From 2 November 2020, the autumn semester 2020 will take place online. Exceptions: Courses that can only be carried out with on-site presence. Please note the information provided by the lecturers via e-mail.

Rahul Pandharipande: Catalogue data in Spring Semester 2016

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
401-3146-12LAlgebraic Geometry10 credits4V + 1UR. Pandharipande
AbstractThis course is an Introduction to Algebraic Geometry (algebraic varieties and schemes).
Objective
LiteratureThe main reference for the course is
* Robin Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, Springer.

For the exercises we will also use
* Joe Harris, Algebraic Geometry, A First Course, Graduate Texts in Mathematics, Springer.

There are also some very good texts that are freely available online. I recommend two of them:
* J.S. Milne, Algebraic Geometry, http://www.jmilne.org/math/CourseNotes/AG.pdf (mainly about abstract algebraic varieties - schemes only appear in the very end)
* Ravi Vakil, Foundations of Algebraic Geometry, http://math.stanford.edu/~vakil/216blog/ (quite abstract)

Further readings:
* I. R. Shafarevich, Basic Algebraic geometry 1 & 2, Springer-Verlag.
* Ulrich Görtz and Torsten Wedhorn, Algebraic Geometry I, Advanced Lectures in Mathematics, Springer.
* Jean Gallier and Stephen S. Shatz, Algebraic Geometry http://www.cis.upenn.edu/~jean/algeom/steve01.html
Prerequisites / NoticeRequirement: Commutative Algebra course.
401-5000-00LZurich Colloquium in Mathematics Information 0 creditsW. Werner, P. L. Bühlmann, M. Burger, S. Mishra, R. Pandharipande, University lecturers
Abstract
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.