Mikael Vejdemo-Johansson started out in computational homological algebra, studying algorithms for computing invariants of Tor modules and A∞-algebra structures on the modular group cohomology rings of p-groups. After finishing his PhD, he has worked during postdoctoral studies at Stanford University (2008-2011), University of St Andrews (2011-2012), KTH Royal Institute of Technology (2012-2013, 2014-2015) and the Institute of Mathematics and its Applications, University of Minnesota (2013-2014) on Topological Data Analysis: using persistent homology and cohomology to compute descriptors for abstract point clouds, and the Mapper algorithm generalizing Reeb graphs and nerve simplicial complex constructions to produce intrinsic topological model spaces for arbitrary data. He seeks out application realms anywhere he can find them, and has published work on applications to parliamentary voting records, to the statistics of color naming systems in linguistics, to motion capture data.
In addition to these primary research interests, he has worked on enumerating tie knots, finding 262862 possible tie knots using formal languages and algebraic systems of equations.
Fil. kand., Stockholm University
Fil. mag., Stockholm University
Dr.rer.nat. Friedrich-Schiller-Universität Jena
Scholarship / Publications
A comprehensive list of Mikael Vejdemo-Johansson’s publications can be found on Google Scholar: https://scholar.google.com/citations?hl=en&user=XJN1TGIAAAAJ
Some highlights include
1. Vejdemo-Johansson M. Sketches of a platypus: persistent homology and its algebraic foundations. Algebr Topol Appl New Dir. 2014;(620):295--320.
2. Vejdemo-Johansson M, Vejdemo S, Ek C-H. Comparing Distributions of Color Words: Pitfalls and Metric Choices. PLOS ONE. 2014;9(2):e89184.
3. Vejdemo-Johansson M, Pokorny F, Skraba P, Kragic D. Cohomological learning of periodic motion. Appl Algebra Eng Commun Comput [Internet]. 2015;1–22. Available from: http://dx.doi.org/10.1007/s00200-015-0251-x
4. Berwald J, Gidea M, Vejdemo-Johansson M. Automatic recognition and tagging of topologically different regimes in dynamical systems. Discontinuity Non-Linearity Complex. 2015;3(4):413–426.
5. de Silva V, Morozov D, Vejdemo-Johansson M. Dualities in persistent (co)homology. Inverse Probl [Internet]. 2011 Dec 1 [cited 2012 Aug 29];27(12):124003. Available from: http://iopscience.iop.org/0266-5611/27/12/124003
6. Hirsch D, Markström I, Patterson ML, Sandberg A, Vejdemo-Johansson M. More ties than we thought. PeerJ Comput Sci [Internet]. 2015;1:e2. Available from: https://dx.doi.org/10.7717/peerj-cs.2
7. Lum PY, Singh G, Lehman A, Ishkanov T, Vejdemo-Johansson M, Alagappan M, et al. Extracting insights from the shape of complex data using topology. Sci Rep [Internet]. 2013 Feb 7 [cited 2013 Feb 7];3. Available from: http://www.nature.com/srep/2013/130207/srep01236/full/srep01236.html
8. Morozov D, de Silva V, Vejdemo-Johansson M. Persistent Cohomology and Circular coordinates. Discrete Comput Geom. 2011;45(4):737--759.
9. Tausz A, Vejdemo-Johansson M. JavaPlex: A research software package for persistent (co) homology. 2011.
10. Wang B, Summa B, Pascucci V, Vejdemo-Johansson M. Branching and Circular Features in High Dimensional Data. Vis Comput Graph IEEE Trans On. 2011;17(12):1902–1911.
Last Updated: 07.12.17