Geometry

Description

The School is aimed at students that have completed at least two years of undergraduate studies in Mathematics and therefore have a basic background in algebra, analysis and topology. Physics students with this basic knowledge of mathematics are also welcome to apply. Geometry is understood in a broad sense: the courses will touch on algebraic geometry, differential geometry, and algebraic topology, and will highlight interactions with fields like number theory, group theory and mathematical physics.

The Summer School on Geometry is organised by the Utrecht Geometry Centre (UGC), which encompasses all the research groups on fundamental mathematics within the Mathematical Institute of Utrecht University. The mini-courses offered during the School are thus a reflection of the research directions pursued at UGC.

Each day of the programme will be dedicated to a concrete topic. This will involve, roughly, four lectures of 45 minutes as well as two exercise sessions of 90 minutes each.

Target audience

Mathematics students with at least two years of mathematics at bachelor's level, including basic (abstract) algebra (groups and rings), (mathematical) analysis in several variables, linear algebra and point-set topology. Physics students with this basic knowledge of mathematics are also welcome to apply. Students from universities in The Netherlands, including Utrecht University, and from universities elsewhere, are welcome to apply.

Aim of the course

Each day of the School aims to cover a different facet of modern Geometry. Topics covered in previous years include: Algebraic Geometry, Arithmetic Geometry, Differential Topology, Algebraic Topology, Symplectic Geometry, Complex Geometry, Number Theory, Lie Theory, Logic, and applications to Physics.

Study load

Lectures and exercise sessions in the morning and afternoon (09.00 to 17.00 hours, including lunch and other breaks).