The security of the majority of public key cryptographic protocols employed nowadays is based on two mathematical problems: factoring large integers and the discrete logarithm problem. In 1994 Shor showed that both problems can be solved in polynomial time with a quantum computer. Therefore, the cryptographic community has been looking for alternatives which are not based on them. This research area is called post-quantum cryptography. Algebraic geometry and the neighbouring fields of arithmetic geometry and commutative algebra have been a fruitful source of mathematical primitives for post-quantum cryptography. In this symposium we will focus on two mathematical objects that are highly relevant in post-quantum cryptography: multivariate polynomial systems and isogenies between elliptic curves. They are employed respectively in multivariate cryptography and isogeny-based cryptography. In the last year, there has been a tremendous breakthrough in both areas. Systems that have been considered secure for a long time, such as Rainbow and SIDH, were broken. These attacks highlight that our understanding of the mathematics behind multivariate and isogeny-based cryptography is limited and there is still work to be done. In this symposium we will bring together experts in both areas that will present the recent developments in the field.