Organizers: Alan Zhao, Austin Lei

As the set of primes eludes a global pattern, two approaches to studying their behavior stand out in the literature: sieves manufactured to target certain primes and the probabilistic approach that captures data on the distribution of all primes. In this seminar, we will follow the recent revival of the targeted sieving approach, initiated first by Zhang and quickly after by Maynard.

If you are not a graduate student and interested in attending, or interested in being added to a mailing list, please email Austin (email can be found on website).

## References

- Bounded gaps between primes (Zhang)
- Small gaps between primes (Maynard)
- Large gaps between primes (Maynard)
- Small gaps between Primes or Almost Primes (Goldston-Graham-Pintz-Yildrim)
- Sieves in Number Theory (Greaves)
- Sieve Methods (Richert and Halberstam)
- Opera de Cribro (Friedlander and Iwaniec)
- A Large Sieve for a Class of non-Abelian L-functions (Goldfeld)
- The large sieve and L-functions over finite fields (Kowalski)
- An Introduction to Sieve Methods and their Applications (Cojocaru and Murty)
- "An exposition of Selberg's Sieve" (Dalton)
- "Applications of the Selberg Sieve" (Oh)
- "Sieving Using Dirichlet Series" (Murty)
- "A Large Sieve Zero Density Estimate for Maass Cusp Forms" (Lewis)

## Schedule

We will meet Tuesdays from 5:45-6:45 pm in Math 507.