On Tuesday 17 December and Wednesday 18 December, I organize a workshop on the occasion of the thesis defence of Qizheng YIN.
There is no registration fee but we do ask that you register as a participant. (Clicking this link will open a new tab.) Only this way we know how many people to expect. For registered participants, lunches are provided.
The lectures are given in the Huygens Building. On Tuesday 17 December, the lectures are in room HG01.028 (first floor). On Wednesday 18 december, the lectures are in room HG00.071. (ground floor). Address of the Huyghens Building: Heyendaalseweg 135, Nijmegen. The Huygens building is approximately 250 meters from train station Nijmegen Heyendaal. From Nijmegen central station it can also be reached by taking bus number 10, which takes only 5 minutes to the University. (Recommended stop: Huygensgebouw.) See also the map of the campus.
The thesis defence of Qizheng Yin is on Wednesday 18 December 2013 at 10:30am. This takes place in the Aula, address: Comeniuslaan 2, 6525 HP Nijmegen.
| 10:30-11:00 | Welcome with coffee and tea |
| 11:00-12:00 |
Gerard van der Geer (Amsterdam),
Cycle classes of a stratification on the moduli of K3 surfaces
Abstract: We calculate the cycle classes of the strata defined by
the height and Artin number on the moduli of K3 surfaces in positive
characteristic. The formulas generalize Deuring's famous formula
for the number of supersingular elliptic curves.
This is joint work with Torsten Ekedahl.
|
| 12:00-13:00 | Lunch |
| 13:00-14:00 |
Dan Petersen (Zürich),
Counterexamples to the Gorenstein conjecture
Abstract: Faber and Pandharipande formulated a "trinity" of conjectures regarding the tautological rings of moduli spaces of curves. Specifically, they conjectured that we have Poincaré duality in the tautological ring of the space of n-pointed genus g curves that are either (i) stable, or (ii) of compact type, or (iii) with rational tails. I will explain that there are now two known counterexamples to this conjecture: in the stable case, it fails when g=2 and n is at least 20 (this is due to joint work with Orsola Tommasi), and in the compact type case, it fails when g=2 and n is at least 8.
|
| 14:00-14:30 | Coffee break |
| 14:30-15:30 |
Arnaud Beauville (Nice),
Surfaces with maximal Picard number
Abstract: For a smooth complex projective variety, the rank ρ of the
Néron-Severi group is bounded by the Hodge number h1,1. Varieties with ρ = h1,1 have interesting properties, but are rather sparse, particularly in dimension 2. I will discuss
a number of examples, in particular those constructed from curves with special Jacobians.
|
| 15:30-16:00 | Coffee break |
| 16:00-17:00 |
Qizheng Yin (Nijmegen),
Tautological cycles on curves and Jacobians
Abstract: We build connections between two notions of tautological rings: one for the moduli space of curves (following Mumford, Faber, etc.), the other for the Jacobian of a curve (following Beauville, Polishchuk, etc.). We then explore a number of consequences on both the curve and Jacobian sides.
|
| 10:30-11:30 | Thesis defence Qizheng Yin (Location: Aula) |
| 11:30-13:00 | Reception and Lunch |
| 13:00-14:00 |
Lenny Taelman (Leiden),
Characteristic classes for families of genus one curves
Abstract: In many ways the stack M1 of curves of genus one (without a
chosen section) is a rather wild object. Yet it is an Artin stack and
its cohomology has a surprisingly elegant description in terms of
modular forms. In this talk I will discuss the computation of its
cohomology, and relate some of the cohomology classes to various
geometric constructions with curves of genus one.
|
| 14:00-14:30 | Coffee break |
| 14:30-15:30 |
Claire Voisin (École Polytechnique),
Infinitesimal invariants for cycles modulo algebraic equivalence
and 1-cycles on Jacobians
Abstract: We describe infinitesimal methods allowing to
decide whether, given a relative cycle Z in a family
X → T, the fiber Zt is not algebraically equivalent to 0
modulo torsion in Xt, for t a very general point of the base T.
We apply this to the family of Jacobians J → T associated to a family of
curves C → T, and to the relative
1-cycle Z of J (well defined up to translation, hence modulo algebraic
equivalence) determined by an embedding of C into J; this gives new
results on the length of the Beauville decomposition
of the 1-cycle Zt of Jt.
|
| 15:30-16:00 | Coffee break |
| 16:00-17:00 |
Sergey Shadrin (Amsterdam),
Double ramification cycles on the moduli space of curves
Abstract: Double ramification cycles are defined as the push-forwards of
the virtual fundamental classes of the stable maps to P1 relative to
two points. I'll make a short survey of recent results and conjectures
about this cycles and will show how they can be used for various
computations in the tautological ring of the moduli space of curves.
The talk will follow the lines of my joint works with A. Buryak, L. Spitz,
and D. Zvonkine.
|
For further information, please contact Ben Moonen, b.moonen at science.ru.nl, or +31 (0)24 3653220. We hope to see you in December!
We gratefully acknowledge the financial support of the IMAPP of Radboud University Nijmegen and of the Foundation Compositio Mathematica.
