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.