Examensarbete i matematik

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MASTER'S THESIS IN MATEMATIK
ALGEBRA AND GEOMETRY



Are you interested in doing an MASTER'S THESIS in Algebra and Geometry?
These pages contain relevant information, as well as a list of finished theses, and a list of finished Ph.D's.


WHO ARE WE? The research group in Algebra and Geometry is a quite big and socially active group (present members). We are all active in research and have sincere interest in teaching and mentoring. Our location is at the Department of Mathematics, Lindstedtsvägen 25.

Our research interests include moduli spaces, Hilbert schemes, graded modules, toric geometry, and homotopy theory. We have broad international cooperation and contacts, mainly with universities and mathematicians in Europe, Canada and USA. During the year we have numerous guests. Our personal homepages as well as the research articles will give you a more detailed description of our research profile.

Together with the University of Stockholm we run a weekly seminar, and usually we also run a local seminar. Furthermore, our group of graduate students is usually big enough to run reading seminars and thematic workshops. We are also involved in the activity at the famous Mittag-Leffler Institute, located in Djursholm. Recently we played an important role in their program during the academic year 2006/07. The next time we will be fully involved is during spring 2011.

All together these seminars and the people in the group will give you lots of exposure to new and exciting mathematics within the huge and active field that is covered by Algebra and Geometry. There is a selection of suggested problems for an Examensarbete available, only a small sample is provided below.


MASTER'S THESIS? A Master's Thesis is a half year study program where you get research training, and experience in writing and presenting scientific material. Some suggestions of possible problems are listed below. We are however flexible and will most certainly be able to tailor an Examensarbete that fits your interest.

In order to get an idea about the actual project you might want to look at the list of previous students that have achieved an Examensarbete within our group. It is not a big secret that many of our students continue doing their Ph.D. in mathematics as well, and here is a list of graduated students. Even though we certainly appreciate you heading for a Ph.D. in mathematics, we also welcome those of you who are interested in doing different careers.


MATS BOIJ:
WOJCIECH CHACHOLSKI:
SANDRA DI ROCCO:
CAREL FABER:
ROY SKJELNES:
  • The Grassmannians are generalizations of projective spaces, and their cohomology ring is known. Understanding these objects gives a glimpse into both classical and modern algebraic geometry. The project is to define the Grassmannians and Schubert cells, and to understand the intersection theory on the Grassmannian.
  • The power series ring is an algebraic analogue of an analytic disc. In some sense the disc contains only one single point, but the Hilbert scheme parametrizing points in the disc is quite a complicated object. The project is to describe the Hilbert scheme of points on the algebraic disc.


  • COURSES The courses in algebra and geometry are coordinated with the University of Stockholm (see their home page as well as the home page of the KTH mathematics department for a list of present courses). The first course in algebra is "Groups and Rings" which is given every year. A second course in algebra is also given annually, but the topic is varying; usually alternating between "Homological Algebra and Algebraic Topology" and "Commutative Algebra and Algebraic Geometry". In addition there are other non-regular advanced courses, graduate courses, thematic seminars and research seminars.


    KANDIDAT EXAMENSARBETE It is possible to take a Kandidat Examensarbete in mathematics. Within the field of Algebra and Geometry, that work will be integrated with the course "Groups and Rings", given every spring. Follow this link for more information.



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    Sidansvarig: Roy Skjelnes