Applied l-adic Cohomology I - Lecture 3

Watch a lecture from the Ramanujan Lectures series where Philippe Michel from École Polytechnique Fédérale de Lausanne explores applied l-adic cohomology and its impact on modern analytic number theory. Delve into how trace functions and l-adic cohomology developments, particularly through works by Katz and Laumon, have influenced the field. Examine the fundamental concept of congruence introduced by Gauss and its relationship to analyzing prime numbers through periodic functions like Gauss sums, Jacobi sums, and Kloosterman sums. Learn from Michel, an accomplished mathematician whose research spans analytic number theory, arithmetic geometry, and automorphic forms, as he shares insights from collaborative works with E. Fouvry, E. Kowalski, and W. Sawin in this 1 hour and 51-minute presentation delivered at the International Centre for Theoretical Sciences in Bengaluru.