
Intercity Number Theory SeminarMarch 16, CWI Amsterdam. room L01612:0012:45  Hendrik Lenstra, The transfer map and determinants Abstract. In 1970, Cartier defined a map that generalizes the transfer map
from group theory. We review his definition, and prove that in
certain situations his map coincides with a determinant map. This
result has recently been applied to local fields, and there is a
second application to groups generated by pseudoreflections.  13:4514:30  Hendrik Lenstra, Groups generated by pseudoreflections Abstract. In the lecture we shall define the notion of a pseudoreflection
with respect to a finite collection of onedimensional subspaces
of a finitedimensional vector space over a field. The group
generated by these pseudoreflections can be seen as an algebraic
group. Cartier's transfer map plays a role in its study.  14:4515:30  Maarten van Pruijssen, Multiplicity free systems Abstract. A multiplicity free system is a triple (G,K,F) where G is a simple complex reductive group, K a connected reductive subgroup of G and F a face of the positive Weyl chamber of K such that the following holds: any irreducible Krepresentation of highest weight μ in F occurs at most once in the restriction to K of every irreducible Grepresentation. Any Gelfand pair (G,K) together with the face F={0} gives an example. In this talk we give a classification of the multiplicity free systems (G,K,F) where (G,K) is of rank one and we discuss (very briefly) an application in the branche special functions.  15:4516:30  JanHendrik Evertse, Effective results for unit equations over finitely generated domains Abstract. Let A=Z[x_{1},...,x_{r}] be an integral domain which is finitely
generated over Z. We allow A to contain both algebraic and
transcendental elements.
Denote by A* the unit group of A. We deal with socalled
unit equations in two unknowns
(1) ax+by=c in x,y from A*
where a,b,c are nonzero elements of A.
First Siegel, Mahler and Parry in special cases, and finally Lang in 1960
for arbitrary finitely generated domains,
proved that Eq. (1) has only finitely many solutions.
Their proofs are ineffective in the sense that they do not provide a method
to determine the solutions of (1) in principle.
In 1979, Györy gave an effective proof of the Siegel...Lang
theorem, but only in the special case that A is contained in the
algebraic
closure of Q. His proof uses estimates of Baker and Coates on
lower bounds for linear forms in logarithms.
In 1984, Györy extended his effective proof to a restricted class
of integral domains which contain also transcendental elements.
Recently, Kálmán
Gyöy and I gave a general effective finiteness proof for Eq. (1)
for arbitrary finitely generated domains
which are explicitly given in a welldefined sense.
In my lecture I will present our new results. 

Intercity number theory seminarApril 13, Eindhoven. Auditorium building, room 1.
This meeting is the day after the
NMC 2012 featuring the Beeger lecturer.
There will be tea at 15:20.11:0011:50  Yuri Bilu, Effective Diophantine analysis on modular curves Abstract. I will speak on two effective methods in Diophantine analysis: Baker's
method and Runge's method, with a special emphasize to modular curves.
The talk is partially based on a joint work with Pierre Parent and
Marusia Rebolledo.
 12:0012:50  Mohamed Barakat, ExtComputability of the category coherent sheaves on a projective scheme. Abstract. In this talk I will present an approach to the computability of the
category
of coherent sheaves on a projective scheme which implies the computability of
long
exact sequences, several spectral sequences, modules of twisted global sections,
higher sheaf cohomology and Ext groups. This approach uses some new categorical
tools
that came out of an abstract computer implementation of the relevant algorithms.
 13:3014:20  Viktor Levandovskyy, Stratification of affine spaces, arising from BernsteinSato polynomials Abstract. Over the field of complex numbers, the famous functional
equation of J. Bernstein involves an important object, related to
the given hypersurface at a given point. This is a
monic univariate polynomial, called the local BernsteinSato polynomial.
There are remarkable connections between singularities
and the local/global BernsteinSato polynomials of a hypersurface.
An algorithm to compute the finite stratification of an affine space into
the strata, such that the local BernsteinSato polynomial of a given hypersurface
is constant on each stratum. Moveover, to each stratum one can naturally attach a
holonomic module over Weyl algebra, and
the sum of these gives a wellknown module, directly related to the hypersurface.
Following Budur, Mustata, and Saito, this approach can be generalized
to the case
of an affine variety.
