K-theoretic enumerative invariants are defined by holomorphic Euler characteristics of coherent sheaves on moduli spaces. In this talk, I will give an introduction to quantum K-theory whose definition involves moduli spaces of stable maps to given target spaces. I will mention its connections to birational geometry, combinatorics, and number theory. In joint work with Yang Zhou, we proved wall-crossing formulas of quantum K-invariants for any orbifold GIT quotient. These formulas can be used to compute quantum K-invariants. When the target space is an orbifold, quantum K-theory turns out to be quite different from its cohomological counterpart--quantum cohomology. I will present some of these new phenomena.

Classical comparison theorem established the isomorphism between singular cohomology and de Rham cohomology for smooth manifolds. The p-adic analogy aims to compare p-adic etale cohomology to de Rham cohomology for projective smooth schemes. In this talk, I will review and explain p-torsion version of such comparison and discuss how prismatic cohomology, recently invented by Bhatt-Scholze,  can help to promote such p-torsion comparison.  This is joint work with Shizhang Li.