math_groups_discgeom

Published

Focus Area 1 Focus Area 2 Focus Area 3

Focus Area 1: High-complexity Geometry

Karim Adiprasito, Raman Sanyal

An Alexander-type duality for valuations                                                                                                                          

Preprint: arXiv:1303.1708, 7 May 2013, 14 pages                                                                                                                  

Published in: Proc. Amer. Math. Soc. 143 (2015), no. 2, 833–843.                                                                               

Karim Adiprasito, Günter M. Ziegler

Many projectively unique polytopes 

Preprint: arXiv:1212.5812, 23 Dec 2012, 44 pages                                                                                                                

Published in: Inventiones math. 199 (2015), 581-652.                                                                                                           

Anton Dochtermann, Raman Sanyal

Laplacian ideals, arrangements, and resolutions

Preprint: arXiv:0910.4987, 26 Dec 2012, 18 pages                                                                                                                

Published in: J. Algebraic Combin. 40 (2014), no. 3, 805–822.                                                                                   

Katharina Jochemko, Raman Sanyal

Arithmetic of marked poset polytopes, monotone triangle reciprocity,and partial colorings

Preprint: arXiv:1206.4066,  18 Jun 2012, 16 pages                                                                                                                  


Published in: SIAM J. Discrete Math. 28 (2014), no. 3, 1540–1558.                                                                                  

Andreas Loos, Günter M. Ziegler

Teaching and Learning "What is Mathematics"

Published in: Proc. International Congress of Mathematicians, Seoul 2014, Volume IV, 1201-1215                                                                                                                                               

Michael Joswig, Günter M. Ziegler

Foldable triangulations of lattice Polygons

Preprint: arXiv:1207.6865, 30 Jul 2012, 6 pages

Published in: American Math. Monthly, Volume 121 (Oct 2014), 706-710                                                                               

Justin Malestein, Louis Theran

Frameworks with forced symmetry II: Orientation-preserving crystallographic groups

Preprint: arXiv:1304.0756, 1 Apr 2013, 46 pages

Published in: Geometriae Dedicata June 2014, Volume 170, Issue 1, pp 219-262                                                                 

Justin Malestein, Igor Rivin, Louis Theran

Topological designs

Preprint: arXiv:1101.1008.1837, 11 Aug 2010, 61 pages

Published in: Geometriae Dedicata, February 2014, Volume 168, Issue 1, pp 221-233                                                          

Tim Netzer, Raman Sanyal

Smooth Hyperbolicity Cones are Spectrahedral Shadows

Preprint: arXiv:1208.0441, 2 Aug 2012, 8 pages

Published in: Mathematical Programming, Feb 2014                                                                                                               

Dirk Frettlöh, Edmund Harriss

Parallelogram tilings, worms and finite orientations

Preprint: arXiv:1202.4686, 21 Feb 2012

Published in: Discrete & Computational Geometry, April 2013, Volume 49, Issue 3, pp 531-539                                           

E. Paulo Bugarin, M. Louise A.N. de las Penas, Dirk Frettlöh

Perfect colourings of cyclotomic integers

Preprint: arXiv: 0905.4048, 25 May 2009, 11 pages

Published in: Geometriae Dedicata 162 (2013) 271-282                                                                                                          

Justin Malestein, Louis Theran

Generic combinatorial rigidity of periodic frameworks

Preprint: arXiv: 1008.1837, 11 Aug 2010, 61 pages

Published in: Advances in Mathematics, 233(1), 291–331, 2013                                                                                             

Ragnar Freij, Matthias Henze, Moritz W. Schmitt, Günter M. Ziegler

Face numbers of centrally symmetric polytopes from split graphs

Preprint: arXiv:1201.5790, 27 Jan 2012, 10 pages

Published in: Electronic J. Combinatorics, vol 20 (2) (2013)                                                                                                    

Cesar Ceballos, Günter M. Ziegler

Realizing the associahedron: Mysteries and questions

Preprint: arXiv:1110.4059, 18 Oct 2011, 9 pages

Published in:  “Associahedra, Tamari Lattices and Related Structures”, Tamari Memorial Festschrift Progress in Mathematics, Vol. 299, Springer Basel 2012, 119-127;                                                                                                             

Valérie Berthé, Dirk Frettlöh, Victor Sirvent

Selfdual substitutions in dimension One

Preprint: arXiv:1108.5053v2, 25 Aug 2011, 28 pages

Published in: European Journal of Combinatorics 33 (2012) 981-1000.                                                                                  


Focus Area 2: Delaunay Geometry

Ivan Izmestiev

A porism for cyclic quadrilaterals, butterfly theorems, and  hyperbolic geometry.                                                          

Preprint: arXiv:1408.2247  10 Aug 2014, 9 pages      

Published in: To appear in Amer. Math. Montly, 9 pages.                                                                                                       

Karim Adiprasito, Ivan Izmestiev

Derived subdivisions make every PL sphere polytopal 

Preprint: arXiv:1311.2965, 12 Nov 2013, 7 pages              

Published in: To appear in  Israel J. Math.                                                                                                                               

Ivan Izmestiev

Infinitesimal rigidity of convex polyhedra through the second  derivative of the Hilbert-Einstein functional.

