My name is Roman Kogan. I am a math PhD student at Texas A&M University. My undergraduate degree was from SUNY Stony Brook.
Curriculum Vitae: [PDF]
Research and other work
- On a Basis for the Framed Link Vector Space Spanned by Chord Diagrams. (with B.Bischof, D.N.Yetter). Accepted for publication in Journal of Knot Theory and Ramifications. Preprint at ArXiv.
- With Metric Estimates and Membership Complexity for Archimedean Amoebae and Tropical Hypersurfaces (with M.Avendano, M.Nisse, J. M. Rojas), presented at MEGA 2013. [PDF].
- [PDF] Algorithms and Software for Computation in n-dimensional Thompson Groups nV.
Presented at Growth ... in Groups, Paris, 2015 (an update of poster from YGGT4, 2015).
- [PDF] Amoebas, Archtrop and all that Jazz. TAMU GSO Seminar slides, March 2014.
- [PDF] Proving Benniquin Inequality from Knot Diagrams. SUNY Stony Brook, 2010.
- NvTrees, n-dimensional Thompson groups calculator (Java Applet and Standalone);
- Chord Diagrams, a Java/Mathematica software for the paper above;
- Evolutes, a program that draws involutes, evolutes an osculating circles for a given curve.
- If you are into computational geometry, you might like the Delaunay triangulation applet, which illustrates the algorithm of computing it by a lift to paraboloid;
- If you need to visualize the Newton polyhedron of a polynomial and count lattice points inside it, Newton Polytope applet does precisely that.
Github: See my GitHub for the most recent source code.
Teaching: MAT 152 Honors Fall 2015.
- Listen to my music (and check back for new stuff once in a while!).
- See some interactive math art and explore the Mandelbrot Set in a cool way (dynamic rendering, made with Processing);
- Try the arcball interface implemented in Processing JS and learn how quaternions are useful in computer graphics;
- Read a survey of history of elctronic music (also as [PDF]);
- If you have a webcam, play with the Webcam Scanner Camera. Take pictures with one dimension in space, and another in time;
- Check out the ever-to-be-updated 3D printing adventures album.