(magyar nyelven itt)
|my family name at math dot
titech dot ac dot jp
|mail code H-214
Department of Mathematics
Tokyo Institute of Technology
2-12-1 Ookayama, Meguro-ku
In the second quarter of Spring 2017, I am teaching a lecture course in
first-year linear algebra. For further
information, please visit the website
for the class.
My graduate seminar meets on Tuesday afternoons from 2 to 4 pm (on most
weeks) in room 340.
Here are the websites of the Tokyo Tech
topology seminar (Wednesdays from 3:30 to 5) and the Komaba
topology seminar (Tuesdays from 5 to 6:30).
I am a researcher and instructor of mathematics.
I am fortunate to have spent time at the following great
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. Recently I started doing work on graphs and
hypergraphs, too. I introduced two new polynomial invariants of integer
polymatroids that generalize one-variable valuations of the Tutte
polynomial. Through combinatorics, I found interesting new connections
between knot polynomials and Floer homology.
- Part of my undergraduate
thesis (Stable maps of surfaces
into the plane) was published at Topology
and its Applications.
- With my undergraduate advisor András Szűcs,
we co-authored another paper
(On double points of immersed surfaces)
in the same journal.
- My doctoral
dissertation (Contact homology
and one parameter families of Legendrian knots) was published at
Geometry and Topology.
- A follow-up paper
(Braid-positive Legendrian links)
appeared in the International
Mathematics Research Notices.
- This manuscript
(Maximal Thurston-Bennequin number of
+adequate links) was published in the Proceedings of the American Mathematical Society.
- This article
(Rulings of Legendrian knots as
spanning surfaces) appeared in the Pacific
Journal of Mathematics.
- This paper (Isotopies of Legendrian 1-knots and
Legendrian 2-tori), joint with Tobias
Ekholm, was published in the Journal of Symplectic Geometry.
- 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.
- The paper Inner products on the Hecke algebra of the
braid group was published in Topology
and its Applications.
- My first paper
on combinatorics, A version of
Tutte's polynomial for hypergraphs, appeared in Advances
in Mathematics. I gave several versions of
on the results in it.
- 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.
- 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.
- My joint paper
Murakami, titled Root polytopes, parking functions, and the
HOMFLY polynomial, has now appeared in Quantum
- With Alexander
Postnikov, we wrote a paper on Root
polytopes, Tutte polynomials, and a duality theorem for bipartite graphs.
It has been published in the Proceedings of the London Mathematical Society.