Mirko Klukas, Ph.D.
I am a post doctoral researcher and a member of the working group of Prof. H. Geiges.
My research interests lie in the field of geometric and differential topology, with a strong focus on contact and symplectic geometry. Furthermore I am interested in topological data analysis and machine learning.
I recently started a blog on data science and machine learning.
Contact
Mirko Klukas
Dr. rer. nat. (Ph.D.)
Mathematisches Institut
Universität zu Köln
Weyertal 86 - 90
D-50931 Cologne
Germany
Room: R 206
Phone: +49 / (0) 221 / 470 - 43 47
E-mail: mklukas@math.uni-koeln.de
Office hours: Tuesday & Friday, 10am - 11am
What am I working on
My research interests lie in the field of geometric and differential topology, with a strong focus on contact and symplectic geometry . The main results of my PhD thesis explore several 3-dimensional constructions of contact manifolds, homotopical questions, and symplectic handle constructions.
Another focus of my research is the relationship of contact and symplectic geometry with a certain class of geometric structures on parallelizable 4-manifolds, namely Engel structures .
Publications & Preprints
-
The fundamental group of the space of contact structures on the 3-torus, with Hansjörg Geiges
Math. Res. Lett. 21 (2014), 1257-1262.
Abstract | Full-text PDF -
On prolongations of contact manifolds, with Bijan Sahamie
Proc. Amer. Math. Soc. 141 (2013), no. 9, 3257-3263.
Abstract | Full-text PDF -
Open book decompositions of fibre sums in contact topology
Algebr. Geom. Topol., to appear.
Preprint available at ArXiv:1207.3958 -
Open books and exact symplectic cobordisms
Preprint available at ArXiv:1207.5647 -
Isotopy Classification of Engel Structures on Circle Bundles, with Bijan Sahamie
Preprint available at ArXiv:1209.1368 - ...
Links
Coding ∩ Math :
- My coding/math blog: Maps, functions, and arrows
Conferences and other events:
- Schedule of the working group symplectic topology
Lunchbreak:
- Here is an index of the "What Is...?" column in the Notices of the AMS.
- Allen Knutson on the Mathematics of Juggling
- The Geometry of 3-Manifolds: Curtis McMullen talks about the shape of the universe.
- Video lectures of the MSRI: Among others there are also a lot of lectures introducing the world of contact- and symplectic-topology.
Prolongation of standard contact structure
Visualization of the standard Engel structure:
The Movie shows a visualization of the standard Engel structure, which is obtained by prolongation of the standard contact structure (indicated by the plane field colored in gray).
Identifying the time interval in the movie with the unit interval [0,1] the movie can be understood as follows. The pictured space corresponds for each point t∈[0,1] in time to a hypersurface ℝ3×{ei2πt} in ℝ3×S1. Now, the standard Engel structure is given by the intersection of the plane fields in direct sum with the subspace spanned by ∂t.