The GTA 2021 conference will bring together world class researchers in mathematics and computer science. Its main objectives are to discuss recent advances in the fields of algebraic geometry, number theory and their applications, as well as to foster international collaborations on connected topics. While contributions from all related areas of mathematics and computer science are welcome, particular emphasis will be placed on research interests of our late colleague Alexey Zykin, namely: global fields and abelian varieties; zeta-functions and L-functions; algebraic geometry over finite fields; their applications to cryptography, error-correcting codes, sphere packing, etc.