# 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, I am currently trying to compute the cohomology of "picture groups" by studying the combinatorics of the "picture space" which Eric Hanson is working to verify that this is a K(pi,1) as expected so that this is the correct method of calculation. I often teach advanced graduate courses in Algebra and Topology. WebpageCourses Taught

MATH | 28b | Introduction to Rings and Fields |

MATH | 39a | Introduction to Combinatorics |

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

MATH | 104a | Introduction to Topology |

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

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).