 14:3015:20  Emil Horobet (Universitatea BabesBolyai), Basic algebra of a skew group algebra Abstract. We give an algorithm for the computation of the basic algebra Morita
equivalent to a skew group algebra of a path algebra by obtaining formulas
for the number of vertices and arrows of the new quiver.
 15:4016:30  Daniel Robertz, Implicitization of Parametrized Families of Analytic Functions Abstract. The correspondence between solution sets of systems of algebraic
equations and radical ideals of the affine coordinate ring is
fundamental for algebraic geometry. This talk discusses aspects of
an analogous correspondence between systems of polynomial differential
equations and their analytic solutions. Implicitization problems for
certain families of analytic functions are approached in different
generality. While the linear case is understood to a large extent,
the nonlinear case requires new algorithmic methods, e.g., the use of
differential inequations, as proposed by J. M. Thomas in the 1930s.


RISC / Intercity number theory seminarApril 27, CWI Amsterdam. RoomL016. This day is focused on fully homomorphic encryption.12:0012:45  Vadim Lyubashevsky, Ideal Lattices and FHE, part 1  13:4514:30  Vadim Lyubashevsky, Ideal Lattices and FHE, part 2 Abstract. In the first part of the talk, I will cover the RingLWE problem (Learning with Error over Rings), its
hardness, the equivalence of its search and decision versions, and explain
what little is known about the hardness of problems in ideal lattices. In
the second part, I will present two (similar) constructions of
encryption schemes based on RingLWE. Then I will present the
NTRU
cryptosystem and sketch how it can be easily modified to become a
"somewhathomomorphic" encryption scheme that supports several additions
and multiplications, and then finally present the "bootstrapping" technique
that converts "somewhathomomorphic" schemes that meet certain requirements
into fullyhomomorphic ones. (NB: the NTRUbased scheme that I will
present does not meet these requirements, but can be modified to meet them
using recent techniques.)
 14:4515:30  Erwin Dassen, Brakerski's scale invariant homomorphic scheme Abstract. In a recent preprint, Brakerski introduced what he called a "scale invariant" homomorphic scheme.
The name comes from the fact that, contrary to other schemes, its homomorphic properties depend
only on the modulustonoise ratio. Furthermore, while in previous works noise would grow
quadratically with each multiplication, here it grows linearly. The aim of the talk is to describe
this scheme in detail.
 15:4516:30  Alice Silverberg, Some Remarks on Latticebased Fully Homomorphic Encryption Abstract. The talk will include an overview of some latticebased Fully Homomorphic Encryption schemes such
as those proposed by SmartVercauteren and GentryHalevi. We will also discuss balancing
cryptographic security with ease of decryption, for latticebased FHE schemes.


Intercity Number Theory SeminarMay 11, Leiden. Room 40711:4512:30  Michiel Kosters, Futile algebras Abstract. Let R be a commutative ring and let A be an Ralgebra. Then
A is called Rfutile if it has only finitely many Rsubalgebras. The
problem of classifying futile Ralgebras for a fixed ring R has been
studied before by other people, and this turns out to be more
complicated than one might expect. In this talk we will discuss this
problem in the case where R is a finite ring, a field or Z.  13:3014:15  Andrea Siviero (Leiden), Equidistribution of the Galois module structure of rings of integers with given local behavior Abstract. Let K be a number field and let G be a finite abelian group.
A couple of years ago Melanie Wood studied the probabilities of various
splitting types of a fixed prime in a random Gextension of K. When the number fields are counted by
conductor, she proved that the probabilities are as predicted by a
heuristic and independent at distinct primes.
In the same period Adebisi Agboola studied the asymptotic behavior of the
number of tamely ramified Gextensions of K with ring of integers of fixed
realizable class as a Galois module, proving that an equidistribution
result exists when the extensions are counted by the absolute norm of the
ramified primes of K.
One may wonder if the two distributions of Wood and Agboola are independent.
