Emplacement
Dates
Présentation
Combinatorics is at the centre of a variety of areas in pure and applied mathematics. For
instance, in recent years problems arising in algebra and geometry have been better understood
and in many cases fully solved by exploiting their relation to certain discrete objects.
At this school we aim to explore modern geometric techniques that have been used in recent
years to solve long standing conjectures in combinatorics and other areas.
Format:
-We will have four minicourses by leading experts in their fields. These minicourses will have four one hour lectures followed by 90 minutes of problem sets.
-Participants at different stages will be mixed into groups to think about the exercises.
-There will be two plenary lectures.
-In addition there will be a call for talks and posters so that students have the opportunity to present their latest work.
-We do two panels of particular topics where students can ask questions to senior professors.
Le programme scientifique est disponible sur le site local de l'Ecole : https://ecco2024.combinatoria.co/
Langue officielle de l'Ecole : Anglais
Coordinateurs administratifs et scientifiques
Programme scientifique
Cours 1: "introductory course - I will describe the recent breakthroughs in the classification of f-vectors for different classes of simplicial complexes. In notorious cases there is a complete classification, as in boundary of polytopes, and in others we will study upper bound and lower bound results. We will be developing the necessary tools from commutative algebra as we need them.", Isabella NOVIK (University of Washington, United States)
Cours 2: "introductory course - Ehrhart theory is the study of sequences recording the number of integer points in non-negative integral dilates of rational polytopes. This study combines convex geometry with combinatorics and uses the toolkit from commutative algebra. We will survey the general results in the area as well as recent developments and open problems.", Benjamin BRAUN (University of Kentucky, United States)
Cours 3: "introductory course - Complete log-concavity is a generalization of hyperbolicity for multivariate polynomials that is closed related to notions of discrete convexity, including matroids, submodular functions, and generalized permutohedra. Many of the nice properties of hyperbolic polynomials extend to this more general class. These polynomials can be defined and understood in elementary terms. I will introduce this class of polynomials, the underlying real algebraic geometry, and some important examples coming from combinatorics and convex optimization.", Cynthia VINZANT (University of Washington, United States)
Cours 4: "introductory course - Toric varieties are right in the middle of combinatorics, discrete geometry and algebraic geometry. There is an extensive dictionary that allow us to translate ideas from lattice polytopes to geometrical results about the toric variety and conversely. We will study several instances of this two-way street between the topics.", Hal SCHENCK (Auburn University, United States)
Cours 5: "programming sessions - Sage is free, open-source math software that supports research combinatorics, among many other areas. We will do a demonstration of software with examples relevant from the lectures and also show how to contribute to SAGE.", Jean-Philippe LABBÉ (École de Technologie supérieure, Canada)
Site internet de l'école
Comment participer
Pour s'inscrire et postuler à un financement CIMPA, suivre les instructions données ici https://www.cimpa.info/en/node/40
Date limite d'inscription : mars 15, 2024