Oleksiy Klurman

Is a Random Polynomial Irreducible? Very Likely!

Consider a polynomial of degree n with coefficients ±1, chosen randomly and independently. What is the probability that it is irreducible over the rationals? This question remains widely open, but significant progress has been made in recent years, blending ideas from several areas including analysis, number theory, and random walks on groups. In this talk, I will briefly survey some of these advances on this and related questions.

In the second part of the talk, I plan to discuss my trip to Oberwolfach last week, which resulted in a very modest contribution to this area.