**Speaker:** Dr. Akshaa Vatwani from IIT Gandhinagar (invited by Arindam Roy)

**Title:** Limitations to equidistribution in arithmetic progressions

**Abstract:** We will discuss the distribution of prime numbers lying in an arithmetic progression *a* modulo *q* with *a* coprime to *q*. Dirichlet observed that any such sequence contains infinitely many primes. Moreover, for a fixed *q*, the proportion of primes in each such progression is the same. As *q* varies, more questions can be asked regarding how far such equidistribution persists. We will explore this theme and discuss some variants and applications. This talk is based on joint work with Aditi Savalia.