- Docente: Nicola Arcozzi
- Credits: 6
- SSD: MAT/05
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 8208)
Learning outcomes
The course will cover some advanced topics in Complex Analysis. At the end of the course the student will know and be able to use tools from complex analysis in various branches of mathematics and to read research literature in the field.
Course contents
The course has as a prerequisite the course of Complex Analysis of the Laurea Triennale. Based on that, it will develop a selection of more advanced topics in holomorphic function theory.
-Conformal maps (Riemann mapping theorem; Schwarz-Christoffel formula; an overview of the non simply connected case) and some of their applications (Green's functions).
-Entire functions: relatione between growth and zeros.
-The analytic Hardy space and some of its applications to functional analysis and control theory.
-The Prime Number Theorem proved by meann of the Riemann Zeta function.
Other topics might be added if the class expresses interest in this sense.
Readings/Bibliography
Lars Ahlfors, Complex Analysis McGraw-Hill Education; 3 edizione (1978) International Series in Pure and Applied Mathematics ISBN-10: 0070006571 ISBN-13: 978-0070006577
Mats Andersson, Topics in Complex Analysis Springer; 1997 edition (1996) ISBN-10: 038794754X ISBN-13: 9780387947549
Elias M. Stein, Rami Shakarchi Complex Analysis Princeton University Press (2003) ISBN 9780691113852
Teaching methods
Blackboard lectures
Assessment methods
Oral exam. The students are encouraged to deliver a seminar on a special topic during the class.
Teaching tools
Class notes will be available on IOL
Office hours
See the website of Nicola Arcozzi