Research of Tomaž Košir
Research interests
My
interests are in applications of algebra (commutative and associative) and
algebraic geometry to the problems in linear algebra and partial differential equations.
Major part of my published work is in multiparameter spectral theory, but I am
also interested in a number of related problems in the areas of commuting
matrices, commuting varieties, representations of commutative zero-dimensional
algebras, matrix groups and semigroups,
and others. My interests were greatly influenced by concrete applied
problems. I also help in developing numerical algorithms that can be applied to
such problems.
Editorial work:
I am a member of the editorial board of the Rendiconti dell’Istituto di
Matematica dell’Università di
Recent Publications:
- with A. Buckley: Plane
curves as Pfaffians, submitted.
- with P. Oblak: On pairs of commuting nilpotent matrices. Transform.
Groups 14 (2009),
no. 1, 175-182. pdf
- with K. Cvetko-Vah, D. Kokol-Bukovšek, G.
Kudryavtseva, Y. Lavrenyuk,
and A. Oliynyk:
Semitransitive and transitive subsemigroups of the inverse symmetric semigroups, Semigroup Forum 78
(2009), no. 1, 138-147.
- with
J. Bernik, R. Drnovšek, D.
Kokol-Bukovšek, and M. Omladič: Reducibility and triangularizability
of semitransitive operator spaces,
- with J.
Bernik, R.
Drnovšek, L.
Livshits, M.
Mastnak, M. Omladič, and H. Radjavi: Approximate permutability of traces on semigroups of matrices, Oper. Matrices 1
(2007), no. 4, 455—467. pdf
- with A. Buckley:
Determinantal representations of smooth cubic surfaces, Geometria Dedicata 125 (2007), 115-140. pdf
- with D. Kokol Bukovšek,
N. Novak, and P. Oblak: Products of
commuting nilpotent operators, Electronic Journal of Linear Algebra
16 (2007), 237-247. pdf.
- with A. Buckley:
Construction of self-adjoint determinantal representations of smooth cubic
surfaces, Proceedings of EUROSIM 2007,
- with
B.A. Sethuraman we wrote an appendix to J. Holbrook
and J. P. Schoch: Moving zeros among matrices, Linear Algebra and its Applications 424 (2007), 83-95, pdf
- Semitransitivity Working Group at LAW'05, Bled: Semitransitive subspaces of
matrices, Electronic Journal of
Linear Algebra 15, (2006), 225-238. pdf
- with B.A. Sethuraman: A
Groebner basis for the 2 x 2 determinantal ideal mod t
, Journal of Algebra 292 (2005), 138-153, pdf.
Related S-polynomial computations are available following this link.
- with B.A. Sethuraman: Determinantal Varieties Over Truncated
Polynomial Rings, Journal of Pure and Applied Algebra 195 (2005),
75-95. pdf
- with J. Bernik, R. Drnovšek,
T.J. Laffey, G. MacDonald, R. Meshulam, M.
Omladič, and H. Radjavi: Common fixed points and common eigenvectors
for sets of matrices, Linear and
Multilinear Algebra 53 (2005), 137-146. pdf
- with P.
Binding: Root Vectors for Geometrically Simple Two-Parameter
Eigenvalues, Transactions Amer. Math. Soc. 356 (2004), 1705-1726. pdf
- Root Vectors for Geometrically
Simple Multiparameter Eigenvalues, Integr. Eq. Op. Theory 48
(2004), 365-396. pdf
- with R. Drnovšek:
Irreducible Operator Semigroups such that AB and BA are Proportional, Linear Algebra and its Applications.
Special Issue in honor of Heydar Radjavi. Vol. 383 (2004),
113-118. pdf
- with M.E. Hochstenbach
and B. Plestenjak:
A Jacobi-Davidson Type Method for the Two-Parameter
- with J. Bernik, R.
Drnovšek, M. Omladič, and H. Radjavi: Irreducible
semigroups of matrices with eigenvalue one, Semigroup Forum 67
(2003), 271-287.
- The Cayley-Hamilton Theorem and
Inverse Problems for Multiparameter Systems, Linear Algebra and its
Applications 367 (2003), 155-163. pdf
- with B. Plestenjak: On stability
of invariant subspaces of commuting matrices, Linear Algebra and
its Applications 342 (2002),
133-147. pdf
Link to the
complete bibliography
Help in organizing meetings
IN ALGEBRA:
We are
organizing a Linear Algebra Workshop (LAW) in
IN FINANCIAL MATHEMATICS:
I also helped organizing the Summer school in financial
mathematics in
IN ALGEBRAIC GEOMETRY:
With
researchers from the Universities of Trieste and