Priv.-Doz. Dr. Frank H. Lutz

Phone:	+49-30-314-78648
Fax:	+49-30-314-21117
Email:	lutzmath.tu-berlin.de
Room:	MA 521

Research Interests

• Discrete & Computational Topology
• Triangulations of Manifolds
• Algebraic Topology
• Topological Combinatorics
• Optimization
• Visualization of Topological Spaces
• Polyhedral Surfaces
• Discrete Geometry
• Geometry and Topology of Materials
• History of Geometry and Topology

Journal Publications

• Bruno Benedetti, Crystal Lai, Davide Lofano, and Frank H. Lutz.   Random simple-homotopy theory.   Preprint, 23 pages, 2021; arXiv:2107.09862v2; J. Appl. Comput. Topol., to appear.
• Michael Joswig, Davide Lofano, Frank H. Lutz, and Mimi Tsuruga.   Frontiers of sphere recognition in practice.   J. Appl. Comput. Topol. 6, 503-527 (2022).
• Matthew Kahle, Frank H. Lutz, Andrew Newman, and Kyle Parsons.   Cohen–Lenstra heuristics for torsion in homology of random complexes.   Exp. Math. 29, 347-359 (2020).
• Frank H. Lutz and Jesper M. Møller.   Chromatic numbers of simplicial manifolds.   Beitr. Algebra Geom. 61, 419-453 (2020).
• Frank H. Lutz, Jeremy K. Mason, Emanuel A. Lazar, and Robert D. MacPherson.   Roundness of grains in cellular microstructures.   Physical Review E 96, 023001 (2017).
• Karim A. Adiprasito, Bruno Benedetti, and Frank H. Lutz.   Extremal examples of collapsible complexes and random discrete Morse theory.   Discrete Comput. Geom. 57, 824-853 (2017).
• Frank H. Lutz and Eran Nevo.   Stellar theory for flag complexes.   Math. Scand. 118, 70-82 (2016).
• Bruno Benedetti and Frank H. Lutz.   Random Discrete Morse Theory and a New Library of Triangulations.   Exp. Math. 23, 66-94 (2014).
• Bruno Benedetti and Frank H. Lutz.   Knots in collapsible and non-collapsible balls.   Electron. J. Comb. 20, No. 3, Research Paper P31, 29 p. (2013).
• Stefan Hougardy, Frank H. Lutz, and Mariano Zelke.   Surface realization with the intersection segment functional.   Exp. Math. 19, 79-92 (2010).
• Thom Sulanke and Frank H. Lutz.   Isomorphism-free lexicographic enumeration of triangulated surfaces and 3-manifolds.   Eur. J. Comb. 30, 1965-1979 (2009).
• Frank H. Lutz, Thom Sulanke, and Ed Swartz.   f-vectors of 3-manifolds.   Electron. J. Comb. 16, No. 2, Research Paper R13, 33 p. (2009).
• Frank H. Lutz.   Combinatorial 3-manifolds with 10 vertices.   Beitr. Algebra Geom. 49, 97-106 (2008).
• Frank H. Lutz.   Enumeration and random realization of triangulated surfaces.   Discrete Differential Geometry (A. I. Bobenko, P. Schröder, J. M. Sullivan, and G. M. Ziegler, eds.). Oberwolfach Seminars 38, 235-253. Birkhäuser, Basel, 2008.
• Péter Csorba and Frank H. Lutz.   Graph coloring manifolds.   Algebraic and Geometric Combinatorics, Euroconf. Math., Anogia, Crete, Greece, 2005 (C. A. Athanasiadis, V. V. Batyrev, D. I. Dais, M. Henk, and F. Santos, eds.). Contemporary Mathematics 423, 51-69. American Mathematical Society, Providence, RI, 2006.
• Michael Joswig and Frank H. Lutz.   One-point suspensions and wreath products of polytopes and spheres.   J. Comb. Theory, Ser. A 110, 193-216 (2005).
• Frank H. Lutz.   Small examples of non-constructible simplicial balls and spheres.   SIAM J. Discrete Math. 18, 103-109 (2004).
• Frank H. Lutz.   Examples of Z-acyclic and contractible vertex-homogeneous simplicial complexes.   Discrete Comput. Geom. 27, 137-154 (2002).
• Frank H. Lutz.   Some results related to the Evasiveness Conjecture.   J. Comb. Theory, Ser. B 81, 110-124 (2001).
• Anders Björner and Frank H. Lutz.   Simplicial manifolds, bistellar flips and a 16-vertex triangulation of the Poincaré homology 3-sphere.   Exp. Math. 9, 275-289 (2000).
• Wolfgang Kühnel and Frank H. Lutz.   A census of tight triangulations.   Periodica Math. Hung. 39, 161-183 (1999).

