April 16 – June 8, 2018
Centre de Recerca Matemàtica
This intensive research program will consist of 8 weeks of activities focused on hot topics in discrete, combinatorial and computational geometry and their intricate relationships. The program will bring together leading researchers from all over the world to work on open problems, and to analyze its present state and perspectives. The program has been designed to be interesting for both senior researchers and advanced PhD students. The planned activities combine learning opportunities and research collaboration chances in problems of theoretical nature in combinatorial and discrete geometry, algorithmic problems from computational geometry, and implementation issues in specialized software.
Structure of the program
The central part of the program is composed of 5 consecutive weeks, including two advanced courses, each followed by a week of topic-related inspiring lectures, and a hand-on course on geometric software:
In addition, the central part of the program will be followed by three more weeks of activities:
- May 22-25: Working and interacting week, with seminar talks.
- May 28-June 1: CONNECT workshop on geometric and algorithmic aspects of networks
- June 4-8: 5th Austrian-Japanese-Mexican-Spanish workshop on discrete geometry
- Oswin Aichholzer (TU Graz, Austria)
- Prosenjit Bose (Carleton U, Canada)
- Erik Demaine (MIT, USA)
- Clemens Huemer (UPC, Spain)
- Joe Mitchell (Stony Brook U, USA)
- János Pach (EPFL Lausanne, Switzerland and Renyi Institute Budapest, Hungary)
- Vera Sacristán (UPC, Spain) (coordinator)
- Rodrigo I. Silveira (UPC, Spain)
Details of the activities
Advanced Course I: Advanced Techniques for Algorithmic Geometry
This course will survey some of the most recent algorithmic paradigms and data structures that have led to the latest advances in the state of the art of computational geometry.
Topics: to be precised together with the lecturers. Possible topics include the latest approximation techniques based on local search, sparse approximation methods, and some of the most recent advances in dynamic data structures for point location, range searching and other fundamental geometric problems.
Advanced Course II: New Results In Combinatorial & Discrete Geometry
- Bojan Mohar (Simon Fraser University & University of Ljubljana)
- Gelasio Salazar (Univ. Autónoma San Luis Potosí)
This course will cover hot topics in combinatorial and discrete geometry, focusing on a selection of techniques that have enabled some of the latest breakthroughs in the area.
Topics: to be precised by the lecturers. Possible topics include algebraic and probabilistic methods in combinatorial geometry, spectral techniques for graphs and combinatorics, new advances in graph drawing, topological graph theory and crossing numbers.
Inspiring Lectures I: Computational Geometry Towards Applications
- Sergio Cabello (University of Ljubljana)
- Erik Demaine (Massachusetts Institute of Technology)
- Tamal Dey (The Ohio State University)
- Vida Dujmovic (University of Ottawa)
- Dan Halperin (Tel Aviv University)
- Marc van Kreveld (Utrecht University)
This activity will consist of 1-2 lectures per day, focusing on open problems on different topics, in relation to the subjects of Advanced Course I. The remaining of the day, attendees will have plenty of time to work and interacting with each other.
Topics: Computational Geometry challenges in Geographic Information Science, Meshing, Robotics, Surface Reconstruction, Visualization,…
Inspiring Lectures II: Challenges in Combinatorial & Discrete Geometry
- Karim Adiprasito (Hebrew University of Jerusalem)
- Imre Bárány (Hungarian Academy of Sciences)
- Alexander Barvinok (University of Michigan)
- Fabrizio Frati (Università Roma Tre)
- Adam Sheffer (California Institute of Technology)
- Csaba D. Tóth (California State University Northridge)
This activity will consist of 1-2 lectures per day, focusing on open problems on different topics, in relation to the subjects of Advanced Course II. The remaining of the day, attendees will have plenty of time to work and interacting with each other.
Topics: to be precised by the lecturers, based on the final topics of Advanced Course II.
Hands-on course on Geometric Software
This activity is intended to provide practical knowledge about important software tools relevant to researchers dealing with geometric problems. It will include lectures as well as practicum.
Topics and lecturers:
- CGAL, by Andreas Fabri (Geometry Factory)
- GeoGebra, by Zoltan Kovacs (Johannes Kepler Universität)
- OpenGL, by Nicolai Hähnle (AMD)
- Polymake, by Michael Joswig (TU Berlin)
During the whole duration of the program we will hold a regular weekly seminar in which other visitors will be able to present recent results on the topics of the program. The frequency of the seminar will depend on the number of visitors, but we expect to have at least one and at most two talks per week. These seminars will be open to the whole Mathematics community.
In addition, all students participating in the program will be invited to give a talk about their current work in a student seminar that will take place regularly in the afternoons during the five central weeks of the program. The frequency of the talks will depend on the number of students, but we expect to have at most two talks per day. Other visitors, including students and also more senior researchers will be encouraged to attend.
The intensive research program is organized by