
January 30

Leiden, room 312

11:2012:05
12:1513:00

R. van Luijk,
An elliptic K3 surface associated to Heron triangles
Abstract A rational triangle is a triangle with rational
sides and rational area. A
Heron triangle is a triangle with integral sides and integral area. In
this talk we will see that there exist infinitely many rational
parametrizations, in terms of t, of rational triangles with
perimeter 2t(t+1) and area t(t^{2}1). As a corollary, there exist
arbitrarily many Heron triangles with all the same area and the same
perimeter. The proof uses an elliptic K3 surface with NéronSeveri
group of rank 18.

13:0014:10
 Lunch

14:1015:00,
15:1016:00

Noriko Yui,
On the Modularity of CalabiYau Varieties
An abstract is avalable in PDF.

Hendrik Lenstra invites all participants for a drink in his
new apartment (Hooigracht 84A, Leiden) at 17:00.
At 18:30 we will have dinner in a restaurant nearby.

February 13

Utrecht, room K11 of the Math building: joint session with the
Algebraic Geometry seminar.

11:1513:00

Bas Edixhoven,
Stacks: sheaves and cohomology

14:1516:00

Noriko Yui,
On the modularity of nonrigid CalabiYau varieties,
An abstract is available in PDF.


February 27

Groningen, room RC 255

11:3012:30

Remke Kloosterman,
Locally constant families of hyperelliptic curves
Abstract:
which pairs (P, C), in which P is a point and C a reduced
plane cubic curve, have the following property: almost every line
through P yields four points (P, P_{1}, P_{2}, P_{3}), namely P and the
intersection points of C with the line, and for some permutation of
these
points the cross ratio they define is independent of the line.
The talk answers this question and a generalization of it to
curves C of higher degree.

13:0014:00

Harm Voskuil,
Amalgams and discrete subgroups of PGL(2,K).
Abstract:
The classification of amalgams of finite groups that can be embedded
as discrete subgroups into the group PGL(2,K) over a local
field K is discussed. The main focus of the talk is on the
exceptional groups in characteristic zero that give rise to coverings
of the projective line with only three branch points. Such groups
only occur when the characteristic of the residue field is 2, 3 or 5.

14:1515:15
15:3016:30

Noriko Yui,
CalabiYau orbifolds of CM type
Abstract:
We will consider CalabiYau threefolds defined
over Q in weighted projective 4spaces obtained
from hypersurfaces of Fermat type via the orbifolding process.
These motives are all of CM type. We will introduce motives
associated to them, and then compute motivic Hodge numbers,
Betti numbers and Euler characteristic. Finally, we calculate
the Lseries of CalabiYau threefolds.


March 5

Leiden room 312.

13:0014:00

Bill Hart,
Evaluation of Eta Quotients
Abstract:
As an analogue of modular equations for the $j$ function we
also have modular equations for the Weber functions. These Weber
functions are defined as quotients of the Dedekind eta function. I
will
speak about one use of the modular equations for these functions,
namely
obtaining explicit generators for Hilbert class fields of imaginary
quadratic fields.
Further to this, generalizing the Weber functions to various sets of
`higher level' functions, I have been able to obtain some new modular
equations and thus further explicit generators of Hilbert and ring
class
fields. The talk will start with what is known classically and finish
with some explicit examples of my new higher level functions, their
modular equations and some explicit eta quotient evaluations arising
from them.

14:1515:15

JanHendrik Evertse,
On the number of equivalence classes of binary forms of given degree
and given discriminant.
Abstract:
Two binary forms (homogeneous polynomials) F(X,Y) and
G(X,Y) with rational integral coefficients are called
equivalent if F can be transformed into G
by means of a transformation from GL(2,Z).
Two equivalent binary forms are known to have the same discriminant.
By classical work of Gauss, the binary quadratic forms of given
discriminant with coefficients in Z
fall apart into finitely many
equivalence classes.
Hermite proved the same for binary cubic forms of given
discriminant with coefficients in Z. In 1972, Birch and
Merriman succeeded to prove that the binary forms in
Z[X,Y]
of given degree r larger than 3 and of given discriminant
lie in only finitely many equivalence classes.
The proof of Birch and Merriman uses among others
the theorem of Siegel, Mahler and Lang that
if G is any finitely generated multiplicative subgroup of
the field of algebraic numbers, then the
Diophantine equation x+y=1 has only finitely many solutions
in x,y from G.
In my lecture I will discuss a quantitative version of the result
of Birch and Merriman giving an explicit upper bound for the
number of equivalence classes.
This is joint work with Attila Bérczes and Kálmán
Györy (Debrecen).

