| 11. January |
Algebra lunch and planning session
|
| 18. January |
Kristian Ranestad (Oslo)
The convex hull of a space curve
Abstract:
The boundary of the convex hull of a compact algebraic
curve in real 3-space defines a real algebraic surface. For general
curves, that boundary surface is reducible, consisting of tritangent
planes and a scroll of stationary bisecants. In recent work with
Sturmfels we extend classical formulas to express the degree of this
surface in terms of the degree, genus and singularities of the
curve. For rational curves we present methods for computing their
defining polynomials, and exhibit a range of examples.
|
| 25. January |
Lunch
|
| 1. February |
Lunch (and discussing the seminar series)
|
| 8. February |
Lunch
|
| 15. February |
Lunch
|
| 22. February |
Michal Kapustka (Oslo)
A duality for K3 surfaces of genus 10
|
| 1. March |
Seminar series on Moduli Stacks, talk 1
John Christian Ottem (Oslo)
Introduction and examples
|
| 8. March |
Lunch
|
| 15. March |
Seminar series on Moduli Stacks, talk 2
Jan Christophersen (Oslo)
Etale topology and algebraic spaces
|
| 22. March |
Seminar series on Moduli Stacks, talk 3
Arne B. Sletsjøe (Oslo)
Groupoids and stacks I
|
| 29. March |
Easter break
|
| 5. April |
Easter break
|
| 12. April |
Seminar series on Moduli Stacks, talk 4
Daniel Larsson (HiO)
Groupoids and stacks II
|
| 19. April |
Lunch
|
| 26. April |
Seminar series on Moduli Stacks, talk 5
Geir Ellingsrud (Oslo)
Applications of stacks to moduli questions
|
| 3. May |
Anthony Iarrobino (Northeastern University)
Commuting nilpotent matrices and Artin algebras
Abstract
|
| 10. May | Helge Maakestad
On
the annihilator ideal of a highest weight vector
Abstract:
Let E be a finite dimensional vector space over an algebraically
closed field K of characteristic zero and let G=SL(E) be the special
linear group on E. Let V be an irreducible finite dimensional
G-module with highest weight vector v and highest weight \lambda. Let
ann(v) in U(sl(E)) be the left annihilator ideal of v and let ann_l(v)
be its canonical filtration. In this talk I will construct a
complement
U_l(sl(E)) = U_l(n)\oplus ann_l(v)
of the
annihilator ideal ann_l(v). The complement is given by the universal
enveloping algebra of a sub Lie algebra n=n(E_*) in sl(E) depending on
a flag E_* in E determined by the highest weight \lambda for V. I will
use the complement U_l(n) to define a canonical basis for U_l(sl(E))v
- the canonical filtration for V. I will also calculate the dimension
of U_l(sl(E))v.
The canonical filtration U_l(sl(E))v is related to
the fiber of the jet bundle J_l(L)(e) where L in Pic^G(G/P) and P in G
is a parabolic subgroup. There is an isomorphism
J_l(L)(e)^*
\cong U_l(sl(E))v
of P-modules.
If time permits I will discuss
the relationship between the canonical filtration, jet bundles and
discriminants of linear systems on flag schemes. To the discriminant
of a linear system on any flag scheme one may associate a double
complex - the discriminant double complex - and to determine this
complex one needs information on the jet bundle. It is hoped the
relationship between the jet bundle and the canonical filtration will
give enough information on the jet bundle to be able to determine if
the discriminant double complex may be used to construct a resolution
of the ideal sheaf of the discriminant.
|
| 17. May |
Bank holiday
|
| 24. May |
Bank holiday
|
| 31. May |
Lunch
|
| 7. June |
Abdul Mohammad (Oslo)
Smooth rational surfaces of degree eleven and sectional genus
eight in the projective fivespace
|
| 14. June |
Lunch
|
| 21. June |
Lunch
|
