Algebraic Geometry - Summer School

Gulbenkian Foundation, LISBON — 14 to 18 JULY 2014



sketch for the panel Começar by José de Almada Negreiros - image reproduced with kind permission of the Gulbenkian Foundation

Program

This school comprises three 5-lecture courses (in English) aimed at 1st- or 2nd-year undergraduate students of mathematics, complemented by problem sessions.

Courses

Plane algebraic curves

by Carolina ARAUJO (IMPA)

Abstract: These lectures provide an introduction to the classical theory of plane algebraic curves. After discussing some basic notions, such as affine and projective plane curves, singular points, tangent lines and inflection points, we will turn our attention to Bézout's theorem, which counts the number of intersection points of two projective plane curves. We will also investigate properties of dual curves, and use Bézout's theorem to establish the classical Plücker formulae, relating invariants of a projective plane curve with those of its dual curve.


Enumerative geometry of linear spaces and quadrics

by Izzet COSKUN (University of Illinois, Chicago)

Abstract: In these lectures, I will introduce several examples of parameter spaces such as Grassmannians and spaces of quadrics. I will develop the beginnings of intersection theory to solve several classical enumerative geometry problems such as: How many lines intersect 4 general lines in space? How many conics intersect 8 general lines in space?


What is algebraic geometry?

by Lucia CAPORASO (University of Rome: Roma Tre)

Abstract: The purpose of these lectures is to introduce the most basic notions and tools of complex algebraic geometry: Algebraic sets given by polynomial equations in affine and projective spaces; Hilbert's Nullstellensatz and the Zariski topology; Algebraic curves, Riemann surfaces an branched coverings of a line.
Useful background: Abstract algebra (rings and fields) and point set topology.

Schedule

The opening of the school will be in Auditório 3 at 9.30 on Monday with the presence of
  • Representative of the Ministry of Education and Science of Portugal
  • Eduardo Marçal Grilo (Member of the Board of Directors of the Gulbenkian Foundation)
  • Orlando Neto (Member of the Scientific Committee of the Program "Novos Talentos em Matemática")
Monday, July 14 Tuesday, July 15 Wednesday, July 16 Thursday, July 17 Friday, July 18
9:30-10:00 opening
10:00-11:00 L. CAPORASO L. CAPORASO C. ARAUJO I. COSKUN L. CAPORASO
11:00-11:30 coffee break coffee break coffee break coffee break coffee break
11:30-12:30 I. COSKUN L. CAPORASO C. ARAUJO I. COSKUN I. COSKUN
12:30-14:00 lunch break lunch break L. CAPORASO
(until 13.30) 		lunch break lunch break
14:00-15:00 C. ARAUJO I. COSKUN C. ARAUJO C. ARAUJO
15:00-15:30 coffee break coffee break coffee break coffee break
15:30-17:00 PROBLEM SESSION PROBLEM SESSION PROBLEM SESSION PROBLEM SESSION

Friday, July 18th at 17h30, after the problem session, there will be a meeting in Auditório 3 where the participants will be able to talk to the lecturers about academic life in a relaxed setting.

Afterwards, there will be a dinner at 8.30pm at Restaurante d'Bacalhau at Parque das Nações. Here are instructions on how to get to the restaurant from the school venue.

Mini-conference

On Saturday, July 19th, there will be a student mini-conference at the Gulbenkian Foundation which will include a talk by Prof. Coskun.
All school participants are invited to attend this mini-conference. Here is the schedule of the mini-conference.

Venue

The school takes place in the headquarters of the Gulbenkian Foundation (Avenida de Berna, Lisbon), with lectures and problem sessions in Sala 1, with exception of the opening which will take place in Auditório 3.