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Forschung
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Lehre und Betreuung
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aktuelle Lehrveranstaltungen (Sommersemester 2018)
alte Lehrveranstaltungen
Wintersemester 2017/18
Sommersemester 2017
Wintersemester 2016/17
Forschungsinteressen und Arbeitsgebiete:
- Diskrete Geometrie
- Kombinatorik
- Coxetergruppen
- Topologie
Eigene Projekte und Aufgaben:
- Projekt A03 Geometric Constraints for polytopes, DFG SFB/Transregio 109 Discretization in Geomtry and Dynamics» (2nd funding period, since 06/2016)
- Schnupperstudium Mathematik, einwöchiger Kompaktkurs für alle Studieninteressierten ab Klassenstufe 10
Teilprojekt von TUM-Individual im Rahmen der Initiative Aufstieg durch Bildung des Bundesministeriums für Bildung und Forschung.
- TUM-Mathezirkel, wöchentlicher Mathematikzirkel für Klassenstufe 7-10 der TU München.
Publikationen:
- Associahedra via spines
with Vincent Pilaud
Combinatorica (online first»), 44 pages.
- Frustration index and Cheeger inequalities for discrete and continuous magnetic Laplacians
with Shipling Liu, Norbert Peyerimhoff and Olaf Post
Calculus of Variations and Partial Differential Equations 54 (2015), pp. 4165-4196.
- Minkowski decomposition of associahedra and related combinatorics
Discrete and Computational Geometry 50 (2013), pp. 903-939.
- Optimal topological simplification of discrete functions on surfaces
with Ulrich Bauer and Max Wardetzky
Discrete Computational Geometry 47 (2012), pp.347-377.
- Permutahedra and generalized associahedra
with Christophe Hohlweg and Hugh Thomas
Advances in Mathematics 226 (2011), pp. 608-640.
- Isometry classes of generalized associahedra
with Nantel Bergeron, Christophe Hohlweg and Hugh Thomas
Seminaire Lotharingien de Combinatoire 61A (2009), 13 pages.
- Zur Geometrie von Frühstückseiern(in german)
with Konrad Polthier and Udo Simon
Mathematische Semesterberichte 56 (2009), pp. 1-14.
- Realizations of the associahedron and cyclohedron
with Christophe Hohlweg
Discrete and Computational Geometry 37 (2007), pp. 517-543.
- On generalized Kneser hypergraph colorings
with Günter M. Ziegler
Journal of Combinatorial Theory, Series A 114 (2007), pp. 159-166.
- Anisotropic smoothing of point sets
with Konrad Polthier
Computer Aided Geometric Design 22 (7) (2005), pp 680--692.
- Box complexes, neighbourhood complexes, and the chromatic number
with Peter Csorba, Ingo Schurr, and Arnold Wassmer
Journal of Combinatorial Theory, Series A 108 (2004), pp. 159-168.
Preprints:
- Cambrian acyclic domains: counting c-singletonsr
with Jean-Philippe Labbe
arXiv».
Vorträge :
- Cayley graphs of finite Coxeter groups, Colin de Verdiere matricess and convex polytopes
EPSRC Workshop Geometry and Computation on Groups and Complexes, Newcastle University, June 2016.
- Cayley graphs of finite Coxeter groups, Colin de Verdiere matricess and convex polytopes
Oberseminar Theoretische Informatik, ETH Zürich, May 2016.
- Generaliyed permutahedra and signed Minkowski decompositions
Forschungsseminar Algebra/Algebraische Geometrie, FU Berlin, June 2015
- Signed graphs, nested set complexes and spines
Kolloquium des SFB/Transregio 109 Discretization in Geometry and Dynamics, TU München, January 2015.
- Many polytopal realizations of generalized associahedra
GGA-Seminar, Newcastle University, March 2014.
- Many polytopal realizations of generalized associahedra
Geometry and Topology Seminar, Durahm University, March 2014.
- Revisit constructions of associahedra
Oberseminar Algebra und Geometrie, Otto-von-Guericke Universität Magdeburg, January 2014.
- Realizations of generalized Associahedra and related combinatorics
Oberseminar Algebra und Algebraische Kombinatorik, Leibniz Universität Hannover, January 2014.
Betreuungsmöglichkeiten
Projektvorschläge Diskrete Geometrie III (FU Berlin, Wintersemester 2018/19):
Fünf Literaturvorschläge für mögliche Projekte im Rahmen der Vorlesung. Alternative Projektthemen sind nach Absprache möglich.
- Projekt 1: Sven Herrmann, On the facets of the secondary polytope, J. Combin. Theory A 118 (2011), 425-447
- Projekt 2: Margeret Bayer, Bernd Sturmfels, Lawrence polytopes, Can. J. Math 42 (1990), 62-79
- Projekt 3: Louis J. Billera, Paul Filiman, Bernd Sturmfels, Construction and Complexity of Secondary Polytopes, Adv. Math. 83 (1990), 155-179
- Projekt 4: Louis J. Billera, Bernd Sturmfels, Fibre polytopes, Ann. Math. 135 (1992), 527-549
- Projekt 5: Louis J. Billera, Israel M. Gelfand, Bernd Sturmfels, Duality and Minors of Secondary Polyhedra, J. Combin. Theory B 57 (1993), 258-268
Sonstiges:
ma.tum.de