# Summer 2023

## Introduction to tropical geometry

**Lecturer:**Alheydis Geiger**Date:**Monday and Tuesday 9-11**Room:**MPI MiS G3 10**Keywords:**tropical geometry, polyhedral geometry, algebraic geometry, applications**Prerequisites:**Linear Algebra, knowledge about algebraic geometry (especially varieties) is helpful, but not necessary.**Remarks:**Homepage for the lecture is: https://sites.google.com/view/tropicalgeometry2023

## Abstract

This lecture course features an introduction to tropical geometry, including the necessary parts of polyhedral and convex geometry. This course is meant to bridge the pure-mathematical view of tropical geometry towards a more computational and applied perspective. For this we will use mathematical software in exercises and examples, and, additionally, in the last few weeks, we will consider tropical geometry in the context of neural networks and/or extreme value statistics. During this course exercises will be handed out, which will include computing examples using the software package OSCAR in Julia. It is recommended to install these before the course. Installation instructions can be found here. The lecture course is also open for students from Leipzig University.To keep informed about changes to this lecture subscribe to lecture mailinglist

## Algebraic Geometry II -- Intersection Theory

**Lecturer:**Rainer Sinn**Date:**Montags von 11 bis 13 Uhr und Donnerstags von 15 bis 17 Uhr (tentative)**Room:**Montags in SG 3-12 und Donnerstags in SG 2-14**Keywords:**intersection theory: line bundles and divisors, Chow rings (in particular of Grassmannians), Chern classes, projective bundles, Segre classes**Prerequisites:**Basic notions in algebraic geometry (affine/projective variety, morphism, dimension, Grassmannian)

To keep informed about changes to this lecture subscribe to lecture mailinglist

## Algebraic Methods in Combinatorics

**Lecturer:**Raul Penaguiao**Date:**Wednesday, 9am - 11am**Room:**Raum SG 2-14**Keywords:**graph theory, convex geometry, extremal combinatorics, ham sandwich theorem**Prerequisites:**Abstract algebra, linear algebra**Remarks:**There is more info at: https://sites.google.com/view/amc-2023/home

## Abstract

Combinatorics using some algebraic constructions. We use dimension arguments to get bounds on interesting combinatorial numbers. We study the eigenvalues of adjacency matrices on graphs to get information about graphs at hand. This has great applications in the so called extremal combinatorics. In combinatorial geometry we will be studying combinatorial identities and inequalities that relate to point sets and polytopes. For instance, how many points in R^d can you find such that the distance between any two of them is one of two given real numbers? We will find bounds for these quantities using linear algebra. Finally, we will be studying spectral theory on graphs. This has some interesting combinatorial consequences on graph properties.To keep informed about changes to this lecture subscribe to lecture mailinglist

## Number Theory meets Tropical Geometry

**Lecturer:**Sachi Hashimoto**Date:**April 14, 2-3pm, April 17 - 20 2pm - 5pm, April 21 10am - 12pm**Room:**MPI MiS G3 10**Keywords:**Tropical Geometry, Number Theory, Semistable Models, Berkovich Spaces**Additional information:**See the file or external link

## Abstract

April 14, 2-3pm: Preliminary lecture with background on semistable reduction, number theory, tropical geometry April 17 - 20 2pm - 5pm, April 21 10am - 12pm: 1 hr lecture, break, then computational working session Lecture topics TBATo keep informed about changes to this lecture subscribe to lecture mailinglist

## Let’s get \(\mathbb{R}\)eal

**Lecturer:**Chiara Meroni**Date:**June 7 and 8**Room:**MPI MiS G3 10

## Abstract

This 2-days event is dedicate to real algebraic geometry, and related areas. We will learn what a real closed field and a real variety are, we will play with semialgebraic sets, and explore many applications, including convex geometry and optimization. There will be lectures and exercise sessions, as well as time for questions and discussions.To keep informed about changes to this lecture subscribe to lecture mailinglist