Preprint: arXiv:1105.5066  25 May 2011, 42 pages 

Published in: In Canad. J. Math., 66(4):783--825, 2014.                                                                                                          

Robert Haller-Dintelmann, Wolfgang Höppner, Hans-Christoph Kaiser, Joachim Rehberg, Günter M. Ziegler

Optimal elliptic Sobolev regularity near three-dimensional, multi-material Neumann vertices

Preprint: opus4-matheon

Published in: Functional Analysis Applications, Volume 48 (2014), 208-222                                                                           

Tuan Tran, Günter M. Ziegler

Extremal edge polytopes

Preprint: arXiv:1307.6708, 25 Jul 2013,  18 pages

Published in: Electronic J. Combinatorics, vol 21 (2) (2014)                                                                                                   

Bernd Gonska, Günter M. Ziegler

Inscribable stacked polytopes

Preprint: arXiv:1111.5322, 22 Nov 2011, 15 pages

Published in: Advances in Geometry, Volume 13, Issue 4 (October 2013)                                                                              

Ivan Izmestiev, Rob Kusner, Günter Rote, Boris Springborn, John M. Sullivan

There is no triangulation of the torus with vertex degrees 5, 6, ..., 6, 7 and related results: Geometric proofs for combinatorial theorems

Preprint: arXiv:1207.3605, 16 Jul 2012, 14 pages

Published in: Geom. Dedicata, 166 (2013), 15-29                                                                                                                    

Ivan Izmestiev

Infinitesimal rigidity of smooth convex surfaces through the second derivative of the Hilbert-Einstein functional

Preprint: arXiv:1105.5067, 25 May 2011, 60 pages

Published in: Dissertationes Math., 492 (2013), 58 pp.                                                                                                            

Ivan Izmestiev

Variational properties of the discrete Hilbert-Einstein  functional.

Preprint: arXiv:1312.6314 21 Dec 2013, 10 pages      

Published in: Actes des rencontres du CIRM, 3(1):151--157, 2013.                                                                                        

Francisco Santos, Günter M. Ziegler

Unimodular triangulations of dilated 3-polytopes

Preprint: arXiv:1304.7296, 26 Apr 2013, 23 pages

Published in: Transactions Moscow Math. Soc. 74 (2013), 293-311                                                                                        


Focus Area 3: Topological connectivity and diameter of Discrete Structures

Pavle V. M. Blagojević, Wolfgang Lück, Günter M. Ziegler

On highly regular embeddings

Preprint: arXiv:1305.7483, 3 Sep 2014, 20 pages 

Proc. "Combinatorial Methods in Topology and Algebra", to appear                                                                                          

Pavle V. M. Blagojević, Benjamin Matschke, Günter M. Ziegler

Optimal bounds for the colored Tverberg problem

Preprint: arXiv:0910.4987, 26 Oct 2009, 11 pages

Published in: Journal of Topology, Online Publication (March 2015)                                                                                       

Pavle V. M. Blagojević, Wolfgang Lück, Günter M. Ziegler

Equivariant topology of configuration spaces

Preprint: arXiv:1207.2852, 12 Jun 2012, 40 pages

Published in: Journal of Topology, Online Publication (March 2015)                                                                                       

Günter M. Ziegler

Cannons at Sparrows

Published in: Newsletter of the European Math. Soc., Issue 95 (March 2015), 25-31                                                             

Pavle V. M. Blagojević, Florian Frick, Albert Haase, Günter M. Ziegler

Topology of the Grünbaum-Hadwiger-Ramos hyperplane mass partition problem

Preprint: arXiv:1502.02975 , 10 Feb 2015, 27 pages

Published in: Oberwolfach Reports, Volume 11, Issue 1 (2015)                                                                                              

Pavle Blagojević, Florian Frick, Benjamin Matschke, Günter M. Ziegler

Tight and non-tight topological Tverberg type theorems

Oberwolfach Reports, Volume 11, Issue 3 (2014), to appear                                                                                                     

Pavle Blagojević, Florian Frick, Günter M. Ziegler

Tverberg plus constraints

Preprint: arXiv:1401.0690, 3 Jan 2014, 11 pages

Published in: Bulletin of the London Mathematical Society, Volume 46 (2014), 953-967                                                        