15:3017:15

Noriko Yui,
Mirror symmetry and mirrormoonshine
Abstract:
We will discuss mirror symmetry proper
for a mirror pair of elliptic curves, $K3$ surfaces, and
CalabiYau threefolds. Lian and Yau formulated the socalled
MirrorMoonshine conjecture. We will discuss a couple of examples
where mirror maps are McKayThompson series arising from
Monstrous Moonshine.


March 19

Utrecht, room K11 of the Math building

11:1513:00

Frits Beukers,
Algebraic solutions of Lamé equations

14:1515:15
 Christophe Ritzenthaler,
Automorphism group of modular curves X(N) in characteristic p
Abstract.
Let q>5 be a prime number. The automorphisms of the modular curve X(q)
are modular and their group is isomorphic to PSL_2(Z/qZ). In 1982, I.
Kuribayashi showed that the automorphism group of X(7) modulo 3 is
PSU(3,3) and A. Adler in 1997 showed that the automorphism group of
X(11) modulo 3 is the Mathieu group M_11, a sporadic group which
contains strictly PSL_2(Z/11Z). May it happen for other values ? We
give a partial answer (negative) : if X(q) modulo p is ordinary and
p>3 the automorphism group is exactly PSL_2(Z/qZ). We also completely
answer the case q=7,11,13.

15:3016:15
 Bart de Smit,
Snakespotting


April 2

Groningen, room RC250

11:3012:30

Robert Carls,
Descent of line bundles along Frobenius and Verschiebung

13:1514:15
 Michael Stoll,
x^{2}
+
y^{3}
=
z^{7}
Abstract.
This equation is a special case of the Generalized Fermat Equation
x^{p}
+
y^{q}
=
z^{r}
It is especially interesting since it is the
extremal ``hyperbolic'' case:
c = 1/p + 1/q + 1/r  1 has the
negative value closest to zero. For negative c, it is known that
the equation has only finitely many primitive integral solutions, and
the closer c is to zero, the more solutions are expected.
I will report on the proof (done jointly with Bjorn Poonen and Ed
Schaefer) that the list of known primitive solutions is complete. The
proof involves the explicit construction of ten twists of the Klein
Quartic whose rational points cover the primitive solutions. This is
done using ideas from the proof of Fermat's Last Theorem and a fairly
recent result by Halberstadt and Kraus on twists of X(7). In a
second step, the set of rational points on each of these ten curves
has to be determined. To achieve this, we set up a 2descent on the
Jacobian to determine the MordellWeil rank. In nine out of the ten
cases, the rank is at most two, and Chabauty's method can be applied
to find the rational points. In the last case, the rank is three, and
we use a sieving argument on the MordellWeil group to rule out the
existence of rational points leading to primitive solutions.

14:3015:30 
Jaap Top,
Pointless

15:4516:45 
Marius van der Put,
Descent for differential and difference equations


April 23

Nijmegen, Room N5 (N0011). To see where to enter the building
please look at the map.
The room is in section N1, and you can enter the building at the
green arrow and the pink dot.