In this talk I address equidistribution of realizable classes for extensions
with a totally split local behavior at one fixed prime.  14:3015:15  Ronald van Luijk, Density of rational points on Del Pezzo surfaces of degree one. Abstract. The SegreManin Theorem implies that if a Del Pezzo surface of degree
at least three, defined over Q, has a rational point, then the
rational points are Zariski dense on the surface. A result of Manin
yields the same for degree two, as long as the initial point avoids a
specific subset. Similar results for Del Pezzo surfaces of degree one
are meager: they either depend on conjectures, or they are restricted
to small families of surfaces. We will give a sufficient, explicitly
computable criterion for the rational points on a general Del Pezzo
surface of degree one to be dense. This is joint work with Cecilia
Salgado. No prior knowledge about Del Pezzo surfaces will be assumed.
 15:3016:15  Alberto Gioia, On a Galois closure for rings Abstract. Given a finite separable field extension L/K there exists a smallest Galois
extension of K containing L, the Galois closure of L/K. Bhargava and
Satriano generalized this construction to commutative algebras of finite
rank over an arbitrary base ring. We will present their construction and
see some properties. 

Intercity Number Theory SeminarMay 25, Groningen. Bernoulliborg, room 26711:4512:45  Anneroos Everts (Groningen), From finite automata to power series and back again Abstract. Christol's theorem links algebra in an unexpected way with a concept
from computer sciences: a power series over a finite field is algebraic if and
only if its coefficients are generated by a finite automaton. We examined the
proof of Christol's theorem to find answers to the following two questions:
Given a finite automaton with m states, what can we say about the algebraic
degree of the corresponding power series? Conversely, given an algebraic power
series of algebraic degree d and bounded coefficients, can we find a bound on
the number of states of an automaton that generates the power series?In this talk I will explain Christol's theorem and the concept of finite
automata, and give answers to the questions above.  13:3014:30  Paul Helminck (Groningen), Tropical elliptic curves and jinvariants Abstract. Any elliptic curve over the field of complex Puiseux series
has a "tropicalization": an associated tropical curve.
We construct, for any elliptic curve over the field of Puiseux series
that has a jinvariant with negative valuation, a model such
that its tropification is a tropical elliptic curve. Moreover,
we show that the tropical jinvariant of this tropical curve
is minus the valuation of the jinvariant.
Special cases of this were already proven by Markwig,
and similar results were obtained quite recently by
M. Baker and by Sturmfels and Chan.  14:4515:45  Wilke Trei (Carl von Ossietzky University Oldenburg), Elliptic Curve Arithmetic on Vectorized Hardware Platforms Abstract. Parallelization of computational intensive algorithms has always been an
important task in computational number theory. Modern hardware requires
a high onchip parallelization for gaining maximum possible performance.
We discuss several mathematical concepts to implement modular arithmetic
with a focus on elliptic curve scalar multiplication on graphic cards and
present a new performance record for Lenstra's elliptic curve factoring
algorithm on an ordinary personal computer. The resulting implementation
is of high cryptographic interest, for instance it can easily be modified to
speed up intermediate factorization in the number field sieve algorithm.  16:0017:00  Arthemy Kiselev (Groningen), The deformation quantisation problem for multiplicative structures on noncommutative jet spaces. Abstract. We outline the basic notions and concepts from the differential
calculus up to the Schouten bracket on a class of noncommutative jet
spaces, and then we pose the deformation quantisation problems for the
nonassociative but commutative multiplications in the two spaces of
differential functions (i.e., the noncommutative fields) and integral
functionals (i.e, the Hamiltonians), aiming to restore the associative
but not commutative starproducts. During the entire talk, the
constructions and reasonings will appeal to the profound properties of a
pair of pants borrowed from the topological closed string theory. 

Intercity Number Theory SeminarJune 8, Utrecht. The lectures are in the Buys Ballot building, the first one in room 001 and the others in room 16111:1512:15  Peter Stevenhagen, Galois groups as arithmetic invariants Abstract. By the work of Neukirch, Uchida and others, we know that number fields K
are completely characterized by their absolute Galois group G_{K}:
if G_{K} and G_{L} are isomorphic as topological groups, then K and L
are isomorphic number fields.
Similar statements hold for the maximal prosolvable quotient of G_{K},
but NOT for the maximal abelian quotient A_{K} of G_{K}.
We focus on this maximal abelian quotient, which admits an explicit
class field theoretical description, and show that there are very
many imaginary quadratic fields having the same "minimal" absolute
abelian Galois group A_{K}.
