Probabilistische Methoden in der Topologie

• Antragsteller: Professor Dr. Dmitry Feichtner-Kozlov
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2011 bis 2016
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 191155460

• Erstellungsjahr: 2016

Zusammenfassung der Projektergebnisse

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.

Projektbezogene Publikationen (Auswahl)

• 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
  (Siehe online unter 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
  (Siehe online unter 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
  (Siehe online unter 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
  (Siehe online unter https://doi.org/10.7151/dmgt.1766)
• Topology of the immediate snapshot complexes. Topology Appl. 178 (2014), 160–184
  Kozlov, Dmitry N.
  (Siehe online unter 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
  (Siehe online unter 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.
  (Siehe online unter https://dx.doi.org/10.4310/HH10.1016/j.topol.2014.08.032.2015.v17.n1.a15)