Bruno Benedetti

The other evening I ran into Isosceles. He has a great idea for a new triangle!
(Woody Allen)


AG. "Theoretical Computer Science"
Institute of Computer Science
Freie Universität Berlin
Takustrasse, 9
D-14195 Berlin, Germany

Room: 122
Tel.: +49 30 838 75164
Email: bruno(at)zedat.fu-berlin.de

I am a postdoc within the Discretization project, mentored by Günter Rote at FU Berlin.
In August 2015 I plan to move to U Miami, Florida, for a tenure-track faculty position.

My research is in Discrete Geometry and Topology. I am currently interested in the following:
(1) triangulations of manifolds and their asymptotic number;
(2) convexity and combinatorics; (e.g. the polynomial Hirsch conjecture in optimization);
(3) discrete Morse theory (also from a computational viewpoint);
(4) algorithmic approaches to PL topology and simple-homotopy theory;
(5) dual graphs of projective curves;
(6) Random topology, knot theory, and continuous metrics on simplicial complexes.

Before coming here, I was a postdoc with Anders Björner at KTH, Stockholm. My PhD advisor (2010) is Günter Ziegler. Here is my cv  (updated Feb. 2015).


   Papers and Publications

  1. Regulating Hartshorne's connectedness theorem (with B. Bolognese and M. Varbaro), June 2015. (See also this announcement, to appear in OWR.)
  2. On the embeddability of contractible complexes (with K. Adiprasito); new version in preparation.
  3. Extremal examples of collapsible complexes, and random discrete Morse theory (with K. Adiprasito and F. Lutz), June 2015; submitted.
  4. Metric Geometry, Convexity and Collapsibility (with K. Adiprasito), March 2013. Submitted.

  1. Smoothing Discrete Morse theory, Annali della Scuola Normale Superiore di Pisa Classe di Scienze, in press (2014).
  2. On the dual graphs of Cohen-Macaulay algebras (with M. Varbaro), International Mathematics Research Notices, in press (2014).
  3. Subdivisions, shellability, and collapsibility of products (with K. Adiprasito), Combinatorica, accepted (subject to minor changes).
  4. Tight complexes in 3-space admit perfect discrete Morse functions (with K. Adiprasito), European Journal of Combinatorics 45 (2015), 71-84.
  5. The Hirsch conjecture holds for normal flag complexes (with K. Adiprasito), Mathematics of Operations Research 39, Issue 4 (2014), 1340–1348. Preprint
  6. Random discrete Morse theory and a new library of triangulations (with F. H. Lutz), Experimental Mathematics, Vol. 23, Issue 1 (2014), 66-94.
  7. Knots in collapsible and non-collapsible balls (with F. H. Lutz), Electronic Journal of Combinatorics 20 (2013), No.3, Paper P31, 29 pages.
  8. Discrete Morse Theory for Manifolds with Boundary. Transactions of the American Mathematical Society 364 (2012), 6631-6670.
  9. On locally constructible spheres and balls (with G. M. Ziegler). Acta Mathematica 206 (2011), 205-243. Preprint.
  10. Collapses, products and LC manifolds, Journal of Combinatorial Theory Ser. A 118 (2011), 586-590.
  11. On locally constructible manifolds. PhD Thesis. Advisor: G. M. Ziegler. Berlin, TU Berlin, 2010, 142 pages.
  12. The dunce hat and a minimal non-extendably collapsible 3-ball (with F. H. Lutz). Electronic Geometry Models , No. 2013.10.001 (2013).
  13. Unmixed Graphs that are domains (with M. Varbaro). Communications in Algebra 39 (2011), 2260-2267.
  14. Dimension, depth and zero-divisors of the algebra of basic k-covers of a graph (with A. Constantinescu, M. Varbaro),  Le Matematiche 63(2008), 117-156.

Extended abstracts:
  1. Balinski's theorem for arrangements of curves. Oberwolfach Reports , in press (2015).
  2. Metric Geometry and Random Discrete Morse Theory. Oberwolfach Reports 9, Issue 2 (2012),  1456-1459.
  3. Non-evasiveness, collapsibility, and explicit knotted triangulations. Oberwolfach Reports 8, Issue 1 (2011),  403-405.
  4. Knot theory and robot arms. Oberwolfach Reports 7, Issue 4 (2010),  2732-2735.

