Autumn Semester 2020 takes place in a mixed form of online and classroom teaching.
Please read the published information on the individual courses carefully.

Rahul Pandharipande: Catalogue data in Spring Semester 2017

Name Prof. Dr. Rahul Pandharipande
FieldMathematics
Address
Professur für Mathematik
ETH Zürich, HG G 55
Rämistrasse 101
8092 Zürich
SWITZERLAND
Telephone+41 44 632 56 89
E-mailrahul.pandharipande@math.ethz.ch
URLhttp://www.math.ethz.ch/~rahul
DepartmentMathematics
RelationshipFull Professor

NumberTitleECTSHoursLecturers
401-4142-17LAlgebraic Curves6 credits3GR. Pandharipande
AbstractI will discuss the classical theory of algebraic curves. The topics will include:
divisors, Riemann-Roch, linear systems, differentials, Clifford's theorem,
curves on surfaces, singularities, curves in projective space, elliptic curves,
hyperelliptic curves, families of curves, moduli, and enumerative geometry.
There will be many examples and calculations.
Objective
ContentLecture homepage: https://metaphor.ethz.ch/x/2017/fs/401-4142-17L/
LiteratureForster, "Lectures on Riemann Surfaces"

Arbarello, Cornalba, Griffiths, Harris, "Geometry of Algebraic Curves"

Mumford, "Curves and their Jacobians"
Prerequisites / NoticeFor background, a semester course in algebraic geometry should be
sufficient (perhaps even if taken concurrently). You should know the definitions
of algebraic varieties and algebraic morphisms and their basic properties.
401-5000-00LZurich Colloquium in Mathematics Information 0 creditsP. L. Bühlmann, M. Burger, S. Mishra, R. Pandharipande, University lecturers
AbstractThe lectures try to give an overview of "what is going on" in important areas of contemporary mathematics, to a wider non-specialised audience of mathematicians.
Objective
401-5140-11LAlgebraic Geometry and Moduli Seminar Information 0 credits2KR. Pandharipande
AbstractResearch colloquium
Objective
406-2303-AALComplex Analysis
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
6 credits13RR. Pandharipande
AbstractComplex functions of one variable, Cauchy-Riemann equations, Cauchy theorem and integral formula, singularities, residue theorem, index of closed curves, analytic continuation, conformal mappings, Riemann mapping theorem.
Objective
LiteratureL. Ahlfors: "Complex analysis. An introduction to the theory of analytic functions of one complex variable." International Series in Pure and Applied Mathematics. McGraw-Hill Book Co.

B. Palka: "An introduction to complex function theory."
Undergraduate Texts in Mathematics. Springer-Verlag, 1991.

R.Remmert: Theory of Complex Functions.. Springer Verlag

E.Hille: Analytic Function Theory. AMS Chelsea Publication
Prerequisites / NoticeThe precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.