NOZAKI Yuta
Associate Professor
Unraveling the mysteries of low-dimensional manifolds
Department of Mathematics, Mathematics
| Theme | Transdisciplinary research in low-dimensional topology and its collaboration with computer science and physics |
| Field | Topology |
| Keyword | low-dimensional manifold, knot, mapping class group of surfaces, homology cobordism |
Introduction of Research
I study global properties of geometric objects and spaces. In particular, I am interested in surfaces and knots, as well as 3- and 4-dimensional manifolds. Although these objects can often be visualized in an appropriate sense, uncovering their underlying geometry is far from straightforward.
My research employs a wide range of mathematical techniques, with particular emphasis on methods from quantum topology. I am also interested in interdisciplinary research and have been involved in collaborative projects related to computer science and physics.
Representative Achievements
M. Boileau, T. Kitano, Y. Nozaki,
On the genera of symmetric unions of knots, Canad. J. Math. (2025), pp.1--26.
Y. Nozaki, M. Sato, M. Suzuki,
Torsion elements in the associated graded of the Y-filtration of the monoid of homology cylinders, J. Topol. (2025).
Y. Nozaki, M. Sato, M. Suzuki,
A non-commutative Reidemeister-Turaev torsion of homology cylinders, Trans. Amer. Math. Soc., 376 (2023), 5045--5088.
Y. Nozaki, M. Sato, M. Suzuki,
Abelian quotients of the Y-filtration on the homology cylinders via the LMO functor, Geom. Topol., 26-1 (2022), 221--282.
