Tamas Kalman

Kálmán Tamás

カールマン タマシュ

Home page

(magyar nyelven itt)                                                                                                                                              日本語版


Contact information

Email address:
my family name at math dot titech dot ac dot jp
Postal Address:
mail code H-214
Department of Mathematics
Tokyo Institute of Technology
2-12-1 Ookayama, Meguro-ku
Tokyo 152-8551


Current activity

My graduate seminar meets online from 2 to 4 pm on Tuesdays. I teach graduate Differential Topology on Mondays from 10:45-12:25.

Here is a combined schedule for all Tokyo Tech mathematics seminars, including our Topology seminar. See also the Komaba topology seminar. Or, actually, you can now attend any math seminar in the world!


Professional Information

I research and teach mathematics. My past and present PhD students are

Kouki Sato (2017)

Keiju Kato (2020)

Keita Nakagane (2021)

I spent time at the following institutions:

For more detailed information, please see my CV.



My main research interests are in low-dimensional geometric topology, in particular in contact 3-manifolds and Legendrian knots (and their Floer homologies), as well as in classical knot invariants such as the Homfly polynomial. I work on graphs and hypergraphs, too. I introduced two new polynomial invariants of integer polymatroids that generalize one-variable valuations of the Tutte polynomial. Recently this has led to a full two-variable extension. Through combinatorics, I found interesting new connections between quantum knot polynomials and Floer homology.

trinity with
              special alternating link
visualizing the interior polynomial



  1. Part of my undergraduate thesis (Stable maps of surfaces into the plane) was published at Topology and its Applications.
  2. With my undergraduate advisor András Szűcs, we co-authored another paper (On double points of immersed surfaces) in the same journal.
  3. My doctoral dissertation (Contact homology and one parameter families of Legendrian knots) was published at Geometry and Topology.
  4. A follow-up paper (Braid-positive Legendrian links) appeared in the International Mathematics Research Notices.
  5. This manuscript (Maximal Thurston-Bennequin number of +adequate links) was published in the Proceedings of the American Mathematical Society.
  6. This article (Rulings of Legendrian knots as spanning surfaces) appeared in the Pacific Journal of Mathematics.
  7. This paper (Isotopies of Legendrian 1-knots and Legendrian 2-tori), joint with Tobias Ekholm, was published in the Journal of Symplectic Geometry.
  8. The manuscript Meridian twisting of closed braids and the Homfly polynomial appeared in the Mathematical Proceedings of the Cambridge Philosophical Society.
  9. The paper Inner products on the Hecke algebra of the braid group was published in Topology and its Applications.
  10. My first paper on combinatorics, A version of Tutte's polynomial for hypergraphs, appeared in Advances in Mathematics. I gave several versions of this talk on the results in it.
  11. Our joint paper with András Juhász and Jake Rasmussen, Sutured Floer homology and hypergraphs, was published at Mathematical Research Letters. It is summarized in these slides.
  12. With Tobias Ekholm and Ko Honda, we wrote a paper on Legendrian knots and exact Lagrangian cobordisms that appeared in the Journal of the European Mathematical Society. I discussed its contents in this talk.
  13. Our joint paper with Hitoshi Murakami, titled Root polytopes, parking functions, and the HOMFLY polynomial,  has now appeared in Quantum Topology.
  14. With Alexander Postnikov, we wrote a paper on Root polytopes, Tutte polynomials, and a duality theorem for bipartite graphs. It was published in the Proceedings of the London Mathematical Society.
  15. With Daniel Mathews, we published the paper Tight contact structures on Seifert surface complements in the Journal of Topology.
  16. Our joint paper with Camden Hine on Clock theorems for triangulated surfaces has also been submitted.
  17. Joint with Lilla Tóthmérész: Hypergraph polynomials and the Bernardi process, Algebraic Combinatorics, link to the paper.
  18. Joint with Seunghun Lee and Lilla Tóthmérész: The sandpile group of a trinity and a canonical definition for the planar Bernardi action, preprint.
  19. Joint with Byung Hee An and Youngjin Bae: Ruling invariants for Legendrian graphs, to appear in the Journal of Symplectic Geometry, preprint.
  20. Joint with Olivier Bernardi and Alexander Postnikov: Universal Tutte polynomial, preprint.
  21. Joint with Lilla Tóthmérész: Root polytopes and Jaeger-type dissections for directed graphs, preprint.