Prerequisites: Linear Algebra and Complex Analysis.

The Fermat (diagonal) variety is a natural generalization of the Fermat curve, which is the Diophantine equation corresponding to Fermat’s Last Theorem.
The goal of the course is to study the topology, algebraic geometry, and arithmetic of these varieties. The Hodge conjecture and the Tate conjecture on $L$-functions of Fermat varieties remain open, and we intend to present and discuss these conjectures in an elementary manner.

References:
Hossein Movasati. A Course in Hodge Theory: With Emphasis on Multiple Integrals, Somerville, MA: International Press Boston, 2021.
Fernando Q. Gouvêa, Norico Yui. Arithmetic of Diagonal Hypersurfaces over Finite Fields, London Mathematical Society Lecture Note Series Book 209.
Frédéric Pham. Generalized Picard-Lefschetz Formulas and Ramification of Integrals. Bull. Soc. Math. France, 93:333–367, 1965.
André Weil. Numbers of solutions of equations in finite fields. Bull. Amer. Math. Soc., 55:497–508, 1949.