| Title: | Using Geometry to do Number Theory |
| Speaker: | Mckenzie West Visiting Assistant Professor Math Department Kalamazoo College Kalamazoo, MI |
| Abstract: | Polynomial equations and their solutions form a cornerstone of mathematics. Solutions with rational coordinates are particularly intriguing; a fantastic surprise is the great difficulty of determining the mere existence of a rational solution to a given equation (let alone the complete set). We will discuss this problem in two cases, diagonal cubic surfaces, \[ax^3+by^3+cz^3+d=0,\] and degree 2 del Pezzo surfaces, \[ax^4+by^4+cx^2y^2+d=z^2.\] A surprising and successful modern approach, the Brauer--Manin obstruction, employs tools from linear algebra, geometry and non-commutative algebra. I will discuss a collection of interesting and motivating examples with simultaneous historical and modern interest, and also explain some of the tools and techniques that form the backbone of my research program. |
| Location: | Palenske 227 |
| Date: | 2/15/2018 |
| Time: | 3:30 PM |
@abstract{MCS:Colloquium:MckenzieWest:2018:2:15,
author = "{Mckenzie West}",
title = "{Using Geometry to do Number Theory}",
address = "{Albion College Mathematics and Computer Science Colloquium}",
month = "{15 February}",
year = "{2018}"
}