- Docente: Giovanni Mongardi
- Credits: 6
- SSD: MATH-02/B
- Language: Italian
- Teaching Mode: In-person learning (entirely or partially)
- Campus: Bologna
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Corso:
First cycle degree programme (L) in
Mathematics (cod. 6061)
Also valid for First cycle degree programme (L) in Mathematics (cod. 6061)
Learning outcomes
Students will learn about holomorphic functions and Riemann surfaces, and will be able to apply this knowledge.
Course contents
Complex analysis in one variable: power series and analytic functions; holomorphic functions and Cauchy-Riemann equations; differential forms and integrations; Cauchy's integral formula and fundamental theorems of the theory of holomorphic functions of one complex variable.
Riemann surfaces theory: abstract surfaces; complex structures on surfaces; Riemann-Hurwitz formula; genus-degree formula; elliptic curves; hyperbolic surfaces. Holomorphic maps and forms, divisors and Riemann-Roch theorem.
Readings/Bibliography
Teaching methods
Lectures with blackboard.
Assessment methods
Students are admitted to the oral exam only if the written exam is sufficient (i.e.16/30). Both tests must be held in the same exam round.
During the written exam, you are allowed to have with you two A4 sheets, handwritten in a reasonable size (no more than one line of text per 1/2 cm), containing any result deemed useful for the exam. No other reference materials, such as books or notes, are allowed.
Office hours
See the website of Giovanni Mongardi