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1
Intro
2
Setting and goals
3
Algebraic domains
4
Overview
5
The Poincaré-Reeb graph
6
The asymptotic Poincaré-Reeb tree
7
Reformulation
8
The polar curve
9
Choosing a generic projection
10
The generic asymptotic Poincaré-Reeb tree
11
The discriminant locus
12
Genericity hypotheses
13
1. Positive asymptotic snake
14
2. Arnold's snake (one variable)
15
Idea of the proof
16
The construction
17
Separable permutations
18
Nonseparable permutation - example
19
Separable tree
20
Passing to the univariate case
21
The contact tree
22
Answer in the univariate case
23
Construction of the desired bivariate polynomial f
24
Flip-Flop Algorithm
25
Vertical planes
26
The topological critical set
27
Domain of finite type
28
Vertical equivalence
29
Complete invariant
30
Invariance of the Euler characteristic
31
Strategy of the proof
32
Non-compact Poincaré-Reeb graphs
Description:
Explore a conference talk on Poincaré-Reeb graphs of real algebraic domains, delivered by Miruna-Stefana Sorea at the Centre International de Rencontres Mathématiques in Marseille, France. Delve into the intricacies of algebraic domains, the Poincaré-Reeb graph, and the asymptotic Poincaré-Reeb tree. Examine concepts such as polar curves, generic projections, and discriminant loci. Investigate Arnold's snake, separable permutations, and the Flip-Flop Algorithm. Learn about vertical planes, topological critical sets, and domains of finite type. Understand the invariance of the Euler characteristic and explore non-compact Poincaré-Reeb graphs. Access this 59-minute recording, complete with chapter markers, keywords, abstracts, and bibliographies, through CIRM's Audiovisual Mathematics Library for a comprehensive exploration of real algebraic geometry.

Poincaré-Reeb Graphs of Real Algebraic Domains

Centre International de Rencontres Mathématiques
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