Ludmil Katzarkov (The University of Vienna) visited IM PAN on February 23 - 24, 2012. He gave three lectures at the IMPANGA seminar. Here are the titles and abstracts:
1) From Higgs Bundles to Stability Conditions.
In this talk we will introduce a new stablity Hodge Structures. We explain
full analogy with Nonabelian Hodge theory. We also give several examples.
2) On Spectra of Derived Categories.
3) On the Shafarevich Conjecture.
We show that the universal covering of smooth projective variety with linear fundamental group is holomophically convex. We suggest ways of generalizing
this result.
Program of Impanga on February 23/24
IM PAN, room 322:
23.02.
17:00 Katzarkov 1.
18:30 P. Krasoń: On arithmetics in Mordell-Weil groups of abelian varieties (joint with G.Banaszak).
We will describe the problem of detecting linear dependence of points in Mordell-Weil groups of abelian varieties. This is done via reduction maps. We determine the sufficient conditions for the reduction maps to detect linear dependence in A(F). We also show that our conditons are very close to be or perhaps are the best possible. In particular, we try to determine the conditions for detecting linear dependence in Mordell-Weil groups via finite number of reductions. The methods combine applications of transcedental, $l$-adic and mod $v$ techniques.
24.02.
9:00 Katzarkov 2.
11:00 A. Langer: Nef line bundles over finite fields.
14:00 M. Michałek: Plethysm, representations of GL(n) and secants of Grassmannians.
We will present an effective approach towards determining cubics vanishing on the (second) secant of any Grassmannian. We will use the representation theory of GL(n), in particular giving the exact decomposition of the space of cubics in the ideal of the secant of the Grassmannian. This is related to some problem of plethysm. Our approach shows
interesting connections with some combinatorial objects, like Pascal matrices.
15:30 Katzarkov 3.
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(Last modified on 25. 02.2012.)