| 23. August |
Algebra lunch and planning session at 12.00
|
| 30. August |
Algebra lunch
|
NB! 2. September
Seminar room 534
14.15-15.15 |
Roland Abuaf (Grenoble)
The
singularities of the projective dual: some new perspectives
Abstract:
The study of the singularities of the projective dual
apparently started in the 80's with Dimca's celebrated
formula. Since then, Parusinski, and after Aluffi-Cukierman, found
closed formulas to express the multiplicity of any point in the
dual of a smooth projective variety. Unfortunately, these formulas
require technical computations in the Chow ring of the variety,
which often seem impossible to be carried out. In this talk, I
will discuss some recent results that decribe the multiplicity of a
point in the dual in terms of 'simple and geometric' invariants of
its tangency locus. The techniques developed to prove these results
seem to be very promising and could be applied in order to work out
an interesting conjecture stated by Ranestad and Sturmfels.
|
| 6. September |
Algebra lunch
|
NB! 7. September
CMA Guest Lecture
Seminar room B1036
10.15-11.00 |
CANCELLED
David Eisenbud (Berkeley)
Vector bundles and free resolutions
Abstract:
Free resolutions of graded modules over polynomial rings are a way of
generalizing the solutions of a system of linear equations over a field.
Their study was initiated by David Hilbert as a way of obtaining
invariants of projective algebraic varieties. Vector Bundles on projective
spaces are a different way of encoding the solution of systems of linear
equations with varying coefficients. A group of remarkable conjectures
about free resolutions by Boij and Soederberg in 2006 suggested a novel
way of thinking about graded modules and set off a wave of activity. The
conjectures have now been proven, and themselves greatly extended. The
proofs have led, among other things, to a still mysterious duality between
a description of the numerical invariants that are possible for the free
resolution of a graded module on one side, and the numerical invariants of
the cohomology of a vector bundle on projective space on the other. As a
result we now have far more precise understanding of both these
geometrically important objects.
I will try to give an accessible description of this new work.
|
| 13. September |
Kristian Ranestad (Oslo)
Grassmannembeddinger av Fanovarieteter av genus 10
Sammendrag:
Jeg vil vise hvordan en Fano 4-fold av genus 10 er et lineært snitt av
G(2,7) og av G(3,6) og gi noen anvendelser av dette.
Resultatene er blitt til i samarbeid med Michal Kapustka.
|
| 20. September |
John Christian Ottem (Oslo/Cambridge)
Elliptiske K3-flater, GIT og Cox ringer
Sammendrag:
Coxringen til en projektiv varietet X generaliserer Cox' homogene
koordinatring for toriske varieteter og kan brukes til å uttrykke X som en
GIT-kvotsient av en kvasiaffin varietet med en torus. I tilfellet der X er en K3
flate med to elliptiske pensler, kan denne realisasjonen brukes til å studere
resolusjonen til Coxringen eksplisitt.
|
| 27. September |
Kristian Moi (Oslo)
E.C.(Etale Cohomology)-seminar, part 1
Etale morfier og topologi/Den lokale ringen (Hensel)/Def. av etale
kohomologi
|
NB! 27. September
4.15p.m., VB,
Science Library-'kick-off' |
Marcus du Sautoy (Oxford)
Symmetry: reality's riddle
|
| 4. October |
Arne B. Sletsjøe (Oslo)
E.C.(Etale Cohomology)-seminar, part 2
Knipper og knippekohomologi for etale topologien
|
| 11. October |
Peter Arndt (Oslo)
E.C.(Etale Cohomology)-seminar, part 3
H^1(X_et, -)
|
| 18. October |
María-Cruz Fernández-Fernández (Sevilla/Oslo)
On the irregularity of hypergeometric D-modules
Abstract:
Hypergeometric D-modules were introduced by Gelfand, Graev,
Kapranov and Zelevinsky and they arise naturally from toric
varieties. They are systems of linear partial differential equations
in several complex variables associated with a full rank matrix A with
integer entries and a vector of complex parameters. In this talk, we
will study the irregularity of such a system by describing their
Gevrey series solutions at singular points along coordinate subspaces
in a combinatorial way.
|
| 25. October |
Jan Christophersen (Oslo)
E.C.(Etale Cohomology)-seminar, part 4
Beregninger og sammenlikningsteoremer
|
| 1. November |
Geir Ellingsrud (Oslo)
E.C.(Etale Cohomology)-seminar, part 5
Etale kohomologi av kurver
|
| 8. November |
Lars Halvard Halle (Oslo)
E.C.(Etale Cohomology)-seminar, part 6
Tate formodningen I
|
| 11.-12. November, in Bergen |
Nasjonalt algebramøte
|
| 15. November |
Lars Halvard Halle (Oslo)
E.C.(Etale Cohomology)-seminar, part 7
Tate formodningen II
|
| 22. November |
Algebra lunch
|
| 29. November |
Nathan Ilten (Bonn)
Partial smoothings of projective toric Fano varieties
Abstract:
K. Altmann has shown how to construct homogeneous deformations of
affine toric varieties using combinatorial techniques. In joint work
with R. Vollmert, we describe the fibers of these deformations, in
particular, the singularities which occur. Following an idea of A.
Mavlyutov, I show how in special situations we can find a flat family
simultaneously inducing several of these homogeneous deformations.
Combining this with our description of the fibers leads to a
sufficient condition for a projective toric Fano variety to have a
smoothing in some fixed codimension.
|
| 6. December |
Elisa Postinghel (Oslo)
Toric degenerations of toric surfaces and k-secant degree
Abstract:
There is a long tradition within algebraic geometry that studies the
secant varieties. Let X in P^r be the projective toric surface
associated to any plane polytope P. We show how informations about the
variety of k-secant (k-1)-planes to X can be derived from planar toric
degenerations of X, which correspond to regular triangulations D of P.
A lower bound to the k-secant degree, by means of the combinatorial
geometry of D, is established for k=2,3. This improves a result by B.
Sturmfels and S. Sullivant.
|
