Sophie Rehberg

Contact

Sophie Rehberg (she/her)
s.rehberg(at)fu-berlin(dot)de

AG Diskrete Geometrie und Topologische Kombinatorik,
Institut für Mathematik,
Freie Universität Berlin

Arnimallee 2,
14195 Berlin, Germany

About Me

I'm a PhD Student in the Discrete Geometry and Topological Combinatorics Group at Freie Universität Berlin. My advisor is Matthias Beck and I'm also a student in the Berlin Mathematical School.

Before that I did my masters in mathematics at the Technische Universität Berlin and spent two semesters at the Charles University in Prague, Czech Republic. My master thesis advisor was Stefan Felsner. I did a Bachelor of Science in Natural Science in the Society of Information (original in German: "Naturwissenschaften in der Informationsgesellschaft") also at TU Berlin and spent a year at Universidad Catolica de Temuco, Chile. I also completed a study program about gender and diversity aspects in STEM (Zertifikat I, information in German here). During high school, I spent one year in Cuenca, Ecuador.

Papers

Preprints:
Acyclotopes and Tocyclotopes, with Eleonore Bach and Matthias Beck,
see arXiv:2409.15227
Published:
Rational Ehrhart Theory, with Matthias Beck and Sophia Elia,
in Integers: the Electronic Journal of Combinatorial Number Theory 23 (2023), A 60,
extended abstract in Séminaire Lotharingien de Combinatoire, 86B (2022), Article 44 (Proceedings of FPSAC'22).
Pruned inside-out polytopes, combinatorial reciprocity theorems and generalized permutahedra,
in The Electronic Journal of Combinatorics 29 (2022) P4.36.

Research Interests

So far my research has been centered around Ehrhart Theory, i.e., counting lattice points in polytopes and their (positive integral) dilates.

My favorite polytopes are those, that come from combinatorial objects, like graphs, signed graphs, hypergraphs or matroids, that is, generalized or deformed permutahedra and their subclasses. I'm interested in understanding structures and coefficients of the Ehrhart polynomial or h*-polynomial, e.g., by generalizing the classical setting to rational dilations of polytopes. Lately, I'm also thinking about Gale duality, Schubert matroids, nested matroids, (word)quasisymmteric functions, Hopf algebras, valuative functions, fiber polytopes, order polytopes, submodular functions, score sequences, deformations of polytopes, ...

hypergraphic polytope as the Minkowski sum of simplizes and convex hull of acyclic orientations

Activities

Last updated: Nov 21, 2024

Planned

Past

Conferences and Workshops (selection)

Seminar talks (selection)

Teaching

Teaching experience

Winter Semester 2024/25
Discrete Geometry I
exercise session, lecturer: Georg Loho.
Summer Semester 2024
Geometrie
exercise sessions, lecturer: Georg Loho.
Winter Semester 2023/24
Discrete Geometry I
exercise session, lecturer: Giulia Codenotti.
Mathematisches Professionswissen für das Lehramt an Grundschulen I.2
Q&A office hours (4h/week), lecturers: Ulrike Bücking, Jan-Hendrik de Wiljes.
Summer Semester 2023
Discrete Geometry II
exercise session, lecturer: Raman Sanyal.
Forschungsmodul: Diskrete Geometrie
seminar together with Raman Sanyal.
Winter Semester 2022/23
Discrete Geometry I
exercise session, lecturers: Christian Haase, and Eran Nevo, joint course with Hebrew University in Jerusalem.
Summer Semester 2022
Discrete Geometry II
exercise session, lecturer: Florian Frick.
Forschungsmodul Diskrete Geometrie: Special Polytopes
seminar together with Florian Frick.
Winter Semester 2021/22
Discrete Geometry I
exercise session, lecturers: Florian Frick, Christian Haase, and Eran Nevo, joint course with Hebrew University in Jerusalem.
Mathematisches Professionswissen für das Lehramt an Grundschulen I.2
tutorial, lecturers: Ulrike Bücking, Christine Scharlach.
Summer Semester 2021
Discrete Geometry II
exercise session, lecturer: Matthias Beck .
(Pro-)Seminar zur Diskreten Mathematik: Alternating Sign Matrices
seminar together with Matthias Beck .
Winter Semester 2020/21
Discrete Geometry III
exercise session, lecturer: Matthias Beck .
(Pro-)Seminar Diskrete Geometrie: Shard Polytopes
seminar together with Matthias Beck .
Summer Semester 2020
Discrete Geometry II
exercise session, lecturer: Matthias Beck .
During Bachelor and Master studies
I taught as a tutor Linear Algebra, Analysis for Engineering students and gave individual tutorials to Engineering students in Temuco, Chile.

Teaching trainings

I am currently working towards a Certificate of Academic Teaching offered by Freie Universität Berlin (more information in German here).