Summer Graduate School

The Whitney Umbrella. Courtesy of Herwig Hauser, Fac. Math., University of Vienna, Austria

The school will introduce students to the fundamental problem of resolution of singularities of varieties and schemes. This is a subject that is relevant for all areas of algebraic geometry and commutative algebra. Students will learn algorithms to resolve singularities, and learn how to apply them in specific situations and understand how these techniques can be used in their research.

School Structure

There will be two lectures series, one taught by Ana Bravo in the morning with a problem session directed by Beatriz Pascual and the other taught by Dale Cutkosky in the afternoon, with a problem session directed by Stephen Landsittel.

Prerequisites

Students should be familiar with basic commutative algebra, such as is covered in the book “Introduction to Commutative Algebra” by Atiyah and MacDonald. They should have some knowledge of Algebraic Geometry, including familiarity with affine and projective varieties and the morphisms between them, and the blow up of an ideal or ideal sheaf. Some references on this material are Chapters 2 -6 and Sections 10.1 - 10.4 of “Introduction to Algebraic Geometry” by Steven Dale Cutkosky, or Section 1, basic notions and Section 2, local properties from Shafarevich’s “Basic Algebraic Geometry 1”, or an a more sophisticated level, Chapters I and II of Hartshorne’s “Algebraic Geometry”.

Application Procedure

SLMath is only able to support a limited number of students to attend this school.  Therefore, it is likely that only one student per institution will be funded by SLMath.

For eligibility and how to apply, see the Summer Graduate Schools homepage.

Venue

Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), University of Tokyo, Japan.