* The Graduate Colloquium* is a colloquium-style series for mathematics graduate students to share their current ideas with the rest of their colleagues. Interspersed within are talks and panels focused on career development.

Date | Speaker | Title |
---|---|---|

Wednesday Aug 23 |
Panel | Q & A with Current Graduate Students locationLeConte 412 @ 11am-1pm |

Tuesday Sept 5 |
Alex Duncan | Hilbert's 13th Problem locationLeConte 412 @ 4:30pm-5:30pm |

Tuesday Sept 12 |
Hays Whitlatch | Phylogeny, Pressing Sequences and Bill Gates' Burnt Pancakes: What do they have in common? locationLeConte 412 @ 4:30pm-5:30pm |

Tuesday Sept 19 |
Panel | The Academic Job Search locationLeConte 412 @ 4:30pm-5:30pm |

Tuesday Sept 26 |
Duncan Wright | TBA locationLeConte 412 @ 4:30pm-5:30pm |

Tuesday Oct 3 |
Zhiyu Wang | Erdős-Szekeres Theorem for Cyclic Permutations locationLeConte 412 @ 4:30pm-5:30pm |

Tuesday Oct 10 |
Josiah Reiswig | Aphid Sequences: Turning Fibonacci Numbers Inside Out |

Tuesday Oct 17 |
Robert Vandermolen | TBA |

Tuesday Oct 24 |
Frank Thorne | The Distribution of the Primes |

Tuesday Oct 31 |
Keller Vandebogert | Classification of Elementary Particles via Symplectic Induction |

Tuesday Nov 7 |
Andy Kustin | Syzygies |

Tuesday Nov 14 |
Alicia Lamarche | Toric Varieties |

Tuesday Nov 21 |
TBA | TBA |

Tuesday Nov 28 |
TBA | TBA |

Tuesday Dec 5 |
TBA | TBA |

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** Panel -- ** Q & A with Current Graduate Students

An open and wide-ranging discussion of the mathematics graduate program at USC led by experienced graduate students and young faculty members.

** Alex Duncan -- ** Hilbert's 13th Problem

The highlight of the standard algebra sequence is the
Abel-Ruffini Theorem, which states that there is no solution in radicals
to a general polynomial equation of degree 5 or greater.
This is not the end of the story, though.
There are many other types of functions besides radicals.
When can equations be solved using more general classes of functions?

David Hilbert, in his 1900 Paris lecture, famously outlined 23 problems
as a challenge to mathematicians for the twentieth century.
His 13th problem asked if there was a solution to a degree 7 polynomial
using only functions of two variables.
Unfortunately, Hilbert was vague about exactly what kind of functions
were allowed --- the answer depends on what kind of mathematician
you are!

In this talk I will explore whether and how we can solve polynomials
of various degrees using assorted kinds of functions.

** Hays Whitlatch -- ** Phylogeny, Pressing Sequences and Bill Gates' Burnt Pancakes: What do they have in common?

** Panel -- ** The Academic Job Search

** Zhiyu Wang -- ** Erdős-Szekeres Theorem for Cyclic Permutations

** Josiah Reiswig -- ** Aphid Sequences: Turning Fibonacci Numbers Inside Out

** Frank Thorne -- ** The Distribution of the Primes

I will explain at least two things in my talk: (1) why such results were firmly expected, long before they were proved, and (2) the first step in any such proof, a "level of distribution" result for the primes: what this means, and why it opens doors for clever people like those listed above.

This talk will be an advertisement for a graduate course on the subject which I plan to teach here, and an accompanying book which I will be writing with Robert Lemke Oliver.

**Keller Vandebogert --** Classification of Elementary Particles via Symplectic Induction

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