This is joint work with my student Athanasios Angelakis.  13:0013:30  Frans Oort, Lifting Galois covers of algebraic curves. Abstract. We discuss the question:
Does a pair (C,H) of an algebraic curve C over a field of positive
characteristic and a subgroup H of Aut(C) admit a lift to
characteristic zero?
 We give motivating (counter)examples and general theory.
 Formulate a conjecture.
 Discuss partial results and possible approaches.
This talk serves as an introduction to the talk by Andrew Obus.
[notes.pdf]  13:4514:45  Andrew Obus, Proof of the Oort Conjecture Abstract. Let G be a cyclic group acting on a smooth, proper curve X in
characteristic p. The Oort conjecture claims that X, along with its
Gaction, should lift to characteristic zero. I will discuss a joint
result with Wewers, stating that the conjecture is true subject to a
certain condition on the higher ramification filtrations of the inertia
groups of G at the various points of X. Pop has recently proved
the entire conjecture, by reducing it to our result.  15:1516:15  Eric Delaygue, Integrality of the Taylor coefficients of mirror maps Abstract. I will present an effective criterion for the integrality of the
Taylor coefficients of power series, called mirror maps, which are of
particular interest in Mirror Symmetry Theory. More precisely, I will
give a necessary and sufficient condition for the integrality of the
Taylor coefficients at the origin of formal power series
q_{i}(z)=z_{i} exp(G_{i}(z)/F(z)), with z=(z_{1},...,z_{d}) and where F(z) and G_{i}(z)+log(z_{i})F( z), i=1,...,d are particular solutions of
certain Ahypergeometric systems of differential equations. I will also
explain how this criterion implies the
integrality of the Taylor coefficients of many univariate mirror maps
listed in "Tables of CalabiYau equations" [arXiv:math/0507430v2,
math.AG] by Almkvist, van Enckevort, van Straten and Zudilin. 

BelgianDutch algebraic geometry dayJune 15, Leuven. The lectures will take place in Huis Bethlehem, Schapenstraat 34 in the historical centre of Leuven, within walking distance from the
train station. There will be coffee at 15:00 and 16:30
14:0015:00  Ted Chinburg, Small generators for Sarithmetic groups Abstract. A surprising discovery of H. W. Lenstra, Jr., was
that one can
find generators of small height for groups of Sunits of number fields
once S is moderately large. I will discuss joint work with Matt
Stover on generalizing Lenstra's results from Sunits to the
Sintegral points of linear algebraic
groups. This has applications to finding presentations for such
groups.
 15:3016:30  Mathieu Romagny, Models of groups schemes of roots of unity Abstract. I will explain the construction of a family of models over
O_{K} of the group scheme μ_{pn,K} of p^{n}th roots of unity over a
padic field K. This construction is inspired by work of Sekiguchi and
Suwa in the late nineties. The contemplation of these models in light of
the recent classification of finite flat group schemes by Breuil and Kisin
leads to conjecture that they exhaust all possible models of
μ_{pn,K}. This is joint work with A. Mézard and D. Tossici.  16:4517:45  Mircea Mustaţă, Adjoint line bundles in positive characteristic Abstract. In characteristic zero, adjoint line bundles enjoy many
positivity properties that
all go back to Kodaira's Vanishing Theorem. I will explain how certain
positivity properties
can be recovered in positive characteristic by making use of the
Frobenius morphism.


Intercity Number Theory SeminarSeptember 28, Leiden. Snellius building, first lecture in room B01 and the others in room 405.11:3012:30  David Holmes (Leiden), Explicit Arakelov theory for NéronTate heights on the Jacobians of curves Abstract. The NéronTate height is a positive definite quadratic form on the group of rational points of an abelian variety (the 'MordellWeil group'). The existence of such a form is important, for example appearing in the proof of the finite generation of the MordellWeil group. However, the exact values of the height are important too; the best known example of this is their appearance in the regulator of an abelian variety, in the conjecture of Birch and SwinnertonDyer.
