Convex and Discrete Geometry Summer School

The school, part of the special semester on Discrete Geometry and Convexity, offers four mini courses on current hot topics in the field given by Vida Dujmovic (University of Ottawa), Apostolos Giannopoulos (University of Athens), Nabil Mustafa (Université Sorbonne Paris Nord) and Márton Naszódi (Rényi Institute), exercise sessions and a small number of additional talks.The courses and the talks are aimed at graduate students and researchers at the beginning of their career, and should be accessible to a wide audience. Apart from presenting the state of the art, many open problems will be discussed.

Schedule

Recordings of the lectures

Financial Support

We can cover the accommodation, and possibly, the travel expenses for a limited number of participants. You can also stay for a longer period after the Summer School.

Please, indicate on the registration form whether you need such financial support and if you want to stay longer. In case you do, please, do not arrange your travel to Budapest, nor your accommodation, as we may do it for you. Also indicate your desired arrival and departure dates.

Deadline for application for financial support: 03. 10. 2023.

• Notification of the result of financial support applications: 03. 15. 2023.

Instructions for application for financial support:

• If you are an MSc or PhD student, please ask your advisor / mentor to send a brief reference email to erdosdgc@renyi.hu with the subject "[Conv. & Disc. Geom. Summer school] + APPLICANT'S FULL NAME".
• If you are a postdoc, please send your CV + research statement by email to erdosdgc@renyi.hu, with the subject "[Conv. & Disc. Geom. Summer school] CV - APPLICANT'S FULL NAME".

Lecture sessions

Vida Dujmovic: Graph Structure and Geometry
   1. Product structure of planar graphs
   2. Applications to geometric graph drawings
   3. Collinear sets and structure 1
   4. Collinear sets and structure 2
   5. Crossings and structure

Apostolos Giannopoulos: Threshold for the Measure of Random Polytopes
   1. Volume threshold: the case of the cube and 0-1 polytopes
   2. Volume threshold: the case of the simplex
   3. Half-space depth and general volume thresholds
   4. Measure threshold: the case of independent coordinates
   5. Measure threshold: a general approach and open questions

Nabil Mustafa: Iterative Reweighing in Discrete Geometry
   1. Introduction: the Erdős-Selfridge strategy
   2. A combinatorial perspective
   3. A geometric perspective
   4. An algorithmic perspective
   5. A game theory perspective

Márton Naszódi: Approximation in Geometry
   1. Approximation of convex bodies by polytopes
   2. John's theorem for log-concave functions
   3. Quantitative Helly-type questions
   4. Approximation of sums of matrices
   5. Open problems