Electronic Geometry Models

• Bruno Benedetti and Frank H. Lutz.   The dunce hat and a minimal non-extendably collapsible 3-ball.   Electronic Geometry Model No. 2013.10.001 (2013).
• Frank H. Lutz and Günter M. Ziegler.   A small polyhedral Z-acyclic 2-complex in R4.   Electronic Geometry Model No. 2008.11.001 (2008).
• Stefan Hougardy, Frank H. Lutz, and Mariano Zelke.   Polyhedral tori with minimal integer coordinates.   Electronic Geometry Model No. 2008.10.001 (2008).
• Stefan Hougardy, Frank H. Lutz, and Mariano Zelke.   Polyhedra of genus 3 with 10 vertices and minimal coordinates.   Electronic Geometry Model No. 2006.02.001 (2007).
• Stefan Hougardy, Frank H. Lutz, and Mariano Zelke.   Polyhedra of genus 2 with 10 vertices and minimal coordinates.   Electronic Geometry Model No. 2005.08.001 (2007).
• Frank H. Lutz.   Vertex-minimal not vertex-decomposable balls.   Electronic Geometry Model No. 2003.06.001 (2004).
• Frank H. Lutz.   A vertex-minimal non-shellable simplicial 3-ball with 9 vertices and 18 facets.   Electronic Geometry Model No. 2003.05.004 (2004).
• Anders Björner and Frank H. Lutz.   A 16-vertex triangulation of the Poincaré homology 3-sphere and non-PL spheres with few vertices.   Electronic Geometry Model No. 2003.04.001 (2003).
• Frank H. Lutz.   Császár's Torus.   Electronic Geometry Model No. 2001.02.069 (2002).

Extended Abstracts

• Michael Joswig, Frank H. Lutz and Mimi Tsuruga.   Heuristics for sphere recognition.   Mathematical Software - ICMS 2014, 4th Internat. Conf., Seoul, 2014 (H. Hong and C. Yap, eds.). Lecture Notes in Computer Science 8592, 152-159. Springer-Verlag, Berlin, 2014.
• Mimi Tsuruga and Frank H. Lutz.   Constructing complicated spheres.   EuroCG 2013, 29-32 (2013).
• Frank H. Lutz.   Periodic foams and simplicial manifolds with small valence.   Oberwolfach Reports 4, No. 1, 228-230 (2007).
• Frank H. Lutz.   Triangulated surfaces and higher-dimensional manifolds.   Oberwolfach Reports 3, No. 1, 706-707 (2006).

Preprints

• Davide Lofano, and Frank H. Lutz.   Hadamard Matrix Torsion.   Preprint, 14 pages, 2021; arXiv:2109.13052v2.
• Frank H. Lutz.   Equivelar and d-covered triangulations of surfaces. II. Cyclic triangulations and tessellations.   Preprint, 27 pages, 2010; arXiv:1001.2779.
• Frank H. Lutz, Thom Sulanke, Anand K. Tiwari, and Ashish K. Upadhyay.   Equivelar and d-covered triangulations of surfaces. I.   Preprint, 21 pages, 2010; arXiv:1001.2777.
• Frank H. Lutz and Nikolaus Witte.   Knotted polyhedral tori.   Preprint, 10 pages, 2007; arXiv:0707.1281.