Until recently, techniques to compute the NéronTate height, or approximate it by a 'naive height', we're restricted to curves of genus at most 3. Using Arakelov theory, we can extend this to give an algorithm for both these problems valid for hyperelliptic curves of arbitrary genus, and effective in some situations in genus up to 10.  13:3014:15  Michiel Kosters (Leiden), Generating the rational points of an elliptic curve over F_{q} by looking at xcoordinates Abstract. Let E/F_{q} be an elliptic curve given in Weierstrass form. In this talk we will discuss a theorem which says that the points of E(F_{q}) with xcoordinates in a subgroup of F_{q} of size more than 6 √q generate E(F_{q}), unless one is in a very specific case.  14:4515:45  Maarten Derickx (Leiden), Torsion points on elliptic curves over number fields of degree 5, 6 and 7. Abstract. B. Mazur proved that there are only finitely many groups which can
arise as the torsion subgroup of an elliptic curve over Q. Later
the uniform boundedness conjecture was stated and proved,
generalizing the previous statement to arbitrary number fields in the
following way: "Let d be an integer, then there exist a number B such
that the torsion subgroup of an elliptic curve over a number field of
degree at most d has at most B elements." In particular, Oesterle
managed to show that if p is a prime dividing the order of the torsion
subgroup of an elliptic curve over a number field of degree d then p
is at most (3^{d/2}+1)^{2}. In this talk I will explain how Sage can be used
to improve this bound for small d. Slides.  16:0017:00  Marco Streng (VU Amsterdam), Smaller class invariants for quartic CMfields Abstract. The theory of complex multiplication allows one to construct elliptic
curves with a given number of points. The idea is to construct a curve
over a finite field by starting with a special curve E in
characteristic 0, and taking the reduction of E modulo a prime number.Instead of writing down equations for the curve E, one only needs the
minimal polynomial of its jinvariant, called a Hilbert class
polynomial. The coefficients of these polynomials tend to be very
large, so in practice, one replaces the jinvariant by alternative
'class invariants'. Such smaller class invariants can be found and
studied using an explicit version of Shimura's reciprocity law. The theory of complex multiplication has been generalized to curves of
higher genus, but up to now, no class invariants were known in this
higherdimensional setting. I will show how to find smaller class
invariants using a higherdimensional version of Shimura's reciprocity
law. 

Intercity Number Theory SeminarOctober 19, Utrecht. Uithof, Buys Ballot Lab (BBL) room 169.13:3014:30  Johan Bosman (Utrecht), Ranks of elliptic curves with prescribed torsion over number fields Abstract. Let d be a positive integer, and let T_d be the set of isomorphism
classes of groups that can occur as the torsion subgroup of E(K),
where K is a number field of degree d and E is an elliptic curve over
K. T_1 is known by Mazur's theorem, T_2 is known as well, and for d
equal to 3 or 4, it is known which groups occur infinitely often.We shall study the following problem: given a d <= 4 and a group T in
T_d, what are the possibilities for the MordellWeil rank of E, where
E is an elliptic curve over a number field K of degree d with the
torsion subgroup of E(K) isomorphic to T. For d = 2 and T = Z/13Z or T
= Z/18Z, and also for d = 4 and T = Z/22Z, it turns out that the rank
is always even. This will be explained by a phenomenon we call "false
complex multiplication". This is joint work with Peter Bruin, Andrej Dujella, and Filip Najman.  15:0016:00  Sander Dahmen (Utrecht), Some generalized Fermat equations of signature (p,p,q) Abstract. We discuss how the method of ChabautyColeman and the modular method
can be combined to attack some cases of the Generalized Fermat
equation x^{p}+y^{p}=z^{q}. In particular, we show how to fully solve this
equation (in coprime integers x,y,z) for (p,q) ∈ { (5,7), (5,19),
(7,5) }. This is joint work with Samir Siksek.  16:1517:15  Frits Beukers (Utrecht), Divisibility sequences among linear recurrent sequences Abstract. It is well known, and easy to prove, that the Fibonacci sequence
u_{n} starting with u_{0}=0,u_{1}=1 has the property that u_{m}u_{n} if mn.
Slightly less trivially, the recurrent sequence
u_{n+4}=u_{n+3}4u_{n+2}2u_{n+1}4u_{n}
with starting values 0,1,11 also satisfies u_{m}u_{n} if mn. Following
a question of Hugh Williams we shall go into the background of such
phenomena. 

Springer DayOctober 26, Utrecht. A day in memory of Tonny Springer, see the website for programme and registration. 