13:0014:00

Lara Thomas,
The ArtinSchreier symbol

14:3015:30
 Andreas Alpers ,
The ProuhetTarryEscott Problem and Discrete Tomography

16:0017:00 
Wieb Bosma,
A bound for codes with the 2identifiable parent property


May 14

Leiden, room 312

11:3012:30

Gabor Wiese,
Dihedral Galois representations and Katz modular forms

13:3015:30

P. Cartier,
An algebraic theory of iterated integrals
Abstract.
We propose an algebraic theory of iterated integrals, a
version of Chen's classical results well suited to applications in
algebraic geometry. Among the applications we shall mention:

a broad generalization of the BlochWigner function (due to
my student Francis Brown);
 geometry of configuration spaces M(0,n);
 algebraic relations among multiple zeta values, and
connections with integral representations of these numbers

16:0017:00

Gunther Cornelissen,
Restrained group actions on curves


Quantum Number Theory Day: September 24
September 24

CWI, room M280

10:4511:45,
12:0013:00

Ulrich Vollmer (Technische Universität Darmstadt),
Quantum Computational Number Theory
[Abstract]

13:0014:00
 Lunch

14:0015:00

Ronald de Wolf (CWI),
Grover's quantum search algorithm
Abstract:
The two most important quantum algorithms to date are Shor's algorithm
for factoring and Grover's algorithm for search. Grover's algorithm
allows us to search through a space of N elements in about
√N
steps,
which is quadratically better than classical brute force search.
Though
its
speedup is not as impressive as Shor's (quadratic vs exponential), its
wide
applicability makes up for that. In this talk we will explain
Grover's
algorithm,
give a simple analysis to show that it works, and prove that its
running
time
is essentially optimal. Time permitting, we will then describe a
number
of applications to other computational problems.

15:1516:15

Serge Fehr (CWI),
An Introduction to Quantum Cryptography: KeyDistribution by
Public Discussion
Abstract: The goal of this talk is to give some ideas why and how
quantum effects can be used to construct cryptographic schemes that
are
provably secure against an allpowerful adversary. We do this by
presenting the quantum keydistribution protocol due to Bennett and
Brassard (1984). This protocol allows two parties to agree on a
cryptographic key, merely by communicating over public (classical and
quantum) channels, such that any attacker (that may observe the full
conversation) has essentially no information about the established
key.

After the talks we're planning to have an early dinner
at Pizza Pino, located at Lange Leidsedwarsstraat 106

October 8

Leiden, room 312

10:5011:50 
T.N. Shorey (Tata Institute),
Powers in products of terms in arithmetic progression
Abstract: A theorem of Euler states that a product of four
terms in arithmetic progression is not a square. A theorem of
Erdös and Selfridge states that a product of two or more
consecutive positive integers is not a power. I shall give several
extensions of these results.

12:0013:00 
Bas Jansen (Leiden),
Classical Iwasawa theory
Abstract:
This talk will be an introduction to Iwasawa theory. We will sketch a
proof of Iwasawa's main theorem and state Iwasawa's main conjecture.
In this way we will have some preparation and motivation for Bill
Hart's talk about modern Iwasawa theory.

14:0015:00, 15:1516:00 
Bill Hart (Leiden),
What is the noncommutative Iwasawa Main Conjecture?
Abstract:
Recent progress has been made in the formulation of a noncommutative
Iwasawa main conjecture by Coates, Fukaya, Kato, Sujatha and Venjakob.
This elegant approach (which the speaker was *not* involved in
personally) was discussed at the recent Iwasawa 2004 meeting by Coates,
at which the speaker was present.
The outline of this talk will be as follows:
1) Where does noncommutative Iwasawa theory come from?
2) Some noncommutative algebra (pseudonullity, Auslander regular
rings, padic lie groups).
3) Introduction to Ktheory and characteristic elements in
noncommutative Iwasawa theory.
4) The noncommutative main conjecture.
All relevant definitions will be given, so the talk is intended for a
general number theoretical audience.


October 22

Groningen, room H 12018 in the "Harmoniegebouw", close to the main
entrance. From the train station to the Harmoniegebouw
is a straight walk of ≤ 10 minutes. Cross the
musuem bridge in front of the train station; keep walking in the same
direction, crossing some streets and the Vismarkt until you are in the
Kijk in 't Jatstraat. The Harmoniegebouw is on your left hand
side;
see the map.

11:15−12:00

M. van Hoeij,
Factoring polynomials over global fields.
Abstract:
Let K be a global field and f in K[X] be a polynomial.
An efficient algorithm is presented which factors f in polynomial
time.