Pavle V. M. Blagojević, Günter M. Ziegler

Convex equipartitions via equivariant obstruction theory

Preprint: arXiv:1202.5504, 24 Feb 2012, 20 pages

Published in: Israel J. Mathematics, Volume 200 (2014), 49-77                                                                                              

Pavle Blagojević, Aleksandra Dimitrijević Blagojević, Ljubiša Kočinac

On diagonal resolvable spheres

Published in: Topology and its Applications, 160 (2013), 2335–2339                                                                                      

Pavle Blagojević, Roman Karasev

The Schwarz genus of the Stiefel manifold and counting geometric configurations

Preprint: arXiv:1211.5003v1, 21 Nov 2012

Published in: Topology and its Applications, Volume 160, Issue 18, 1 December 2013, Pages 2335–2339                           

Raman Sanyal, Bernd Sturmfels, Cynthia Vinzant

The entropic discriminant

Published in: Advances in Mathematics, Volume 244, 10 September 2013, Pages 678–707                                                 

Pavle Blagojević, Aleksandra Dimitrijević Blagojević

A problem related to Barany-Grünbaum conjecture

Published in: Filomat 27:1 (2013), 103-107                                                                                                                              

Pavle Blagojević, Boris Bukh, Roman Karasev

Turán numbers for K(s,t)-free graphs: topological obstructions and algebraic constructions (extended abstract)

Preprint: arXiv:1108.5254 21 Feb 2012

Published in: Electronic Notes in Discrete Mathematics, 38 (2011) 141-145, The Sixth European Conference on Combinatorics, Graph Theory and Applications, EuroComb 2011                                                                                             

Imre Bárány, Pavle Blagojević, Aleksandra Dimitrijević Blagojević

Functions, measures, and equipartitioning convex k-fans

Published in: Discrete & Computational Geometry, March 2013, Volume 49, Issue 2, pp 382-401                                         

Pavle Blagojević, Roman Karasev

Extensions of theorems of Rattray and Makeev

Preprint: arXiv:1011.0869, 3 Nov 2010

Published in: Topological Methods in Nonlinear Analysis, Vol. 40, No. 1, 2012, 189-214                                                       

Bruno Benedetti

Discrete Morse Theory for manifolds with boundary

Preprint: arXiv:1007.3175, 19 Jul 2010, 33 pages

Published in: Transactions of the AMS 364 (2012), 6631-6670                                                                                               

Pavle Blagojević, Aleksandra Dimitrijević Blagojević,John McCleary

Spectral sequences in combinatorial geometry: Cheeses, inscribed sets, and Borsuk–Ulam type theorems

Published in: Topology and its Applications, Volume 158, Issue 15, 15 September 2011, Pages 1920–1936                        

Pavle V.M. Blagojević, Benjamin Matschke, Günter M. Ziegler

The Bárány–Larman conjecture and the colored Tverberg theorems

Published in: Mathematisches Forschungsinstitut Oberwolfach, Topological and Geometric Combinatorics, Report No. 08/2011, pages 358-361                                                                                                                                                             

Pavle V. M. Blagojević, Benjamin Matschke, Günter M. Ziegler

A tight colored Tverberg theorem for maps to manifolds (extended abstract)

Published in: in Proc. FPSAC 2011 (Reykjavík, Iceland), Discrete Mathematics and Theoretical Computer Science (DMTCS), Vol. AO, http://www.dmtcs.org, page 183–190, 2011                                                                                                

Pavle Blagojević, Günter M. Ziegler

The ideal-valued index for a dihedral group action, and mass partition by two hyperplanes

Published in: Topology and its Applications, Volume 158, Issue 12, 1 August 2011, Pages 1326–1351                                

Bruno Benedetti, Günter M. Ziegler

On locally constructible spheres and balls

Published in: Acta Mathematica, June 2011, Volume 206, Issue 2, pp 205-243                                                                      

Pavle Blagojević, Benjamin Matschke, Günter M. Ziegler

Optimal bounds for a colorful Tverberg-Vrecica type problem

Preprint: arXiv:0911.2692, 13 Nov 2009, 12 pages

Published in: Advances in Mathematics, Volume 226, Issue 6, 1 April 2011, Pages 5198–5215                                            

Pavle V. M. Blagojević, Benjamin Matschke, Günter M. Ziegler

A tight colored Tverberg theorem for maps to manifolds

Published in: Topology and its Applications, Volume 158, Issue 12, 1 August 2011, Pages 1445–1452                                

Pavle Blagojević, Boris Bukh, Roman Karasev

Turán numbers for K(s,t)-free graphs: topological obstructions and algebraic constructions

Preprint: arXiv:11108.5254, 26 Aug 2011

Published in: Israel Journal of Mathematics, October 2013, Volume 197, Issue 1, pp 199-214