# Kiyoshi Igusa

Degrees

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

Expertise

Representation theory, Homological Algebra, Algebraic Topology, Differential TopologyProfile

I do research in representation theory of quivers, and its relationship to 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. I often teach advanced graduate courses in Algebra and Topology. And I like to use each field to understand the other. WebpageCourses Taught

MATH | 28b | Introduction to Rings and Fields |

MATH | 39a | Introduction to Combinatorics |

MATH | 47a | Introduction to Mathematical Research |

MATH | 100b | Introduction to Algebra, Part II |

MATH | 131b | Algebra II |

MATH | 151a | Topology I |

MATH | 200a | Second-Year Seminar |

MATH | 202a | Algebraic Geometry I |

MATH | 250b | Complex Algebraic Geometry II |

Awards and Honors

Fellow of the American Mathematical Society (2012)

Sloan Fellowship (1981 - 1983)

Scholarship

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, Hermes, Stephen. "The No Gap Conjecture for tame hereditary algebras." __Journal of Pure and Applied Algebra__ 223. 3 (2019): 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. "Higher Franz-Reidemeister torsion." __AMS/IP Studies in Advanced Mathematics__ 31. (2002).