Graduate level courses at KTH and Stockholm University 2009-2010
Fall 2009
Commutative Algebra
SU, Rikard Bögvad
Room 306, House 6 (SU), Tuesdays at 13-15. Course start: September 8
Course page
During the fall two courses in commutative algebra and algebraic
geometry respectively will be run in parallel. The two subjects are
intimately related and the courses will be coordinated so that a
participant in both of them will benefit particularly.
Commutative algebra is concerned with the theory of commutative
rings with (at least originally) a view towards applications in
algebraic geometry. The course will present the basic results of the
subject. The coordination mentioned above will not mean that
attendance at the course in algebraic geometry will be a requirement
but some understanding of the geometric picture will be an aid to
understand the concepts presented.
Literature:
- Steps in commutative algebra by Ronald Sharp, London
Mathematical Society Student Texts.
Algebraic Geometry
SU, Torsten Ekedahl
Room 306, House 6 (SU), Fridays at 13-15. Course start: September 11
Course page
During the fall two courses in commutative algebra and algebraic
geometry respectively will be run in parallel. The two subjects are
intimately related and the courses will be coordinated so that a
participant in both of them will benefit particularly.
Algebraic geometry which generally can be said to deal with the
geometry of zero sets of polynomials can be today be based either on
the theory of complex analytic functions and differential geometry or
on commutative algebra. The course will exclusively deal with the
second type of foundation. The prospective attendant who does not know
commutative algebra beforehand is strongly recommended to also attend
the course in commutative algebra.
Literature:
- Algebraic Geometry by Robin Hartshorne, Springer Verlag
Geometric Multilinear Analysis
SU, Andreas Axelsson
Course page
Obstacle problems in mathematical physics and industry
KTH, Henrik Shahgholian
Room 3733 (KTH), Tuesdays 13-15. Course start: September 15
Course page
To goal of this course is to learn about certain problems in
mathematical physics related to industrial problems. The prime goal,
besides learning about how mathematics and especially partial
differential equations can be used to formulate problems in physics,
mechanics, finance, biology, and industry, is to introduce students to
real-world problems and problems in the frontier of active
research. The course can be seen as an introduction to the topic
“Free Boundary Problems” and there are possibilities of
further study and “Examensarbete” in mathematics.
Literature:
- Obstacle problems in mathematical physics by
Jose-Francisco Rodrigues (1986), North-Holland, Mathematics
studies 134. (The book is out of print, but we can provide
with some copies from the library.)
- Additional handouts and research papers.
Computational number theory (independent study)
KTH, Pär Kurlberg
Weekly meetings in room 3721 (KTH), Tuesdays 15.15-17.15.
Course page
Literature:
- Prime numbers : a computational perspective by Richard
Crandall and Carl Pomerance, Springer Verlag.
- A course in computational algebraic number theory by
Henri Cohen, Springer Verlag.
Inverse problems
KTH, Anders Szepessy
Room 3721 (KTH), Thursdays 10-12. Course start: September 10
Course page
The goal of this course is to understand basic mathematical and numerical methods to solve inverse problems related to partial differential equations.
Some topics: ill-posed problems and their numerical solution by regularization methods, regularization of linear problems, Tikhonov regularization, regularization of non linear problems.
Some applications: differentation as an invers problem, X-ray tomography, data-assimilation for weather and climate prediction, inverse scattering, optimal design, image processing, parameter identification.
Literature:
- Regulation of Invers Problems by Heinz W. Engl, Martin
Hanke and Andreas Neubauer, Kluwer Academic Publishers. (Main course
book.)
- Computational Methods for Inverse Problems by
Curtis R. Vogel, SIAM.
- Inverse Problem Theory by Albert Tarantola, SIAM
Spring 2010
Dynamics of Strings and Membranes
KTH, Jens Hoppe
Room 3733 (KTH), Tuesdays and Thursdays 15-17. Course start: January 12
The course will be an introduction, including M(atrix)-theory,
to the theory of relativistic extended objects (classically:
time-like manifolds that are stationary points of the volume-functional),
and will be given (with different levels of examination) both as a
higher level course (avancerad kurs) for undergraduate students,
and as a graduate course for PhD students.
Literature:
- A First Course in String Theory by B. Zwiebach
(developed at MIT as a (highly praised) string-theory course for
undergraduates).
- Original research articles
Topics in advanced analysis
SU, Jan-Erik Björk
Course page
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