Rahul Pandharipande: Catalogue data in Spring Semester 2017
|Name||Prof. Dr. Rahul Pandharipande|
Professur für Mathematik
ETH Zürich, HG G 55
|Telephone||+41 44 632 56 89|
|401-4142-17L||Algebraic Curves||6 credits||3G||R. Pandharipande|
|Abstract||I 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.
|Content||Lecture homepage: https://metaphor.ethz.ch/x/2017/fs/401-4142-17L/|
|Literature||Forster, "Lectures on Riemann Surfaces"|
Arbarello, Cornalba, Griffiths, Harris, "Geometry of Algebraic Curves"
Mumford, "Curves and their Jacobians"
|Prerequisites / Notice||For 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.
|401-5000-00L||Zurich Colloquium in Mathematics||0 credits||P. L. Bühlmann, M. Burger, S. Mishra, R. Pandharipande, University lecturers|
|Abstract||The 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.|
|401-5140-11L||Algebraic Geometry and Moduli Seminar||0 credits||2K||R. Pandharipande|
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 credits||13R||R. Pandharipande|
|Abstract||Complex 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.|
|Literature||L. 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 / Notice||The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.|