(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
My graduate seminar meets from 10 to 12 on Thursdays in room 206. My
undergraduate senior seminar is from 2 to 4 on Mondays in room 340. I
teach sophomore Set Theory on Tuesdays from 10:45 to 12:15 in room 103.
Here is a combined schedule for all Tokyo Tech
mathematics seminars (with topology talks usually on Wednesdays
from 3:30 to 5). See also the Komaba
topology seminar (Tuesdays from 5 to 6:30).
I research and teach mathematics. My past and present PhD
Kouki Sato (2017)
I have 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. 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 in 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 in
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.
- 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.
- Our joint paper
Murakami, titled Root polytopes, parking functions, and the
HOMFLY polynomial, has now appeared in Quantum
- With Alexander
Postnikov, we wrote a paper
polytopes, Tutte polynomials, and a duality theorem for bipartite graphs.
It has been published in the Proceedings of the London Mathematical Society.
- With Daniel
Mathews, we submitted the preprint Tight
contact structures on Seifert surface complements for publication.
- Our joint paper with Camden
Hine on Clock theorems for
triangulated surfaces has also been submitted.
- With Lilla
Tóthmérész, we submitted the manuscript Hypergraph polynomials and the Bernardi
process for publication.