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Friday, October 20, 2017 — 3:30 PM EDT

**Title:** The Paulsen problem, continuous operator scaling, and smoothed analysis

Speaker: | Tsz Chiu Kwok |

Affiliation: | University of Waterloo |

Room: | MC 5501 |

**Abstract:**

The Paulsen problem is a basic open problem in operator theory: Given vectors u_{1,} ..., u_{n} in R^{d} that are eps-nearly satisfying the Parseval's condition and the equal norm condition, is it close to a set of vectors v_{1,} ..., v_{n} in R^{d} that exactly satisfy the Parseval's condition and the

equal norm condition? Given u_{1,...,} u_{n}, we consider the squared distance to the set of exact solutions.

Thursday, October 19, 2017 — 3:30 PM EDT

**Title:** Sequences: random, structured or something in between?

Speaker: | Fan Chung Graham |

Affiliation: |
University of California, San Diego |

Room: | MC 5501 |

**Abstract:**

There are many fundamental problems concerning sequences that arise in many areas of mathematics and computation. Typical problems include finding or avoiding patterns; testing or validating various `random-like’ behavior; analyzing or comparing different statistics, etc.

Thursday, October 12, 2017 — 3:30 PM EDT

**Title:** A Short Introduction to Projective Geometry

Speaker: | Chris Godsil |

Affiliation: | University of Waterloo |

Room: | MC 6486 |

**Abstract:**

Basically, see the title. I will be considering the real and complex cases mainly, because that is

what is needed in quantum physics.

Friday, October 6, 2017 — 3:30 PM EDT

**Title:** Enumeration in quantum algebras

Speaker: | Jason Bell |

Affiliation: | University of Waterloo |

Room: | MC 5501 |

**Abstract:**

Many of the classical algebras that occur in algebraic geometry and other mathematical fields have natural quantizations; that is, one can deform the multiplication rule using a parameter *q*, which has the property that when we specialize *q* at 1 we recover the classical object. As part of the general goal of understanding the representation theory of these rings, one often wants to understand the prime spectra of these algebras, that is, the collection of prime ideals in these rigs.

Thursday, October 5, 2017 — 3:30 PM EDT

**Title:** RSKy Business

Speaker: | Nathan Lindzey |

Affiliation: | University of Waterloo |

Room: | MC 6486 |

**Abstract:**

We sketch the Robinson-Schensted-Knuth algorithm, then use it to glimpse into the representation theory of some classical combinatorial objects.

Thursday, October 5, 2017 — 3:30 PM EDT

**Title:** The 8-connected excluded minors for the class of quasi-graphic matroids

Speaker: | Rong Chen |

Affiliation: | Fuzhou University |

Room: | MC 5479 |

**Abstract:**

The class of quasi-graphic matroids, recently introduced by Geelen, Gerards, and Whittle, is minor closed and contains both lifted-graphic matroids and frame matroids, each of which generalises the class of graphic matroids.

Wednesday, October 4, 2017 — 4:30 PM EDT

**Title:** I'll prove the Fundamental Theorem of Algebra

Speaker: | Sam Kim |

Affiliation: | Department of Pure Math, University of Waterloo |

Room: | MC 5501 |

**Abstract:**

Gauss proved that complex polynomials always admit a root. I'll explain how he came to that conclusion and present a proof that rigorizes his argument in a nice way. You will only need to know a little vector calculus and the intermediate value theorem.

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