# Francesco Galuppi: Enumerative geometry

**Lecturer:**Francesco Galuppi**Date:**Wednesday 09:30 - 11:00 and Thursday 13:30 - 15:00**Room:**MPI MiS, G3 10**Language:**English**Target audience:**MSc students, PhD students, Postdocs**Keywords:**Algebraic geometry, 27 lines, 3264 conics, intersection theory**Prerequisites:**An undergraduate course on algebraic geometry. Enthusiasm about doing exercises and about teamwork are very welcome.

## Abstract

We all know that there is exactly 1 conic through 5 general points in the plane, but as soon as we ask how many conics are tangent to 5 given smooth conics the answer is somewhat less obvious. This kind of enumerative questions has been considered since the ancient times.

Enumerative geometry is a great playground and provides plenty of concrete problems to work with, but is sometimes left out of a basic course on algebraic geometry. This reading group aims to fill the gap. We will study how to precisely formulate enumerative questions and how to use intersection theory to find the answers.

While doing that, we will incidentally learn a lot of geometry and bump into key concepts such as Chow rings, Schubert calculus, Grassmanians, Hilbert schemes and Chern classes.

## Regular Lectures (Summer 2019)

**Artiﬁcial Neural Networks and Machine Learning: Theoretical Foundations II**- Nihat Ay
- Thursday, 11:15 - 12:45, MPI MiS A3 01

**Embedding theorems in complex geometry**- Judith Brinkschulte
- Tuesday, 11:15 - 12:45, University Augusteum A-314

**Continuum Mechanics**- Jan Burczak
- Wednesday, 9:15 - 10:45 and Friday, 9:15 - 10:45, University Augusteum A-314

**Modern Algebraic Geometry**- Claus Diem
- Monday, 11:15 - 12:45, University SG 3-13 and Friday, 13:15 - 14.45, University Augusteum A-314

**Introduction to Computer Algebra**- Christian Eder
- Wednesday 13:15 - 14:45, University HS-19 and Thursday 9:15 - 10:45, University SG 3-20

**Enumerative geometry**- Francesco Galuppi
- Wednesday, 09:30 - 11:00, and Thursday, 13:30 - 15:00, MPI MiS G3 10

**Stochastic variational inequalities**- Benjamin Gess
- Monday, 16:15 - 17:45, MPI MiS A3 01

**Schemes and Sheaves**- Jürgen Jost
- Monday, 13:30 - 15:00, MPI MiS A3 01

**Information and Complexity**- Jürgen Jost
- Friday, 13:30 - 15:00, MPI MiS A3 02

**Randomness in PDE–selected topics**- Felix Otto
- Thursday, 9:15 - 10:45, MPI MiS A3 01, starting May 16

**Category theory and applications**- Paolo Perrone
- Wednesday, 11:00 - 12:30, MPI MiS A3 02

**Introduction to Microlocal Analysis**- Angkana Rüland
- Thursday, 11:15 - 12:45, University, SG 311

**Introduction to percolation theory**- Artem Sapozhnikov
- Thursday, 13:15 - 14:45, University, Augusteum A 314

**Hodge Theory and Periods of Varieties**- Emre Sertöz
- May 6 - 10, MPI MiS G3 10, details see extra page

**Introduction to D-modules**- Christian Sevenheck
- Friday, 11:00 - 12:30, MPI MiS G3 10

**Invitation to Nonlinear Algebra**- Mateusz Michałek, Bernd Sturmfels
- June 4 - 14, MPI MiS, details see extra page

**Population Dynamics**- Florian Völlering
- Wednesday and Friday 9:00 - 11:00, University, SG 3-13

**IMPRS-Ringvorlesung**- Felix Otto, Peter Stadler (lectures), Tobias Ried (exercises)
- Lectures: Tuesday, 10:15 - 11:45, MPI MiS G3 10
- Exercises: Thursday, 15:30 - 17:00 (at 04.04.: 13:00 - 14:00), MPI MiS G3 10