum - und dem arithmetischen Modell Kulkarnis. Letzteres hat den Vorteil, dass sich zu jeder Untergruppe von endlichem Index in der Modulgruppe auf effiziente Weise ein Farey-Symbol berechnen lässt, welches die wesentlichen Informationen über die Gruppenstruktur enthält. Demmers Modell ist ein Graph, der das 1-Skelett eines zum modularen Baum dualen, zweidimensionalen Zellkomplexes bildet. Die Menge seiner Kanten ist die Menge der Elemente der Modulgruppe selbst; und sein 0-Skelett ist die projektive Linie über den rationalen Zahlen, der Hendrik Demmer als Menge der "Stern-Brocot-Brüche" zusätzliche arithmetische Struktur verleiht.
Dies erlaubt Demmer, aus einem Fundamentalbereich für eine Untergruppe im modularen Baum ihr Farey-Symbol zu berechnen. Dazu zeigt er, dass er die Fundamentalbereiche im modularen Baum besonders geeignet wählen kann. Die Demmer'schen Fundamentalbereiche nehmen die Bifurkationspunkte in ihr Inneres auf und vermeiden somit, dass eine Bifurkation im Quotientengraph erst nach der Durchführung der Identifikationen sichtbar wird. Auch werden Bifurkationen des modularen Baums nur entweder vollständig in den Demmer'schen Fundamentalbereich aufgenommen, oder als einzelne Kante insofern die Bahn der Letzteren die gesamte Bifurkation enthält. Durch die Striktheit bezüglich der Kanten wird erreicht, dass die Anzahl der Kanten eines solchen Fundamentalbereichs gleich dem Index der jeweiligen Untergruppe ist. Die den Ecken angehefteten Informationen in Form von Stern-Brocot-Brüchen erlauben es nun, mittels eines von Hendrik Demmer konzipierten Algorithmus, die Identifikationen zwischen den Endpunkten des Fundamentalbereichs als Matrizen zu berechnen.
Ausserdem hat Hendrik Demmer Algorithmen zur Umrechnung zwischen Matrizen der Modulgruppe und Wörtern im zu ihr isomorphen freien Produkt aus den beiden endlichen Gruppen der Ordnungen 2 und 3 ausgearbeitet.

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