Number Theory and Algebra Seminar: Partition regularity of Pythagorean pairs
Number Theory and Algebra Seminar: Partition regularity of Pythagorean pairs
Number Theory and Algebra Seminar: Partition regularity of Pythagorean pairs
| A Number Theory, Algebra and Geometry seminar | |
|---|---|
| Speaker(s) | Oleksiy Klurman, University of Bristol |
| Date | 6 December 2023 |
| Time | 14:30 to 15:30 |
| Place | Newman Purple LT |
| Organizer | Dr Julio Andrade |
Event details
Abstract
Abstract: Is there a partition of the natural numbers into finitely many pieces, none of which contains a Pythagorean triple (i.e. a solution to the equation x2+y2=z2)? This is one of the simplest (to state!) questions in arithmetic Ramsey theory which is still widely open. I will present a recent partial result, showing that "Pythagorean pairs" are partition regular, that is in any finite partition of the natural numbers there are two numbers x,y in the same cell of the partition, such that x2+y2=z2 for some integer z (which may be coloured differently). The proof is a blend of ideas from ergodic theory and multiplicative number theory. Based on a joint work with N. Frantzikinakis and J. Moreira.
Abstract: Is there a partition of the natural numbers into finitely many pieces, none of which contains a Pythagorean triple (i.e. a solution to the equation x2+y2=z2)? This is one of the simplest (to state!) questions in arithmetic Ramsey theory which is still widely open. I will present a recent partial result, showing that "Pythagorean pairs" are partition regular, that is in any finite partition of the natural numbers there are two numbers x,y in the same cell of the partition, such that x2+y2=z2 for some integer z (which may be coloured differently). The proof is a blend of ideas from ergodic theory and multiplicative number theory. Based on a joint work with N. Frantzikinakis and J. Moreira.
Location:
Newman Purple LT
