nLab Gunnar Carlsson

• webpage

Selected writings

On cyclic loop spaces:

• Gunnar Carlsson, Ralph Cohen, The cyclic groups and the free loop space, Commentarii Mathematici Helvetici 62 (1987) 423–449 (doi:10.1007/BF02564455, dml:140092)

On an algorithm for topological data analysis by a variant of Reeb graphs:

• Gurjeet Singh, Facundo Mémoli, Gunnar Carlsson, Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition, in: M. Botsch, R. Pajarola (eds.), Eurographics Symposium on Point-Based Graphics (2007) $[$doi:10.2312/SPBG/SPBG07/091-100, pdf$]$

On topological data analysis:

• Gunnar Carlsson, Topology and data, Bull. Amer. Math. Soc. 46 (2009), 255-308 (doi:10.1090/S0273-0979-09-01249-X)

and a flashy exposition for commercial use:

• Gunnar Carlsson, Professor Gunnar Carlsson Introduces Topological Data Analysis $[$video$]$

On persistent homology:

• A. Zomorodian, Gunnar Carlsson, Computing persistent homology, Discrete Comput. Geom. 33, 249–274 (2005)

• Gunnar Carlsson, V. de Silva, Zigzag persistence, arXiv:0812.0197

• Gunnar Carlsson, Persistent Homology and Applied Homotopy Theory, in: Handbook of Homotopy Theory, CRC Press, 2019 (arXiv:2004.00738)

Introducing zigzag persistence, connecting persistent homology to quiver representation-theory, re-proving Gabriel's theorem for the case of A-type quivers and introducing the diamond principle:

• Gunnar Carlsson, Vin de Silva, Zigzag Persistence, Found Comput Math 10 (2010) 367–405 $[$arXiv:0812.0197, doi:10.1007/s10208-010-9066-0$]$

and applied to level sets:

• Gunnar Carlsson, Vin de Silva, Dmitriy Morozov, Zigzag persistent homology and real-valued functions, in: SCG ‘09: Proceedings of the twenty-fifth annual symposium on Computational geometry (2009) 247–256 $[$doi:10.1145/1542362.1542408$]$

• Gunnar Carlsson, Vin de Silva, Sara Kališnik, Dmitriy Morozov, Parametrized Homology via Zigzag Persistence, Algebr. Geom. Topol. 19 (2019) 657-700 $[$arXiv:1604.03596, doi:10.2140/agt.2019.19.657$]$

Related $n$Lab entries

• equivariant stable homotopy theory

• Segal conjecture, Sullivan conjecture

  Burnside ring, stable cohomotopy, equivariant stable cohomotopy

• persistent homology

category: people