As of September 2011, I work at the University of St Andrews in Scotland. Up to date information will be available at m y new website.
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^{*}(C_{n}xC_{m}), Journal of Homotopy and Related Structures, 3(1):1-11, February 2008.
- Persistent cohomology and circular coordinates, joint with
Vin de Silva. SOCG 2009.
Paper version, joint with Vin de Silva and Dmitriy Morozov. DCG. - 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.
- A parallel algorithm Buchberger algorithm for multigraded ideals, joint with Emil Sköldberg and Jason Dusek, submitted to the International Conference on Mathematical Software 2010.
- Dualities in persistent (co)homology, joint with Dmitriy Morozov and Vin de Silva.
Recently given talks will have slides on display, if slides indeed exist, at a dedicated talks page.