# Kiyoshi Igusa

Degrees

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

Expertise

Representation theory, Homological Algebra, Algebraic TopologyProfile

I do research in representation theory of quivers, and its relationship to topology.he main goal of my research is to find connections between different fields of mathematics. For example, I apply concepts from Physics (string theory) to algebra. For example the mutation formula used in algebra was first discovered by Seiberg and was called ``Seiberg duality''. 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 | 39a | Introduction to Combinatorics |

MATH | 104a | Introduction to Topology |

MATH | 200a | Second-Year Seminar |

MATH | 202a | Algebraic Geometry I |

MATH | 223a | Lie Algebras |

MATH | 250b | Complex Algebraic Geometry II |

Awards and Honors

Fellow of the American Mathematical Society (2012)

Sloan Fellowship (1981 - 1983)

Scholarship

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.

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.