Kiyoshi Igusa

Professor of Mathematics

Departments/Programs

Mathematics

Degrees

Princeton University, Ph.D.
University of Chicago, B.A.

Expertise

Representation theory, Homological Algebra, Algebraic Topology, Differential Topology

Profile

Please visit my new faculty profile page.

I do research in representation theory of quivers, and its relationship to differential and symplectic topology. The main goal of my research is to find connections between different fields of mathematics and to give conceptual interpretations of these connections. For example, the algebra which categorifies the grassmannian appears in the calculation which proves that Legendrian knots coming from circle bundles over surfaces are not contact isotopic to their mirror images. (joint paper with Dani Alvarez-Gavela.) This also had a surprising application to representation theory: It lead to a counterexample of the phi-dimension conjecture (joint work with former grad student Eric Hanson). I often teach advanced graduate courses in Algebra and Topology. And I like to use each field to understand the other. Webpage

Courses Taught

MATH	28b	Introduction to Rings and Fields
MATH	47a	Introduction to Mathematical Research
MATH	131b	Algebra II
MATH	151a	Topology I
MATH	221a	Topology III: Vector Bundles and Applications
MATH	250b	Complex Algebraic Geometry II

Awards and Honors

Fellow of the American Mathematical Society (2012)

Sloan Fellowship (1981 - 1983)

Scholarship

Hanson, Eric and Igusa, Kiyoshi. "Pairwise compatibility for the 2-simple minded collections of gentle algebras." Journal of Pure and Applied Algebra 225. 6 (2021).

Igusa, Kiyoshi and Schiffler, Ralf. "Frieze varieties are invariant under Coxeter mutation." Contemporary Mathematics 761. (2021): 103-116.

Igusa, Kiyoshi and Todorov, Gordana. "Picture groups and maximal green sequences." Electronic Research Archive (2021): <doi: 10.3934/era.2021025.>.

Igusa, Kiyoshi. "A Legendrian Turaev torsion via generating families." Journal de l'École polytechnique - Mathematics 8. (2021): 57-119.

Eric Hanson and Kiyoshi Igusa. "Resolution quiver and cyclic homology criteria for Nakayama algebras." Journal of Algebra 553. 1 (2020): 138-153.

Igusa, Kiyoshi. "Continuously triangulating the continuous cluster category." Topology and its Applications 285. 1 (2020).

Igusa, Kiyoshi. "Linearity of stability conditions." Communications in Algebra 48. 4 (2020): 1671-1696.

Garver, Al, Igusa, Kiyoshi, Mathern, Jacob, Ostroff, Jonah. "Combinatorics of exceptional sequences of type A." The Electronic Journal of Combinatorics 26. 1 (2019): <https://www.combinatorics.org/ojs/index.php/eljc/article/view/v26i1p20>.

Igusa, Kiyoshi and Apruzzese, P.J.. "Stability conditions for affine type A." Algebra and Representation Theory (2019).

Igusa, Kiyoshi, Todorov, Gordana. "Cyclic posets and triangulation clusters." Science China Math 62. 7 (2019): 1289–1316.

Kiyoshi Igusa. "Maximal green sequences for cluster-tilted algebras of finite representation type." Algebraic Combinatorics 2. 5 (2019): 753-780.

Igusa, Kiyoshi, Hermes, Stephen. "The No Gap Conjecture for tame hereditary algebras." Journal of Pure and Applied Algebra 223. 3 (2018): 1040–1053..

Igusa, Kiyoshi. "Horizontal and vertical mutation fans." Science China Mathematics 61. (2018): 1-22.

Brustle, Thomas, Hermes, Stephen, Igusa, Kiyoshi and Todorov, Gordana. "Semi-invariant pictures and two conjectures on maximal green sequences." Journal of Algebra 472. 1 (2017): 80-109.

Igusa, Kiyoshi and Ostroff, Jonah. "Mixed Cobinary Trees." Journal of Algebra and Its Applications (2017).

Goodwillie, Thomas, Igusa, Kiyoshi and Ohrt, Chris. "An Equivariant Version of Hatcher's G/O Construction." Journal of Topology 8. 3 (2015): 675-690.

Igusa, Kiyoshi and Todorov, Gordana. "Cluster categories coming from cyclic posets." Communications in Algebra 43. 10 (2015): 4367-4402.

Igusa, Kiyoshi and Todorov, Gordana. "Continuous cluster categories." Algebra and Representation Theory 2015. 18 (2015): 65–101.

Kiyoshi Igusa and Gordana Todorov. Continuous Frobenius categories. Proc. of Abel Symposium 2011. Trondheim, Norway: Springer, 2014.

Sebastian Goette and Kiyoshi Igusa. "Exotic smooth structures on topological fiber bundles II." Transactions of AMS 366. 2 (2014): 791-832.

Igusa, Kiyoshi, Cesar P. Milies, Ed.. Exceptional sequences, braid groups and clusters. Proc. of XVIII Latin-American Algebra Colloquium. Sao Pedro, Brazil: Contemporary Mathematics, 2011.

Igusa, Kiyoshi. "Twisting cochains and higher torsion." Journal of Homotopy and Related Structures 6. 2 (2011): 213-238.

Kiyoshi Igusa, Shiping Liu and Charles Paquette. "A proof of the strong no loop conjecture." Advances in Mathematics 228 (2011): 2731-2742.

Igusa, Kiyoshi and Schiffler, Ralf. "Exceptional sequences and clusters." Journal of Algebra 323. no. 8 (2010): 2183--2202.

Igusa, Kiyoshi; Orr, Kent; Todorov, Gordana; Weyman, Jerzy. "Cluster complexes via semi-invariants." Compositio Mathematica 145. no 4 (2009): 1001--1034.

Igusa, Kiyoshi. "Axioms for higher torsion invariants of smooth bundles." Journal of Topology 1. 1 (2008): 159-186.

Igusa,Kiyoshi. "Higher Franz-Reidemeister torsion." AMS/IP Studies in Advanced Mathematics 31. (2002).