Probabilistische Methoden in der Topologie

• Applicant: Professor Dr. Dmitry Feichtner-Kozlov
• Subject Area: Mathematics
• Term: from 2011 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 191155460

• Final Report Year: 2016

Final Report Abstract

General investigation of questions in combinatorial topology has been conducted by several researchers as a part of this project. Many of the research directions which were pursued have resulted in publications, in international high-level peer-reviewed journals. The studied topics range from independence complexes of graphs, to Quillen model structures on graphs, and to applications in computer science, such as simplicial methods in theoretical distributed computing.

Publications

• Chromatic subdivision of a simplicial complex. Homology Homotopy Appl. 14 (2012), no. 2, 197–209
  Kozlov, Dmitry N.
  
• Some conjectures concerning complexity of PL subdivisions. Proceedings of the Workshop on Geometric and Topological Methods in Computer Science (GETCO), 153–157, Electron. Notes Theor. Comput. Sci., 283, Elsevier Sci. B. V., Amsterdam, 2012
  Kozlov, Dmitry N.
  
• Stellar discriminants and equipartitions. Topology Appl. 159 (2012), no. 15, 3340–3354
  Kozlov, Dmitry N.
  
• Special cycles in independence complexes and superfrustration in some lattices. Topology Appl. 160 (2013), no. 7, 943–950
  Adamaszek, Michał
  (See online at https://doi.org/10.1016/j.topol.2013.03.009)
• Extremal problems related to Betti numbers of flag complexes. Discrete Appl. Math. 173 (2014), 8–15
  Adamaszek, Michał
  (See online at https://doi.org/10.1016/j.dam.2014.04.006)
• Small flag complexes with torsion. Canad. Math. Bull. 57 (2014), no. 2, 225–230
  Adamaszek, Michał
  (See online at https://doi.org/10.4153/CMB-013-032-9)
• The smallest nonevasive graph property. Discuss. Math. Graph Theory 34 (2014), no. 4, 857–862
  Adamaszek, Michał
  (See online at https://doi.org/10.7151/dmgt.1766)
• Topology of the immediate snapshot complexes. Topology Appl. 178 (2014), 160–184
  Kozlov, Dmitry N.
  (See online at https://doi.org/10.1016/j.topol.2014.08.032)
• Shellability and regularity of chain complexes over a principal ideal domain. Order 32 (2015), no. 1, 1–28
  Grenzebach, Gerrit; Walker, Björn
  (See online at https://doi.org/10.1007/s11083-013-9312-6)
• Topology of the view complex. Homology Homotopy Appl. 17 (2015), no. 1, 307–319
  Kozlov, Dmitry N.
  (See online at https://dx.doi.org/10.4310/HH10.1016/j.topol.2014.08.032.2015.v17.n1.a15)