Minicourse on Convex Geometry

Abstracts for the talks

Venkat Chandrasekaran
California Institute of Technology
Convexity and Optimization

This lecture provides a gentle introduction to elementary aspects of convexity motivated from the perspective of optimization. The objective is to motivate the study of the geometry of convex sets, which is the focus of subsequent lectures. No prior background in convexity or optimization is required.

Chiara Meroni
Max Planck Institute for Mathematics in the Sciences
Algebra and Convexity

In this lecture we will discover the interplay between convex geometry and algebraic geometry. The latter provides powerful tools for studying and describing convex bodies. We focus on the structure of their boundary in the context of algebraic varieties. The case of the convex hull of algebraic curves will be of particular interest.

Isabelle Shankar
Max Planck Institute for Mathematics in the Sciences
Non-polyhedral Convex Sets

Many convex bodies are not polytopes! This lecture introduces some interesting families of non-polyhedral convex sets that arise from convex geometry. We then discuss one way to generalize the notion of neighborliness of polyhedral cones to all convex cones, Terracini Convexity, recently introduced by Chandrasekaran and Saunderson.

Amy Wiebe
Freie Universität Berlin
Polyhedra

This lecture introduces an important class of convex bodies: polytopes. We present polytopes from combinatorial, geometric, and optimization perspectives. In particular, we focus on different descriptions of polytopes, their facial structure, and the concept of duality. Several basic constructions of polytopes are also introduced. Prior knowledge of polytopes is not assumed.

 

Date and Location

July 05 - 16, 2021
Max Planck Institute for Mathematics in the Sciences
Virtual event - Videobroadcast

Scientific Organizers

  • Venkat Chandrasekaran, California Institute of Technology
  • Chiara Meroni, MPI for Mathematics in the Sciences
  • Isabelle Shankar, MPI for Mathematics in the Sciences
  • Amy Wiebe, Freie Universität Berlin

Administrative Contact

Saskia Gutzschebauch
MPI for Mathematics in the Sciences
Contact by Email
19.07.2021, 01:27