Intervenant : Sukumar Das Adhikari (Allahabad, India)

Date et heure : Vendredi 17 juin, 14h-15h


Titre :  Two problems related to integer lattice points in the plane

Abstract :

We shall discuss a couple of problems related to integerlattice 
points in the plane.The first one involves finite colourings of
integer lattice points in the plane.
The question may be said to belong to the subjectof Euclidean 
Ramsey Theory and is related to a conjecture which was suggested
by Gurevich which says that for any finite colouring of the 
Euclidean plane $E2$, there always exists a triangle of unit 
area with monochromatic vertices.
The second problem is on a question of Erd\H{o}s regarding 
visibility of integer lattice points in the plane.
For both the problems, before going into the exact problems 
involved, we give necessary introductions to those themes.
We also mention results related to these problems in the 
higher dimensions.