Schedule
Thursday, 30.01.2020
(lecture hall 1101b305)
Time  Speaker  Title 

14:15  15:15  Kęstutis Česnavičius (Orsay)  Purity for flat cohomology 
15:15  15:45  Coffee break  
15:45  16:45  Marc Paul Noordman (Groningen)  Autonomous first order differential equations 
17:00  18:00  Khazhgali Kozhasov (TU Braunschweig)  On the number of critical points of a real form on the sphere 
19:00  Conference Dinner at restaurant Mikado, Schmiedestr. 3 
Friday, 31.01.2020
(lecture hall 1101b305)
Time  Speaker  Title 

09:00  10:00  Benjamin Schmidt (LU Hannover)  Derived Categories and the Genus of Curves 
10:00  10:30  Coffee break  
10:30  11:30  Andrea Petracci (FU Berlin)  Smoothing toric Fano 3folds 
11:45  12:45  HansChristian Graf v. Bothmer (Hamburg)  Prelog ChowRings 
12:45  14:00  Lunch break  
14:00  15:00  Bruno Klingler (HU)  On the Zariski closure of the positive Hodge locus 
15:00  15:30  Coffee break  
15:30  18:00  Retirement party  for Wolfgang Ebeling with talks by Michael Lönne (Bayreuth) and Sabir GuseinZade (Moscow) 
Abstracts

Prelog ChowRings
HansChristian Graf v. Bothmer (Hamburg)

Purity for the Brauer group of singular schemes
Kęstutis Česnavičius (Orsay)
For regular Noetherian schemes, the cohomological Brauer group is insensitive to removing a closed subscheme of codimension ≥ 2. I will discuss the corresponding statement for schemes with local complete intersection singularities, for instance, for complete intersections in projective space. Such purity phenomena turn out to be low cohomological degree cases of purity for flat cohomology. I will discuss the latter from the point of view of the perfectoid approach to such questions. The talk is based on joint work with Peter Scholze.

On the Zariski closure of the positive Hodge locus
Bruno Klingler (HU Berlin)
Given a variation of Hodge structures V on a smooth complex quasiprojective variety S, its Hodge locus is the set of points s in S where the Hodge structure Vs admits exceptional Hodge tensors. A famous result of Cattani, Deligne and Kaplan shows that this Hodge locus is a countable union of irreducible algebraic subvarieties of S, called the special subvarieties of (S,V). In this talk I will describe the geometry of the Zariski closure of the union of the positive dimensional special subvarieties. Joint work with Ania Otwinowska.

On the number of critical points of a real form on the sphere
Khazhgali Kozhasov (TU Braunschweig)
It is wellknown that a generic real symmetric matrix of size n has exactly n real eigenvalues. Equivalently, a generic real quadratic form in n variables restricted to the unit sphere S has exactly n critical points. If p is a real form (homogeneous polynomial) of degree d≥3, the number C(p) of critical points of its restriction to the sphere S is not generically constant. In my talk I will describe typical values of the number C(p) that a generic p can attain.

Autonomous first order differential equations
Marc Paul Noordman (Groningen)
Autonomous algebraic first order differential equations (i.e. differential equations of the form P(u, u') = 0 for P a polynomial with constant coefficients) can be interpreted as rational differential forms on an algebraic curve. In this talk, based on joint work with Jaap Top and Marius van der Put, I will explain how this perspective clarifies the possible algebraic relations between solutions of such differential equations. In particular, we will see that there are very few algebraic relations between distinct nonconstant solutions of the same differential equation, unless that differential equation comes from a onedimensional group variety.

Smoothing toric Fano 3folds
Andrea Petracci (FU Berlin)
In this talk I will show how to construct smoothings of toric Fano 3folds with Gorenstein singularities starting from some combinatorial input on their associated polytopes. This result extends the toric dictionary between algebraic geometry and the combinatorics of polytopes. Moreover, this result fits into the context of Mirror Symmetry for Fano varieties. This is joint work with Alessio Corti and Paul Hacking.

Derived Categories and the Genus of Curves
Benjamin Schmidt (LU Hannover)
A 19th century problem in algebraic geometry is to understand the relation between the genus and the degree of a curve in complex projective space. This is easy in the case of the projective plane, but becomes quite involved already in the case of three dimensional projective space. I will talk about generalizing classical results on this problem by Gruson and Peskine to other threefolds. This includes principally polarized abelian threefolds of Picard rank one and some Fano threefolds. The key technical ingredient is the study of stability of ideal sheaves of curves in the bounded derived category.