Intercity Number Theory SeminarNovember 2, Eindhoven. Room MF 3.119 in the new building called Metaforum.11:0012:00  Patrik Norén (Aalto), Volumes in algebraic statistics Abstract. There are many convex sets in algebraic statistics. Some important statistical models form convex sets and convex polytopes are central when studying toric ideals. It is natural to ask what is the volume of a given convex set. I present a surprisingly simple formula for the volumes of convex hulls of polynomially parameterized curves. This formula is then applied to answer a question by Sullivant and Drton about the volume of certain mixture models.  13:0014:00  Rob Eggermont (Eindhoven), Degree bounds on tree models Abstract. Tree models are families of probability distributions used in modelling the evolution of a number of extant species from a common ancestor. One method to
describe these models is to view a family as a set in an algebraic variety of the
form V^{⊗m}, where m is the number of extant species, and to try to find polynomial
equations that determine its Zariski closure. One important question in this area of
research is the following: Can we bound the degree of the equations we need independently of the number of extant species? In this talk, I will tell a bit more about
these models and will explain how to prove the existence a bound on the degree of
the needed equations by constructing an infinite limit of models of a specic form.  14:2015:20  Piotr Zwiernik (Eindhoven), Graphical Gaussian models and their groups Abstract. Let G be an undirected graph with n nodes. In statistics, given such a
graph, we consider the space S(G) of all symmetric positive definite
matrices with zeros corresponding to nonedges of G. We call S(G) the
Gaussian graphical model. In this talk we describe the stabilizer in
GL_{n}(R) of the model in the natural action of GL_{n}(R) on symmetric
matrices. This has important consequences for the study of the
Gaussian graphical model which I will discuss in the second part of
the talk.
(joint work with Jan Draisma and Sonja Kuhnt)  15:2016:20  Jan Draisma (Eindhoven), Maximum likelihood duality for determinantal varieties Abstract. In the recent preprint
arXiv:1210.0198
Hauenstein, Rodriguez, and Sturmfels discovered a conjectural
bijection between critical points of the likelihood function on the
complex manifold of matrices of rank r and cricital points on the
complex manifold of matrices of corank r1. I'll discuss a proof of
that conjecture for rectangular matrices and symmetric matrices.
(Joint work with Jose Rodriguez.) 

Intercity Number Theory SeminarNovember 9, Groningen. Bernoulliborg, room 26711:4512:45  Afzal Soomro (Groningen), Maximal curves of genus one and two, and twists Abstract. We discuss the data (restricted to genus one and two) that can be found
on the website www.ManyPoints.org maintained by Howe, Ritzenthaler, Van der Geer and others.
We also describe a construction of Howe, Leprevost, and Poonen which gives
an explicit genus two curve over F_{q} having q+1+2t rational points, given an
elliptic curve over F_{q} having q+1+t points.
 13:3014:30  Osmanbey Uzunkol (Oldenburg), Theta functions and class fields Abstract. I am going to talk about the construction of some explicit class
fields using special values of quotients of theta functions, theta
identities, and the reciprocity law of Shimura together with some
applications of this construction.  14:4515:45  Ane Anema (Groningen), Field extensions over which an elliptic curve reaches the Hasse bound Abstract. Given an elliptic curve E over a finite field k, we discuss the problem of determining
the finite extensions K/k such that #E(K) reaches the Hasse bound on the number of rational points.  16:0017:00  Max Kronberg (Oldenburg), Torsion subgroup of two dimensional abelian varieties with real multiplication Abstract. The group of Krational points of an abelian variety splits into the torsion part and the free part. We are interested in the first of these two parts. While the question of the torsion structures for one dimensional abelian varieties, i.e. elliptic curves, over the rational numbers is completely settled by a result of B. Mazur, for higher dimensional abelian varieties the situation is completely unknown.Since the Siegel moduli space for abelian varieties of dimension two is three dimensional, we restrict to the subspace of abelian varieties with real multiplication (RM), i.e. with an embedding O_{K}→End(A). These varieties arise as simple factors of the jacobian J_{0}(N) of the modular curve X_{0}(N), so this class is of great interest, for example to study the rank of elliptic curves. The moduli space for this class of abelian varieties is given by the Hilbert moduli space which is only two dimensional. Unfortunately the machinery developed by Mazur crucially depends on the fact, that the moduli problem of elliptic curves with a subgroup of order N has a one dimensional moduli space. So it is impossible to expand his results to higher dimensions. The actual approach is to restrict to a one dimensional family of hyperelliptic curves of genus two with real multiplication by ζ_{5}+ζ_{5}^{1} constructed by Tautz, Top and Verberkmoes. The next step would be to extend this approach to the two parameter family of the same objects constructed by Mestre. 

