Rationality problems

Algebraic geometry is the study of algebraic varieties, geometric shapes that arise as solution sets to systems of polynomial equations. Algebraic geometry is a subject of central importance in contemporary mathematics, with multiple connections to other areas, such as number theory, combinatorics, representation theory, analysis, and theoretical physics. The simplest algebraic varieties are rational varieties. Informally speaking, these are varieties that admit a parametric presentation. A solid understanding of rational varieties is important both for theoretical purposes and for applications. The question of whether a specific variety is rational can be very difficult to answer. Questions of this type are called rationality problems. In this project I propose to try to answer questions in this area. Spending a semester at Universite Paris Sud, being mentored by Professor J.-L. Colliot-Thelene, and learning from some of the leading mathematicians in the field is an exceptional and unique opportunity.

Faculty Supervisor:

Zinovy Reichstein

Student:

Partner:

Université Paris Saclay

Discipline:

Mathematics

Sector:

Other

University:

The University of British Columbia

Program: