Welcome
You have reached Mikael Vejdemo Johansson. I was a postdoc at Stanford September 2008 - May 2011, and started a postdoc at St. Andrews September 2011.
More reliable information probably is available at my University homepage.
My main interests lie in the intersections between Algebra, Combinatorics, Topology and Computer Science / Computation. My Master's and PhD projects both dealt with efficient computation of invariants and structures in homological algebra; and my current research is on the efficient computation and application of algebraic topological invariants to data analysis questions.
You might be interested in:
- My public key. My fingerprint is 7E64 04C5 2F0F B8E7 7449 5D3D B549 A90C C07C CCCD. Do note that the key with id E06C EFE4 has been superseded.
- My Erdős number is 4. Erdős path: Mikael Vejdemo-Johansson - Vin de Silva - Gunnar Carlsson - Vance Faber - Pál Erdős.
Research
My Master's degree research was on computing denominator polynomials for the Poincare-Betti series of a monomial ring. My research resulted in a tool for the computation of these denominator polynomials, found at http://math.su.se/~mik/poincare.
My PhD research was on the computation of A∞-algebra structures on group cohomology rings.
My current research is about finding intrinsic parametrizations of datasets using homology and cohomology.
Publications
Publications before 2006 are published under my birth name: Mikael Johansson.
- Computation of denominator polynomials for Poincaré series of monomial rings. Master's thesis, Stockholm University, 2004.
- Computation of Poincaré-Betti series for monomial rings, Rend. Istit. Mat. Univ. Trieste, 37(1-2):85-94 (2006)
- Computation of A∞ algebras in group cohomology, PhD thesis, Friedrich-Schiller-Universität Jena, July 2008.
- A partial A-infinity structure on H*(CnxCm), Journal of Homotopy and Related Structures, 3(1):1-11, February 2008.
- Persistent cohomology and circular coordinates, joint with
Vin de Silva. Symposium on Computational Geometry 2009: 227-236.
Paper version, joint with Vin de Silva and Dmitriy Morozov. Discrete and Computational Geometry 45 (4): 737-759 (2011). - Blackbox computing of A-infinity algebras, Georgian Mathematical Journal volume 17, issue 2, pp 391-404. Also on arXiv
- Operadic Gröbner bases: an implementation, Mathematical Software — ICMS2010, LNCS 6327 pp 249-252.
The LNCS paper is a short communication announcing the results that are accepted for publication in
Implementing Gröbner bases for operads, joint with Vladimir Dotsenko. To appear in Proceedings of Operads 2009, Séminaires et Congrès
Manuscripts
- On low degree regular sequences in group cohomology, preprint.
- Dualities in persistent (co)homology, joint with Dmitriy Morozov and Vin de Silva.
- A parallel Buchberger algorithm for multigraded ideals, joint with Emil Sköldberg and Jason Dusek.
- Interleaved computation for persistent homology, preprint
Recently given talks will have slides on display, if slides indeed exist, at a dedicated talks page.
Software projects
Talks
Here, I will aggregate slides from talks I've given recently. For some subjects, I give several talks with similar, though not identical content, on the same subject matter. These will be listed under a common heading.
Survey or colloquium talks
Topology and data
- Lecture course: 4 lectures at KTH, Stockholm, Sweden, September 2010:
- Introduction
- Chalk talk: no slides. Lecture notes will be online at a later point.
- Available software, and the Klein bottle of image patches, with a companion handout
- Chalk talk: no slides. Lecture notes will be online at a later point.
- Colloquium talk, TU Kaiserslautern, November 2010 — in German
- Informal seminar, Mittag-Leffler Institute, January 2011 — companion slides to a partly chalk talk.
The topology of politics
- 5 minutes of fame: The geometry of politics - Lightning talk at Noisebridge on February 18, 2010
- Seminar talk, Friedrich-Schiller-Universität Jena, Germany, August 2010 — in German
- Seminar talk, Linköpings Universitet, Sweden, August 2010
- Seminar talk, KTH, Stockholm, Sweden, September 2010
Research seminars or conference presentations
Persistent homology of point clouds sampled on algebraic varieties
Persistent cohomology and circular coordinates
- Santa Barbara, Darpa TDA, January 2009
- Banff, Data Analysis using Computational Topology and Geometric Statistics, March 2009
- Duke University, April 1st 2009, seminar talk
- Symposium on Computational Geometry, June 2009
- The de Brún workshop, Galway, July 2009
- TGDA Workshop, Paris, July 2009
- Seminar talk, Pomona College, September 2009
- International Conference on Topology and its Applications, Nafpaktos, Greece, June 2010 — includes more survey-like introduction to topological data analysis
- Colloquium talk, TU Kaiserslautern, November 2010 — in German
- Colloquium talk, North Carolina State University, January 2011 — contains a survey-like introduction to topological data analysis
Period reconstruction using circular coordinates
- Seminar talk, Uppsala Universitet, September 2009
- Conference talk, ATMCS 2010, Münster, Germany, June 2010
- Seminar talk, University of Western Ontario, London, Canada, October 2010
Finite time computation of A-infinity algebra structures on Ext algebras
Operadic Gröbner bases
Persistent homology and algebraic geometry
Teaching
Lecture notes for the MATH198 lecture course Fall 2009 at Stanford on Category Theory and Functional Programming.
I taught MATH 20: Calculus in Spring 2010 at Stanford.
I gave a mini-course on persistent homology at KTH in Stockholm, September 2-7, 2010.