Thời gian: 9h, Thứ 4, Ngày 20/2/2019.
Địa điểm: Phòng 612 Tòa A6 Viện Toán học
Tóm tắt: An integer is called a Polignac number if it can be expressed as the difference of two consecutive primes in infinitely many ways. The French mathematician Polignac conjectured in 1849 that every even integer is a Polignac number.

It had not been known whether Polignac numbers exist until 2013, when Yitang Zhang and James Maynard independently proved that there are infinitely many pairs of consecutive primes whose gaps are bounded.

This talk aims to present the circle of conjectures, results, and techniques that are used to understand gaps between primes. I shall describe the stories of Zhang and Maynard mentioned above. I shall report on related results, including my own work, inspired by the breakthroughs of Zhang and Maynard.