Calendar

Oct
3
Mon
Colloquium: Ken Ono
Oct 3 @ 3:30 pm – 4:30 pm
Oct
12
Wed
Logic seminar: Manabu Hagiwara (Chiba University)
Oct 12 @ 3:00 pm – 4:00 pm

Keller 403

Nov
16
Wed
Logic seminar: Kazuhisa Nakasho (Yamaguchi University)
Nov 16 @ 3:00 pm – 4:00 pm

<p>Title: Formalization of multivariable calculus in Mizar</p>

Abstract:

<p>In this presentation, I will report on the progress of the
formalization of multivariable calculus in Mizar. We are now formalizing
multivariable calculus with the aim of formalizing differential
manifolds, partial differential equations, and numerical analysis. In
the formalization of multivariable calculus, the handling of
higher-order partial derivatives tends to be more troublesome than in
the one variable case, but this can be alleviated somewhat by
introducing the Fréchet derivative in Banach space. I would like to give
an overview of the Mizar project and discuss topics ranging from the
definition of higher-order partial derivatives in normed spaces to
formalization of the implicit and inverse function theorems.</p>

Dec
7
Wed
Logic seminar: Daniel Erman
Dec 7 @ 3:00 pm – 4:00 pm

Speaker: Daniel Erman (University of Wisconsin)
Title: Ultraproducts, Hilbert’s Syzygy Theorem, and Stillman’s
Conjecture
When and where: 3-3:50pm, December 7, in Keller 403

Abstract: Hilbert’s Syzygy Theorem is a classic finiteness result about
a construction in algebra known as a free resolution. Stillman once
proposed an analogue of Hilbert’s result, which involved potentially
considering polynomials in infinitely many variables. Stillman’s
Conjecture was recently solved, and perhaps the simplest proof is based
upon a novel use of an ultraproduct. I’ll give an expository overview
of the history of Stillman’s Conjecture (very little algebraic
background will be assumed), and then explain how and why ultra products
came to play such a key role.

Jan
9
Mon
First Day of Instruction
Jan 9 all-day
May
3
Wed
Last day of instruction
May 3 all-day