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EXAMENSARBETEN I
ALGEBRA OCH GEOMETRI
MASTER'S THESIS: Below we list the students at KTH who have finished their Master's Thesis within our group. In addition to the names of the students you will find the title, a short description, the examination year and the supervisor. Note that many of our students decide to continue their studies in mathematics and become graduate students.
THESIS: Click here to see a list of students that have finished their graduate studies within our group, and received a PhD.
Sebastian Öberg :"Equality in Green's Hyperplane Restriction Theorem"
  • (2010/Boij).
  • Advanced to doing graduate studies at KTH
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    David Goldstein : "A Combinatorial approach to Green's Hyperplane Restriction Theorem"
  • We study a possible combinatorial proof of Green's hyperplane restriction theorem based on the idea to specialize to the generic initial ideal with respect to the reverse lexicographic order, which means that it is sufficient to prove the statement for strongly stable monomial ideals (2009/Boij).
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    Dan Petersen : " Equivariant point counts of involutional hyperelliptic curves"
  • (2008/Faber).
  • Advanced to doing graduate studies at KTH
    		•
    Oscar Forsmann : "The Hilbert scheme of points on the projective line"
  • In this project we study in detail how the Hilbert scheme of points on the affine line glues to form the Hilbert scheme of points on the projective line (2007/Skjelnes).
  • Advanced to doing graduate studies at KTH
    		•
    Sara Bladh : "An approach to determinants via structure theorems "
  • We consider an alternative definition of the determinant of a linear map (2007/Laksov).
    		•
    Andreas Holmström : "Harmonic analysis on number fields "
  • (2005/Faber).
    		•
    David Eklund : "The second fundamental form of a family of surfaces in projective 3-space "
  • In this project the rank of the second fundamental form of a particular family of surfaces in three dimensional projective space is studied (2005/DiRocco).
  • Advanced to doing graduate studies at KTH
    		•
    Jonas Kiessling : "Cellularity of chain complexes"
  • We classify cellular classes of chain complexes over artinian local rings whose maximal ideal is principal and of order two (2005/Chacholski).
  • Advanced to doing graduate studies at KTH
    		•
    Anton Appelgren : "On certain maps of invariant rings"
  • In geometry a canonical map of invariant rings play an interesting role, and in this project we study the algebraic properties of these maps (2004/Skjelnes).
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    Christian Lundkvist : "Hilbert's Nullstellensatz and generalizations "
  • Different versions of Hilbert's Nullstellensatz is considered in this project, in particular versions applicable for not finitely generated algebras (2004/Laksov).
  • Advanced to doing graduate studies at KTH
    		•
    Oscar Axmon : "Determinant of an endomorphism"
  • The determinant we are familiar with, and in this project we study different approaches to define this important multilinear function (2004/Skjelnes).
    		•
    Christian Grundh : "Calculating Fourier coefficients of vector valued Siegel modular forms and traces of Hecke operators "
  • (2003/Faber).
  • Advanced to doing graduate studies at KTH
    		•
    Johanna Nilsson : "Solutions to pXY+qYX=1 over an arbitrary field "
  • The solutions of the equation pXY+qYX=1 as square matrices over algebraically closed fields of characteristic different from two are found. This is a continuation of the Master's thesis "Equations over matrix rings" by John Andersson (2003/Boij).
  • Advanced to doing graduate studies at KTH
    • Dan Sjöstrand : "Cayley-Hamilton theorem"
  • In this project we consider several of the many different proofs of the famous Cayley-Hamilton theorem (2003/Laksov).
    		•
    Fredrik Nordström : "Recovering a module from its local structure"
  • In this project we study what information is needed to rebuild the module from only knowing the information about the stalks around each prime ideal (2003/Skjelnes).
  • Advanced to doing graduate studies at KTH
    		•
    David Rydh : "Chow varieties"
  • The Chow scheme of cycles on projective varieties is considered in this project (2003/Laksov).
  • Advanced to doing graduate studies at KTH
    		•
    John Andersson : "Equations over matrix rings"
  • The solutions of quadratic equations in square matrices over an algebraically closed field of characteristic zero are described and classified (2002/Boij).
  • Advanced to doing graduate studies at KTH
    • Jonas Bergström : "Curves of genus three over finite fields"
  • (2001/Faber).
  • Advanced to doing graduate studies at KTH
    • Jonas Söderberg : "Normal forms for matrices"
  • An alternative normal forms for matrices has been suggested which would give the space of square matrices a nice cell decomposition. This kind of normal forms is studied and proved not to exist in the case of four by four matrices (2001/Boij).
  • Advanced to doing graduate studies at KTH
    • Magnus Hessel : "Weyl groups of matrix groups"
  • The theory of Weyl groups is presented in a purely algebraic manner and some of the aspects of positive characteristic is considered (1998/Boij).
    		•
    Erik Norhammar : "Groups, rings and fields"
  • Here the fundamental algebraic objects are introduced with a didactic point of view (1997/Laksov).
    		•
    Fredrik Andreasson : "Nullstellen theorems"
  • Several Nullstellen theorems and proofs are considered, and in particular versions that hold over non-closed fields (1995/Laksov).
  • Advanced to doing graduate studies at KTH
    • Mats Boij : "Modified Linear Recurrence Sequences "
  • (1990/Laksov).
  • Advanced to doing graduate studies at KTH
    • Lars Ernström : " "
  • (1989/Laksov).
  • Advanced to doing graduate studies at KTH/MIT
    • Karin Westin : ""
  • Versions of the Nullstellen theorems over non-algebraically closed fields are considered (19xx/Laksov).

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    Sidansvarig: Roy Skjelnes