PIMS Network Wide Colloquium: Bryna Kra

Resolving a conjecture of Erdos and Turan from the 1930's, in the 1970's Szemeredi showed that a set of integers with positive upper density contains arbitrarily long arithmetic progressions. Soon thereafter, Furstenberg used Ergodic Theory to gave a new proof of this result, leading to the development of combinatorial ergodic theory. These tools have led to uncovering new patterns that occur in any sufficiently large set of integers, but until recently all such patterns have been finite. Based on joint work with Joel Moreira, Florian Richter, and Donald Robertson, we discuss recent developments for infinite patterns, including the resolution of conjectures of Erdos.

Speaker Biography: 

Bryna Kra is a leader in the area of ergodic theory, and she is especially well known for her work at the interface of ergodic theory and combinatorics. She was a graduate student at Stanford University, and is currently the Sarah Rebecca Roland Professor of Mathematics at Northwestern University. In recognition of her groundbreaking work on additive combinatorics, she was an invited speaker at the International Congress of Mathematicians, and has recently been elected to the National Academy of Sciences. Bryna Kra has served the mathematical community in a wide variety of ways, including as the current President Elect of the American Mathematical Society.