Intercity Number Theory SeminarNovember 16, VU Amsterdam. The first lecture is in F640 of the W&N building, the other lectures are in MFFG1, in the basement of the medical sciences building.11:3012:30  Rob de Jeu (VU Amsterdam), The syntomic regulator for K_4 of curves Abstract. Let C be a curve defined over a discrete valuation field of characteristic zero where the residue field has positive characteristic. Assuming that C has good reduction over the residue field, we compute a certain padic ("syntomic") regulator on a certain part of K_{4}^{(}3) of the function field of C. The result can be expressed in terms of padic polylogarithms and Coleman integration, or by using a trilinear map ("triple index'') on certain functions. This is joint work with Amnon Besser.  13:3014:30  James Lewis (University of Alberta), Regulators of Algebraic Cycles Abstract. This talk concerns the cycle class map from the higher Chow groups
to Deligne cohomology, for a smooth projective variety defined over a subfield
of the complex numbers. One construction of this map, based on the
work of Kerr/Lewis/MuellerStach, makes use of the cubical
description of the Chow groups; however we also explain the map in terms of Bloch's
original formulation of his higher Chow groups (joint work with Matt
Kerr). We illustrate an example situation where Beilinson rigidity translates to a functional equation for the dilogarithm  14:4515:30  FrançoisRenaud Escriva (VU Amsterdam), Point counting and cup product computations Abstract. Kedlaya in 2001 published a point counting algorithm for
hyperelliptic curves over finite fields that is based on
MonskyWashnitzer cohomology. His method, and the extensions by others
to a larger class of curves, all rely strongly on the particular shape
of the equation of the curves. In this talk we present a method that can
deal with very general curves. This is joint work with Amnon Besser and
Rob de Jeu.
 16:0017:00  Deepam Patel (VU Amsterdam), Motives arising from higher homotopy theory Abstract. In his fundamental paper on the projective line minus three points, Deligne constructed certain extensions of mixed Tate motives arising from the fundamental group of the projective line minus three points and related them to special values of zeta functions. Since then, motivic structures on homotopy groups have been studied by many authors. In this talk, we discuss a motivic structure on the (nilpotent completion of) nth homotopy group of P^{n} minus n+2 hyperplanes in general position. 

DIAMANT symposium, special afternoon on algebra and number theory in cryptographyNovember 30, Doorn. Part of the Diamant symposium, which runs from Thursday to Friday. 
2nd BelgianDutch Algebraic Geometry DayDecember 7, UvA Amsterdam. Room A1.10 at Amsterdam Science Park. 13:3014:30  Andrei Caldararu (U. of Wisconsin), Derived intersections Abstract. In recent years there have been remarkable developments in derived algebraic geometry, a field which lies at the confluence of algebraic geometry and algebraic topology. The main objects of study in derived algebraic geometry are dg schemes, and a typical example of dg schemes arises when studying intersection theory of subvarieties. In my talk I shall try to explain some of the fundamental ideas of derived algebraic geometry, and argue that it allows us to get a more geometric understanding of classical results like the proof by DeligneIllusie of the Hodgede Rham degeneration.  15:0016:00  Eduard Looijenga (Utrecht), Cohomological dimension of moduli spaces of curves Abstract. We discuss the following theorem and its consequences: the cohomology of
a constructible abelian sheaf F on the complex moduli stack M_{g,n}(C)
(for the Euclidean topology) vanishes in degree greater than g1 plus
the dimension of the support of F. This implies Harer's bound for the
homotopy type of the underlying complexanalytic space as well as the bound of Diaz on
the maximal dimension of a complete subvariety of M_{g,n}(C). We also
deduce this type of bound for any open subset of the DeligneMumford
compactification that is a union of strata. A minor adaptation of the
proof shows also that the cohomological dimension of for quasicoherent
sheaves of M_{g,n} is at most g1 in characteristic zero. This implies
conjectures of Roth and Vakil.
 16:3017:30  Daniel Huybrechts (Bonn), Cycles on K3 surfaces Abstract. . 


