All talks are at 4:15 in HH231 unless otherwise noted.
To volunteer to give a talk, or for anything else regarding the seminar, contact Megan Patnott.
Date | Speaker | Title |
---|---|---|
Monday, September 7 | Liviu Nicolaescu | Knots and their curvatures |
Monday, September 21 | Megan Patnott | An Introduction to Using Beamer |
Monday, October 5 | Sarah Cotter | Variations on a theme of Helly |
Cancelled due to illness | ||
Monday, November 9 | Bernadette Boyle | Cayley-Bacharach Theorem through the ages |
Monday, November 23 | David Karapetyan | On the Uniqueness of Solutions to the Burgers Equation in Sobolev Spaces |
Monday, December 7 | Brandon Rowekamp | Uniform Distributions Modulo 1 |
Monday, February 1 | MGSA meeting: discussion of departmental changes | |
Monday, February 15 | Katie Grayshan | General Abstract n-sense |
Monday, March 1 | Martha Precup | Counting Nilpotent Ideals of a Borel Subalgebra |
Monday, March 15 | John Engbers | Conway's Solitaire Army Problem |
Monday, March 29 | Jesse Johnson | We're All Mad Here: The Mathematics of Lewis Carroll |
Monday, April 12 | Stephen Flood | What can logic teach us about theorems of ordinary mathematics? |
Monday, April 26 | Don Brower | Independence Relations |
Surprisingly, very little mathematics beyond geometric series is needed, which should be a welcome respite at the end of the first day post-Spring Break.
(See abstract as pdf.)In algebra, we learn every field K has an algebraic closure F. Furthermore, we learn that K is isomorphic to a sub-field of F. Given a computable field, how complicated is F? How complicated is the isomorphic image I of K in F? If F is computable and I is not computable, then more proof-power is needed to produce I than to produce F. If we know that some I must exist, we can prove the existence of certain non-computable sets. In doing this, we have 'reversed' our proof, using the theorem of algebra to proving our set existence 'proof rule'.
In reverse mathematics, we prove and organize this type of result using subsystems of second order arithmetic. Second order arithmetic is a system of formal logic where we can quantify over numbers and sets and do basic arithmetic. By using the close connections that many subsystems of second order arithmetic have to computability theory, we learn more about the computational complexity of standard theorems. This talk will introduce the tools, goals, and practice of reverse mathematics, with examples.
No background in logic, algebra, or arithmetic is assumed.