Researcher Information

SUGAWARA Sakumi

Assistant Professor

Studying the topology of combinatorial and algebraic objects

Department of Mathematics, Mathematics

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Theme

Low-dimensional topology of hyperplane arrangements, algebraic curves and singularity theory

FieldTopology, Hyperplane arrangement
KeywordHyperplane arrangement, Algebraic curve, Handle decomposition, Kirby diagram, Knot theory, Milnor fiber

Introduction of Research

I am interested in the topology of hyperplane arrangements. A hyperplane arrangement is a finite set of hyperplanes in Euclidean space, which is studied in algebraic geometry, combinatorics, topology, representation theory, etc. I am especially interested in studying hyperplane arrangements from the viewpoint of low-dimensional topology (knot theory, 3-, 4-dimensional topology).
Also, one major problem in the topology of arrangements is whether several topological invariants are combinatorially determined. In particular, many invariants of Milnor fibers and covering spaces of the complement are still unsolved for this problem. I am studying such topological invariants towards combinatorial description.

Representative Achievements

S. Sugawara, M. Yoshinaga, Divides with cusps and Kirby diagrams for line arrangements, Topology and Appl., 313 (2022), Paper No. 107989.
S. Sugawara, ℤ-local system cohomology of hyperplane arrangements and a Cohen--Dimca--Orlik type theorem, Internat. J. Math, 34, (2023), no. 8, 2350044.
S. Sugawara, Divides with cusps and symmetric links, Topology Appl., (362), 2025, 109207.
S. Sugawara, Handle decompositions and Kirby diagrams for the complement of plane algebraic curves, arXiv:2306.10519.
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