On the History of Science:
  1. Gli Archivi della Scienza. Genova, Erga, 2001, 576 pages (with Amedeo Benedetti). This is a complete guide to all institutions, archives and museums of scientific relevance and interest in the Italian state.
  2. L'Accademia delle Scienze di Berlino e la sua Biblioteca. Biblioteche Oggi 26 (2008), 41-47. This is an article about the Prussian Academy of Sciences, founded by Leibniz in 1700, and its precious library. The article was published by a librarianship magazine.

Online projects:
  1. The Library of Triangulations (work in progress with Frank Lutz)


   Upcoming events
September 6-9, 2015: Bertinoro, Italy: lectures at Séminaire Lotharingien de Combinatoire and L'Incontro italiano di Combinatoria Algebrica.
October 17-18, 2015: Memphis, Tennessee: talk at AMS meeting.
January 6-9, 2016: Seattle, Washington: talk at AMS meeting.
January 14-15, 2016: Munich, Germany: SFB/Transregio 109 "Discretization in Geometry and Dynamics".
May 29-June 4, 2016: Cortona, Italy: Homological and computational methods in commutative algebra.
June 13-24, 2016: Medellin, Colombia: Algebraic, Enumerative and Geometric Combinatorics.

   Recently I was in...
April 28 - May 2, 2014: Minneapolis, Minnesota: IMA Topology and Geometry of Networks and Discrete Metric Spaces.
June 2-13, 2014: Bogota, Colombia: talk at Cuarto Encuentro Colombiano de Combinatoria.
June 30-July 4, 2014: Bilbao, Spain: talk ( 1 - 2 ) at Joint meeting Italy-Spain.
July 14-30, 2014: Vienna, Austria: 2 talks at IST Austria and at Combinatorics, Geometry, and Physics, Erwin-Schrödinger-Institut.
August 3-9, 2014: Rynartice, Czech Republic: Elbe Sandstones Geometry Workshop.
September 8, 2014: Boston, Massachusetts: talk at GASC Seminar, Northeastern University.
October 25-26, 2014: San Francisco, California: talk at AMS Western Section Meeting.
October 30, 2014: Boston, MA: talk at Geometry-Topology Seminar, Boston College.
January 4-9, 2015: U. Miami, Florida: Wachsfest.
January 21, 2015: TU Graz, Austria: talk on Computational Topology.
January 23-24, 2015: CSU, Fort Collins, Colorado: visit to the Big Data group.
February 1-7, 2015: Oberwolfach, Germany: talk at Geometric and Algebraic Combinatorics.
February 9-13, 2015: Genoa, Italy: Lecturer at HTCA 2015, with Herbert Edelsbrunner and Massimo Ferri
February 15-20, 2015: Pisa, Italy: talk (Feb. 17) at Perspectives in Lie Theory, centro De Giorgi.
March 2, 2015: Geneva, Switzerland: talk at Mathematical Physics Seminar.

   teaching and service
  CV    curiosities
  Last fall I was on a research visit to Alex Suciu,
  at Northeastern University, Boston, MA.
  I also taught Calculus 2 for Science and Engineering.
  curriculum vitae
 (Feb. 2015)
  favorite verses; favorite comic strip
  summer school Geometria, teoria dei grafi e ottimizzazione,
  Bari, July 14-26, 2013
  an old research statement  my dad's webpage (in Italian)
  ACAT Summer school 2013,
  Computational topology & topological data analysis,
  organized by Neza Mramor in Ljubljana, July 1-5, 2013.
  Reference letter writers:
Anders Björner, Sweden
Aldo Conca, Italy
Herbert Edelsbrunner, Austria
Joel Hass, US
David Massey, US
Isabella Novik, US
John Shareshian, US
Alex Suciu, US
Günter Ziegler, Germany
Rade Zivaljevic, Serbia
  my Erdos number is 3, after Martin Aigner and Gunter Ziegler.
  Here is my math family.
  Etna Triangulations and Algebra Meeting,
  Grand Hotel Excelsior, Catania, Sicily.
  a copy of my PhD thesis and diploma.
  Mittag-Leffler Summer School 2012 ,
  Organized with Alex Engström at Institut Mittag-Leffler,
  near Stockholm, from July 18 to August 1, 2012.
  Selected participants.
  program in Italian for the course "Triangolazioni",
  Univ. Genova, Italy, Nov. 21--28, 2011.
  Conference CoMeTA 2013,
  organized in Cortona, Italy, Sep. 9-13, 2013.
  Participants; schedule
  press: interview to Tagesspiegel,
  nov. 2011 (in German)