# Kiyoshi Igusa

Degrees

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

Expertise

Representation theory, Homological Algebra, Algebraic Topology, Differential TopologyProfile

**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).