Arne B.
Sletsjøe
Department of MathematicsUniversity of Oslo, Norway |
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General information Research Teaching Outreach activities Collaborations & Cooperations Professional Activities På norsk |
## General information
## Research(to the top)## Research interestsMy primary research interest is within noncommutative geometry. As a subfield in its own this is a rather young area. It has its origin in classical ring theory, operator algebra theory, quantum groups and of course classical algebraic geometry. In noncommutative geometry one tries to unify algebraic geometrical intuition and noncommutative algebraic technology.My point of view is to try to understand the geometrical structure of the module category of a finitely presented associative algebra, in particular to classify the simple modules and their extensions. As tools are used algebraic methods, geometrical intiution, invariant theory and deformation theory. I have also been interested in homological algebra. Homological algebra is an inportant tool for geometers, topologists and algebraists. But there are also intrinsic problems in homological algebra, which are of great interest. Among these are problems connected to the relation between commutative and noncommutative algebra. ## Publications- Betti numbers of monoid algebras. Application to
2-dimensional torus embeddings. (with O.A.Laudal)
Math. Scand. 56 (1985) pp. 145-162 (.pdf)
- Algebra cohomology of commutative semi-groups.
Preprint, Mat. Inst. Univ. of Oslo, No 1. (1989)
- Cohomology of monoid algebras (contains 1 and 2)
Thesis, Univ. of Oslo (1989)
- Base change, transitivity and Künneth formulas for the Quillen
decomposition of Hochschild homology.(with Chr. Kassel)
Math. Scand. 70 (1992) pp. 186-192 (.pdf)
- Cohomology of monoid algebras.
J. Alg 161(1) (1993) pp.102-128 (.ps)
- Products in the Decomposition of Hochschild Cohomology.
Comm. in Alg. 22(5), (1994) pp. 1899-1911 (.pdf)
- Generators of matrix algebras in dimension 2 and 3.(with
Helmer Aslaksen)
Research Report no. 661 (1995), Nat.Univ. of Singapore
- André-Quillen cohomology of monoid algebras (with Klaus
Altmann)
J. of Alg. 210 (1998) pp. 708-718 (.ps)
- Cohomology of numerical monoids generated by three
elements.
Preprint series, Matematisk institutt, Univ. of Oslo, No. 9-2000 (.pdf)
- Infinitesimal incidence in noncommutative algebraic geometry, with
applications to noncommutative conic sections.
Preprint series, Matematisk institutt, Univ. of Oslo, No. 28-2000 (.ps)
- Noncommutative plane geometry (with O.A.Laudal and
Søren Jøndrup)
math.AG/0405350 (.pdf)
- Finite dimensional Representations of the projective
Modular Group.
math.AG/0610587 (.pdf)
- Generators of matrix algebras in dimension 2 and 3. (with H. Aslaksen)
Linear Algebra and its Applications, Volume 430, No. 1(2009), pp. 1-6 (.pdf)
## Teaching(to the top)
## Possible Masters projects:At the moment I am avaliable for supervision of new Master or Ph.D. students. Possible thesis titles in the future:- Noncommutative algebraic geometry
- Homological algebra
- Projectes in algebra, geometry or history of mathematics for teachers
## Master students supervised:Former and present Master students supervised, with title of their thesis and year of final exam:- Robert Vestgarden: Den homologiske algebraens utvikling med
særlig vekt på kohomologien til algebraer (1996)
- Lene Merete Skaar: Deformasjoner av numeriske monoidealgebraer
(1997)
- Kjerstin Grønstad Olsen: Ikke-kommutative løftinger og
vridd Hochschild-kohomologi (1997)
- Terje Jensen: Representasjoner på matrisealgebraer (1999)
- Ragnar Pettersen: Representasjoner av noen ikke-kommutative
k-algebraer (1999)
- Bjørn Thorsdalen: Ext-grupper på kvanteplynomringer
(1999)
- Ivana Celic: To-dimensjonale representasjoner av ikke-kommutative
elliptiske kurver (2004)
- Olav Gravir Imenes: Electromagnetism in a relativistic
quantum-mechanic model (co-supervisor, main supervisor: O. A. Laudal)
(2005)
- Heidi Elisabeth Iuell Dahl: On noncommutative Varieties (2006)
- Ketil Tveiten: Deformation of vector bundles with
holomorphic connections (2009)
- Håkon Hobæk: Representasjoner av den
modulære gruppa (2009)
- Asmaa Qureshi: Will finish
spring 2011
- Magne Agnalt Myren: Will finish
spring 2011
- Jan Roksvold: (co-advisor: Christin Borge) Will finish
spring 2011
## Outreach activities(to the top)Recommanded website: www.matematikk.org. ## Collaborations & Cooperations(to the top)
## Professional Activities(to the top)The Norwegian parliament founded, january 1, 2002 the Abel prize. The prize will be awarded annually, to a great mathematician of our time. The prize has been awarded three times, in 2003 the winner was Jean-Pierre Serre, in 2004 Sir Michael Atiyah and Isadore Singer, in 2005 Peter D. Lax, in 2006 Lennart Carleson, in 2007 Srinivasa S. R. Varadhan, in 2008 John G. Thompson and Jacques Tits, in 2009 Mikhail Gromov and in 2010 John Tate. Next award ceremony will be held in Oslo in May 2011. My connection to the Abel prize is as responsible for outreach activities. |