Tamas Kalman Kálmán Tamás カールマン　タマシュ    Home page (magyar nyelven itt)                                                                                                                                              日本語版

Contact information

Current activity

From April 2026, I will teach first year Linear Algebra on Tuesdays and Thursdays.

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 (almost) 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)

Yuta Hatasa.

I spent time at the following institutions:

• the Institute of Mathematics at Eötvös Loránd University (Budapest, Hungary), where I received my undergraduate degree in 1999;
• the Department of Mathematics of the University of California at Berkeley, where I was a graduate student (advisors: Michael Hutchings and Rob Kirby) until I received my Ph. D. degree in 2004;
• the University of Southern California's Department of Mathematics, where I spent three years as a non-tenure track assistant professor (2004-2007);
• the Graduate School of Mathematical Sciences at the University of Tokyo, where I was a JSPS research fellow (2007-2008) and a GCOE visiting assistant professor (2008-2010);
• the Tokyo Institute of Technology, where I am an associate professor in the Department of Mathematics.
  
• the Department of Mathematics at the Massachusetts Institute of Technology, where I was a visitor from August 2018 to March 2019.
• the World Premier International Research Center for Sustainability with Knotted Chiral Meta Matter of Hiroshima University, where I am an affiliated member.
  

For more detailed information, please see my CV.

Research

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 constructed the first one-parameter family (loop) of Legendrian knots that is essential even though it becomes trivial when viewed as a loop of smooth knots.

I work on graphs, hypergraphs, and lattice polytopes, too. I introduced two new polynomial invariants of integer polymatroids (aka generalized permutohedra aka M-convex sets) that generalize one-variable valuations of the Tutte polynomial. By now there is also a full two-variable extension. I also think a lot about the related topic of h*-vectors of lattice polytopes; I get particularly excited when they get dissected into unimodular simplices, which happens naturally for root polytopes of graphs. Through this type of combinatorics, I found curious new connections between quantum knot polynomials and Floer homology.

Finally, I have also been interested lately in (continuous and discrete) mathematical models in soft matter Physics.

Publications

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. Here are the slides of a talk I gave on the subject.
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,  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.
17. Joint paper with Lilla Tóthmérész: Hypergraph polynomials and the Bernardi process, came out in Algebraic Combinatorics.
    
18. Joint paper with Seunghun Lee and Lilla Tóthmérész: The sandpile group of a trinity and a canonical definition for the planar Bernardi action, appeared in Combinatorica.
19. Joint paper with Byung Hee An and Youngjin Bae: Ruling invariants for Legendrian graphs, appeared in the Journal of Symplectic Geometry.
20. Joint paper with Olivier Bernardi and Alexander Postnikov: Universal Tutte polynomial, published in Advances in Mathematics.
21. Joint paper with Lilla Tóthmérész: Root polytopes and Jaeger-type dissections for directed graphs, appeared in Mathematika.
22. Joint with Lilla Tóthmérész: Ehrhart theory of symmetric edge polytopes via ribbon structures, preprint.
23. Joint paper with Lilla Tóthmérész: h*-vectors of graph polytopes using activities of dissecting spanning trees, appeared in Algebraic Combinatorics.
24. Joint paper with Lilla Tóthmérész: Degrees of interior polynomials and parking function enumerators, appeared in the SIAM Journal on Discrete Mathematics (SIDMA).
25. Joint paper with Xiaxia Guan and Xian'an Jin:  A deletion-contraction formula and monotonicity properties for the polymatroid Tutte polynomial, appeared in the International Mathematics Research Notices.
26. Joint paper with Yuta Nozaki, Masakazu Teragaito, and Yuya Koda: Homotopy classification of knotted defects in ordered media, appeared in the Proceedings of the Royal Society A.
27. Joint paper with Chaviva Sirote-Katz, Yair Shokef et al.: Breaking mechanical holography in combinatorial metamaterials, appeared in Physical Review Research.
    
28. Joint paper with Chaviva Sirote-Katz, Yair Shokef et al.: Defect positioning in combinatorial metamaterials, appeared in Physical Review Research.
29. Joint preprint with Soheil Azarpendar and András Juhász On Fox's trapezoidal conjecture.
30. Joint preprint with Lilla Tóthmérész: Graph minors, Ehrhart theory, and a monotonicity property.
31. Joint preprint with Karola Mészáros and Alexander Postnikov: Trapezodial property of the generalized Alexander polynomial.