# Kiyoshi Igusa

Degrees

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

Expertise

Representation theory, TopologyProfile

I do research in representation theory of quivers, which can be viewed as advance linear algebra, and its relationship to topology. The main goal of my research is to find connections between different fields of mathematics. I teach advanced graduate courses in Algebra, Topology and I have also taught Mathematical Statistics and Stochastic Processes. WebpageCourses Taught

MATH | 22a | Linear Algebra and Intermediate Calculus, Part I |

MATH | 22b | Linear Algebra and Intermediate Calculus, Part II |

MATH | 23b | Introduction to Proofs |

MATH | 30a | Introduction to Algebra, Part I |

MATH | 104a | Introduction to Topology |

MATH | 200a | Second-Year Seminar |

MATH | 202a | Algebraic Geometry I |

MATH | 205b | Commutative Algebra |

MATH | 223a | Lie Algebras |

Awards and Honors

Fellow of the American Mathematical Society (2012)

Sloan Fellowship (1981 - 1983)

Scholarship

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.

Sebastian Goette, Kiyoshi Igusa and Bruce Williams. "Exotic smooth structures on topological fiber bundles I." __Transactions of AMS__ 366. 2 (2014): 749-790.

Ibrahim Assem, Juan Carlos Bustamante, Kiyoshi Igusa and Ralf Schiffler. "The first Hochschild cohomology group of a cluster-tilted algebra revisited." __International Journal of Algebra and Computation__ 23. 4 (2013): 729-744.

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.