Title of the course: An Introduction to p-adic Analysis
Instructor: Dr. Fırtına Küçük
Institution: University College Dublin
Dates: 19-25 August 2024
Prerequisites: Abstract algebra and real and complex analysis/basic topology knowledge would be enough, even though familiarity with Algebraic Number theory and commutative algebra could be very helpful too.
Level: Advanced undergraduate and graduate level.
Abstract: The analytic construction of the p-adic numbers is very similar to the construction of real numbers from rational numbers: they are the completion of Q with respect to a certain absolute value. On the other hand, this absolute value is non-archimedean, which causes p-adic numbers to enjoy some strange topological properties. In this course we will study the basics of p-adic numbers and certain function spaces (for instance, power series and locally analytic functions). At the end, we will give a (rather) elementary construction of the first example of a p-adic L-function so called Kubota-Leopoldt p-adic L-function and emphasise its importance.
Language: TR, EN