12:15−13:00

F. Ulmer,
On a parametrized differential system of Lame type
Abstract:
We study a differential system ramified in 4 points depending on
parameters and whose differential Galois group is a subgroup of the
infinite dihedral group. The differential Galois group is either a
reducible group, a finite dihedral group or the infinite dihedral
group. We give a method to compute the parameter values corresponding
to the various possibilities. This is a joint work with Frank Loray
and Marius van der Put.

13:40−14:25

F. Loray,
Algebraic solutions of Painlevé VI equations
Abstract:
I introduce the sixth Painlevé equation PVI from the
isomonodromic deformations of rank 2 Fuchsian system with 4 singular
points over the Riemann sphere. Although the generic solution of PVI
is very transcendental, special algebraic solutions can be derived
from deformations of Fuchsian systems having finite monodromy group.
I will give examples.

14:30−15:30

F. Beukers,
Monodromy of the complex spherical pendulum

16:15 
Thesis defense of Maint Berkenbosch
in the Academiegebouw.


November 5

Eindhoven. The morning program will take place in room 1.50 of the
Matrixgebouw (accross the road from the main entrance of the
Hoofdgebouw). After lunch we move to HG 6.96 in the
Hoofdgebouw.

11:15−12:15

Sergei Haller (Eindhoven),
Twisted forms of linear algebraic groups: some aspects of computation.
Abstract [PDF]. 
12:25−13:15

Die Gijsbers (Eindhoven),
BMW Algebras of Simply Laced Type
Abstract:
Recently discovered representations of the Artin groups of type
A_{n},
the braid groups, can be
constructed via BMW algebras. We introduce similar algebras of type
D_{n} and E_{n} which also lead
to faithful representations of the Artin groups of the corresponding
types. These finite
dimensional algebras have a chain of ideals I_{m} such that the quotient
with respect to I_{1} is the Hecke algebra and
I_{1} / I_{2} is a module for
the corresponding Artin group generalizing the
LawrenceKrammer representation. Some properties of other quotients
are discussed which lead to abetter understanding of the BMW algebras
and their dimensions.

14:15−15:15

Hendrik Lenstra (Leiden),
Groups with a character of small degree
Abstract:
Suppose that a finite group of order n has a complex
irreducible character of degree d. Then there is a nonnegative
integer e with n = d(d+e), and
if e is 'small' then the
character degree d is 'large', as a function of n. The case
e = 1 can be completely classified; it occurs for all values of
n of the form q(q−1), where q is a power of a prime number.
On the other hand, each fixed value of e different from 1
occurs in only finitely many cases; more specifically, one has
n ≤ e^{4e2} whenever e ≠ 1.
A proof of this result,
obtained in collaboration with Noah Snyder (Berkeley), will be
given in the lecture.

15:30−16:30

Jos Brakenhoff (Leiden),
Comparing the representation ring
and the center of the group ring
Abstract:
For a finite group G the representation ring and the center of
the group ring are both reduced commutative rings whose additive group
is free of rank c, where c is the number of conjugacy
classes of G. When G is abelian the rings are
isomorphic. In this talk we will compare the discriminants and the
induced Qalgebras.


November 26

Groningen, room 02 of
Het Tehuis
on the Lutke Nieuwstraat.
Het Tehuis is shown on the
the map,
just north of the AKerk
See the map.

11:00−11:45

Gerhard Frey,
Curves over fields of finite type with infinite rational fundamental group

12:00−12:45

Jean Francois Mestre,
On the 3rank of quadratic fields

13:30−14:15

Peter Stevenhagen,
Elliptic curves in polynomial time
Abstract:
In the last two decades, we have seen that the number N of points
of an elliptic curve over a finite field can be computed in polynomial
time. This talk shows how to produce, on input N, an elliptic curve
over a finite field for which the group of points has order N.
If N is provided in factored form, the heuristic run time is
polynomial in log N.

14:45

Thesis defense Robert Carls (Aula, Akademiegebouw)



