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Course format and Information
Course format and Information
Lecturer: Alheydis Geiger
Format: two 90 min lectures each week (15 weeks)
Time: 9-11 a.m. Monday & Tuesday
Location: at MPI MiS (Inselstr. 22, Leipzig, room G310)
Duration: summer semester (Start: 3. April 2023)
Office: G3 07, MPI MiS (Inselstr. 22, Leipzig)
Office hours: After the first lecture each week
Contact: geiger[at]mis.mpg.de
Language: The course will be held in English. Questions can be asked in German.
For math students at University Leipzig: The course can be examined as part of the diploma examinations. For details, talk to Rainer Sinn.
What is this course about?
What is this course about?
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.
Course Outline
Course Outline
This is a preliminary outline.
Tropical arithmetic and motivation
Basics of polyhedral geometry
Subdivisions and tropical hypersurfaces
Fundamental and Structure Theorem for tropical hypersurfaces
The secondary fan
Tropical linear spaces, matroids and the Dressian
Applied topics in the area of neural networks and/or extreme value statistics
Prerequisites
Prerequisites
Linear Algebra
Knowledge about algebraic geometry (especially varieties) is helpful, but not necessary.
Exercises and Course Material
Exercises and Course Material
will be available here as soon as the course starts.
References
References
"Introduction to tropical geometry" by Diane Maclagan and Bernd Sturmfels, American Mathematical Society, Graduate Studies in Mathematics Volume 161, 2015
"Essentials of tropical Combinatorics" by Michael Joswig, American Mathematical Society, Graduate Studies in Mathematics Volume 219, 2021
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