Summer Graduate School

This two week school on Noncommutative Algebraic Geomery will be held at the University of Antwerp in Belgium.  The school will consist of two courses: Homological Mirror Symmetry and Algebraic Models for Spaces. These courses will be planned and taught by organisers with the help of teaching assistants for the problem sessions. The school will be aimed at a wide range of graduate students, from students with a Bachelor degree to beginning PhD students. The lectures and problem sessions will be complemented by a poster session in week one and a total of four introductory research talks on Friday afternoons. 

School Structure

Most days will consist of two lectures and two problem sessions.  A poster session and reception will be held on the first Tuesday.  On Friday afternoons, there will be research seminars with two one-hour talks.

Prerequisites

In the following list, items marked with (*) constitute optional, more advanced study material, which will be recalled during the courses when used. 
• Tensor product, eg. Sections 1 - 5 of https://kconrad.math.uconn.edu/blurbs/linmultialg/tensorprod.pdf 

• Basic category theory, eg. Sections 1.1 - 1.6 and 2.1, 2.2 of https://math.jhu.edu/ eriehl/context.pdf 

• Algebraic Topology - Allen Hatcher: 

– Chapter 0: Introduction + Homotopy and Homotopy Type + Cell Complexes 
– Chapter 1: Introduction and 1.1: Paths and Homotopy

* Chapter 1: The Fundamental Group of the Circle + Induced Homomorphisms 

– Chapter 2: Introduction and 2.1: ∆-complexes 

* Chapter 2: Simplicial Homology + Singular Homology + Homotopy Invariance 

• An elementary illustrated introduction to simplicial sets - Greg Friedman: https://arxiv.org/pdf/0809.4221.pdf 

– Section 2: A build-up to simplicial sets 

* Section 3: Simplicial sets and morphisms 

• An Introduction to Homological Algebra - Charles A. Weibel: Chapter 1: 1.1 Complexes of R-Modules + 1.2 Operations on Chain Complexes + 1.3 Long Exact Sequences + 1.4 Chain Homotopies 

• Algebraic Geometry - Robin Hartshorne: 

– Chapter II, 1. Sheaves + 2. Schemes + 5. Sheaves of modules 
– Chapter III, 1. Derived Functors + 2. Cohomology of sheaves 

* Chapter III, 3. Cohomology of Noetherian Affine schemes + 4. Cech Cohomology + 5. The Cohomology of Projective Space

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

Lectures will take place at the Middelheim Campus of the University of Antwerp. Students will be housed near the campus.