Una mattinata di Combinatoria a Via dei Taurini
2015-09-15
Martedì 15 settembre, dalle ore 11:00 alle ore 13:00, presso la Stanza 116, piano 1 di via dei Taurini 19, Francis Lazarus (Gipsa-lab, CNRS, Grenoble) e Martin Loebl (Department of Applied Mathematics, Charles University, Praha) animeranno la mattinata con due seminari di combinatoria secondo il seguente programma: 11:00-11:55, Francis Lazarus, Introduction to persistent homology. 12:00-12:55, Martin Loebl, Deciding 4-colorability of planar triangulations.
A Combinatorial morning at Via dei Taurini.
11:00-11:55, Francis Lazarus, Introduction to persistent homology
Persistent homology was introduced in the early 2000s for thepurpose of data analysis from the topological viewpoint. In thistalk, I will introduce the basics of this theory and present its mainresult concerning stability. The talk is intended for beginners anddoes not assume specific knowledge in the field.
12:00-12:55, MartinLoebl, Deciding 4-colorability of planar triangulations
Weshow, without using the Four Color Theorem, that for each planartriangulation the number of its proper vertex colorings by 4 colorsis a determinant and thus can be calculated in a polynomial time. Inparticular, we can efficiently decide if the number is non-zero. Ourconstruction builds upon results in the areas of edge-colorings,combinatorial nullstellensatz, and Pfaffian method.
