Michigan State University has a large and active research group in topology, and closely related areas of geometry. Among the research areas represented by the group are: knot theory and 3- and 4-manifolds, Floer homology, hyperbolic geometry, quantum invariants and their categorification, equivariant stable homotopy theory, algebraic K-theory, geometric group theory, topological data analysis, symplectic geometry, geometric analysis, gauge theory, cluster algebras, and Teichmuller space and its quantization and generalizations.
Bodie Beaumont-Gould***, Erik Brodsky***, Vijay Higgins*, Alaina Hogan***, Joseph M. Melby**, Joshua Piazza***, Power sum elements in the G_2 skein algebra, to appear in Algebr. Geom. Topol., arXiv:2310.01773.
Vijay Higgins*, Miraculous cancellations and the quantum Frobenius for SL3 skein modules, preprint, arXiv:2409.00351.
E. Kalfagianni- J. Melby**, ``Constructions of $q$-hyperbolic knots”, Annales de l'institut Fourier (accepted 2024)
R. McConkey**, ``Linear bounds on crosscup numbers”, Algebraic and Geometric Topology, accepted (2024)
Francis Bonahon, Vijay Higgins*, Central elements in the SL_d-skein algebra of a surface, Math. Z. 308, 1 (2024). https://doi.org/10.1007/s00209-024-03559-9
E. Kalfagianni -R. McConkey**, ``Crossing numbers of cable knots”, Bullettin of London Math Society, published on line August 26, 2024
S. Kumar- J. Melby**: ``Asymptotic additivity of the Turaev-Viro invariants under cabling”, International Journal of Math,Volume 34, Number 11, 23 pages.(2023)
S. Kumar- J. Melby**: ``Asymptotic additivity of the Turaev-Viro invariants for a family of 3-manifolds”, J. of London Math Soc. Volume 106, Issue 4, 3043-3068 (2022).
* postdoc
** graduate student
*** undergraduate student