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Documents authored by Feichtner-Kozlov, Dmitry

Document
DOI: 10.4230/DagRep.14.2.206
Applied and Combinatorial Topology (Dagstuhl Seminar 24092)

Authors: Paweł Dłotko, Dmitry Feichtner-Kozlov, Anastasios Stefanou, Yusu Wang, and Jan F Senge

Published in: Dagstuhl Reports, Volume 14, Issue 2 (2024)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 24092 "Applied and Combinatorial Topology". The last twenty years of rapid development of Topological Data Analysis (TDA) have shown the need to analyze the shape of data to better understand the data. Since an explosion of new ideas in 2000’ including those of Persistent Homology and Mapper Algorithms, the community rushed to solve detailed theoretical questions related to the existing invariants. However, topology and geometry still have much to offer to the data science community. New tools and techniques are within reach, waiting to be brought over the fence to enrich our understanding and potential to analyze data. At the same time, the fields of Discrete Morse Theory (DMT) and Combinatorial Topology (CT) are developed in parallel with no strong connection to data-intensive TDA or to other statistical pipelines (e.g. machine learning). This Dagstuhl Seminar brought together a number of experts in Discrete Morse Theory, Combinatorial Topology, Topological Data Analysis, and Statistics to (i) enhance the existing interactions between these fields on the one hand, and (ii) discuss the possibilities of adopting new invariants from algebra, geometry, and topology; in particular inspired by continuous and discrete Morse theory and combinatorial topology; to analyze and better understand the notion of shape of the data. The different talks in the seminar included both introductory talks as well as current research expositions and proved fruitful for the open problem and break-out sessions. The topics that were discussed included 1) algorithmic aspects for efficient computation as well as Morse theoretic approximations 2) topological information gain of multiparameter persistence 3) understanding the magnitude function and its relation to graph problems.
Cite as

Paweł Dłotko, Dmitry Feichtner-Kozlov, Anastasios Stefanou, Yusu Wang, and Jan F Senge. Applied and Combinatorial Topology (Dagstuhl Seminar 24092). In Dagstuhl Reports, Volume 14, Issue 2, pp. 206-239, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{dlotko_et_al:DagRep.14.2.206,
  author =	{D{\l}otko, Pawe{\l} and Feichtner-Kozlov, Dmitry and Stefanou, Anastasios and Wang, Yusu and Senge, Jan F},
  title =	{{Applied and Combinatorial Topology (Dagstuhl Seminar 24092)}},
  pages =	{206--239},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2024},
  volume =	{14},
  number =	{2},
  editor =	{D{\l}otko, Pawe{\l} and Feichtner-Kozlov, Dmitry and Stefanou, Anastasios and Wang, Yusu and Senge, Jan F},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.14.2.206},
  URN =		{urn:nbn:de:0030-drops-205059},
  doi =		{10.4230/DagRep.14.2.206},
  annote =	{Keywords: Applied Topology, Topological Data Analysis, Discrete Morse Theory, Combinatorial Topology, Statistics}
}
Document
DOI: 10.4230/DagRep.6.7.31
Topological Methods in Distributed Computing (Dagstuhl Seminar 16282)

Authors: Dmitry Feichtner-Kozlov and Damien Imbs

Published in: Dagstuhl Reports, Volume 6, Issue 7 (2016)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 16282 "Topological Methods in Distributed Computing", which was attended by 22 international researchers, both junior and senior. In the last 10--15 years, there has been an increasing body of work on applications of topology in theoretical distributed computing. This seminar brought together computer scientists working in theoretical distributed computing and mathematicians working in combinatorial topology, leading to interesting new collaborations. This report gathers abstracts of the talks given by the participants and of the group research sessions that happened during the seminar.
Cite as

Dmitry Feichtner-Kozlov and Damien Imbs. Topological Methods in Distributed Computing (Dagstuhl Seminar 16282). In Dagstuhl Reports, Volume 6, Issue 7, pp. 31-41, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@Article{feichtnerkozlov_et_al:DagRep.6.7.31,
  author =	{Feichtner-Kozlov, Dmitry and Imbs, Damien},
  title =	{{Topological Methods in Distributed Computing (Dagstuhl Seminar 16282)}},
  pages =	{31--41},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2016},
  volume =	{6},
  number =	{7},
  editor =	{Feichtner-Kozlov, Dmitry and Imbs, Damien},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.6.7.31},
  URN =		{urn:nbn:de:0030-drops-67614},
  doi =		{10.4230/DagRep.6.7.31},
  annote =	{Keywords: combinatorial topology, concurrency, distributed protocols, shared-memory communication, solvability}
}
Document
DOI: 10.4230/DagRep.2.3.50
Applications of Combinatorial Topology to Computer Science (Dagstuhl Seminar 12121)

Authors: Lisbeth Fajstrup, Dmitry Feichtner-Kozlov, and Maurice Herlihy

Published in: Dagstuhl Reports, Volume 2, Issue 3 (2012)

Abstract
This report documents the program of Dagstuhl Seminar 12121 "Applications of Combinatorial Topology to Computer Science". The seminar brought together researchers working on applications of combinatorial topology to various fields of computer science. The goal was to foster communication across these fields by providing researchers in each field the opportunity to explain their research programs to the others. The fields covered included distributed computing, persistent homology, semantics of concurrency, and sensor networks.
Cite as

Lisbeth Fajstrup, Dmitry Feichtner-Kozlov, and Maurice Herlihy. Applications of Combinatorial Topology to Computer Science (Dagstuhl Seminar 12121). In Dagstuhl Reports, Volume 2, Issue 3, pp. 50-66, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@Article{fajstrup_et_al:DagRep.2.3.50,
  author =	{Fajstrup, Lisbeth and Feichtner-Kozlov, Dmitry and Herlihy, Maurice},
  title =	{{Applications of Combinatorial Topology to Computer Science (Dagstuhl Seminar 12121)}},
  pages =	{50--66},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2012},
  volume =	{2},
  number =	{3},
  editor =	{Fajstrup, Lisbeth and Feichtner-Kozlov, Dmitry and Herlihy, Maurice},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.2.3.50},
  URN =		{urn:nbn:de:0030-drops-35363},
  doi =		{10.4230/DagRep.2.3.50},
  annote =	{Keywords: Combinatorial topology, Distributed computing, Persistent homology, Program semantics, Sensor networks}
}
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