Conferences and Workshops

• 2021, Thematic Einstein Semester "Geometric and Topological Structure of Materials", TU Berlin, Germany
  (Myfanwy Evans, Kathryn Hess Bellwald, Frank H. Lutz, Dmitriy Morozov, Ileana Streinu)
  
  
• 2018, "Hot Topics: Shape and Structure of Materials", MSRI, Berkeley, CA
  (Myfanwy Evans, Frank H. Lutz, Dmitriy Morozov, James A. Sethian, Ileana Streinu)
  
  
• 2017, Minisymposium "Geometry of Materials", SIAM Conference on Applied Algebraic Geometry, Atlanta, GA
  (Frank H. Lutz, Ileana Streinu)
  
  
• 2015, Minisymposium "Experimental Mathematics", Jahrestagung DMV, Hamburg
  (Søren Eilers, Frank H. Lutz)
  
  
• 2015, "Shape up 2015 -- Exercises in Materials Geometry and Topology", TU Berlin, Germany
  (Myfanwy E. Evans, Andrew M. Kraynik, Frank H. Lutz, Gerd Schröder-Turk, Bodo Wilts)
  
  
• 2014, Workshop "Discrete, Computational, and Algebraic Topology", Københavns Universitet
  (Herbert Edelsbrunner, Lisbeth Fajstrup, Frank H. Lutz, Konstantin Mischaikow)
  
  
• 2012, Oberwolfach-Workshop "Triangulations"
  (William H. Jaco, Frank H. Lutz, Francisco Santos, John M. Sullivan)

The Manifold Page

Books

• Frank H. Lutz.   Triangulated Manifolds with Few Vertices and Vertex-Transitive Group Actions.   Dissertation.   Shaker Verlag, Aachen, 1999.

• Frank H. Lutz.   Triangulated Manifolds.   Springer-Verlag, to appear   (with contributions by Anders Björner, Michael Joswig, Volker Kaibel, Ekkehard G. Köhler, Wolfgang Kühnel, Arnold Waßmer).

• Michael Joswig.   Computing Invariants of Simplicial Manifolds.   Preprint, 13 pages, 2004; arXiv:math/0401176.
• Frank H. Lutz.   Triangulated Manifolds with Few Vertices: Geometric 3-Manifolds.   Preprint, 48 pages, 2003; arXiv:math/0311116.
• Frank H. Lutz.   Triangulated Manifolds with Few Vertices: Centrally Symmetric Spheres and Products of Spheres.   Preprint, 26 pages, 2004; arXiv:math/0404465.
• Frank H. Lutz.   Triangulated Manifolds with Few Vertices: Combinatorial Manifolds.   Preprint, 37 pages, 2005; arXiv:math/0506372.
• Ekkehard G. Köhler and Frank H. Lutz.   Triangulated Manifolds with Few Vertices: Vertex-Transitive Triangulations I.   Preprint, 74 pages, 2005; arXiv:math/0506520.

Schnellkurs Ingenieurmathematik

• TU intern:  Aus drei mach eins: Schnellkurs Mathematik für Ingenieure.

• Frank H. Lutz und Brigitte Lutz-Westphal.   Schnellkurs Ingenieurmathematik - Pilotprojekt an der TU Berlin.   DMV-Mitteilungen 3/2005, 188-191.

Topological Software (in GAP)

• BISTELLAR (Version Nov/2003): heuristics to reduce the size of a given triangulated manifold; it can be used to recognize combinatorial d-spheres and therefore to test whether a pure simplicial complex is a combinatorial manifold.

• BISTELLAR_EQUIVALENT (Version Feb/1999)

• FundamentalGroup (Version Nov/2003): routine to compute a ``small´´ presentation of the fundamental group of a finite simplicial complex.

• MANIFOLD_VT (Version Apr/2002)

• SEIFERT (Version Nov/2003): produces triangulations of all Seifert manifolds.

• DiscreteMorse (Version May/2015): searches for discrete Morse vectors with few critical cells.

Last modified: Fri Dec 10 07:41:08 CEST 2021