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Explore the mathematical connections between bounded gaps in prime numbers and equidistribution estimates for primes in arithmetic progressions in this 27-minute conference talk. Discover how Zhang's groundbreaking work on bounded gaps between primes has led to significant advances in improving upper bounds on the smallest integer that appears infinitely often as the gap between consecutive primes. Learn about the crucial role that equidistribution estimates for primes in specific arithmetic progressions play in Zhang's proof and subsequent work by the Polymath project. Examine the fundamental links between bounded gaps and primes in arithmetic progressions, while understanding the obstacles researchers face and recent successes in applying both classical and novel equidistribution estimates to enhance the Polymath results for bounded gaps between primes. Gain insights into current research directions in analytic number theory and the ongoing efforts to understand the distribution of prime numbers through this mathematical presentation delivered at the Centre International de Rencontres Mathématiques during their thematic meeting on "Prime numbers and arithmetic randomness."
