
Intercity number theory seminar and the inaugural lecture of Gunther CornelissenJanuary 16, Utrecht. See announcement for details 
Intercity number theory seminarFebruary 13, Leiden. Today's program is dedicated to the visit of five number theorists
from Taiwan to Leiden.
See also this week's colloquium lecture.
The first lecture is in room 403, the others in room 402.11:3012:20  Yifan Yang, Construction and application of a class of modular functions Abstract. In this talk, we focus on a class of modular
functions, known as the generalized Dedekind eta functions or
the Siegel functions, and discuss several applications of these
modular functions, including defining equations of modular curves,
structure of the cuspidal rational torsion subgroup of the
Jacobian J_{1}(N), and the gonality of X_{1}(N).  13:3014:20  ChiehYu Chang, On periods and logarithms for Drinfeld modules of rank 2 Abstract. In this talk, we will present motivic methods to determine the
algebraic relations
among the periods and logarithms of algebraic points for rank 2 Drinfeld
modules. Two major
applications will be also discussed.  14:3015:20  ShuYen Pan, On local theta correspondence of supercuspidal representations Abstract. The local theta correspondence asserts a onetoone correspondence
between certain irreducible admissible representations of two classical
groups over a padic field. The preservation principle of local
theta correspondence predicts the extistence of a chain of irreducible
supercuspidal representations of padic classical groups.
In the talk, we want to investigate and describe these supercuspidal
representations in certain circumstance.  15:3016:20  JengDaw Yu, Ordinary crystals with logarithmic poles Abstract. We study the abstract formalism of crystals with logarithmic poles
and give some properties that generalize some of the work of Deligne in the
1970's. 

Intercity number theory seminarMarch 6, Delft. Snijderzaal11:0012:00  Tom Schmidt, Mediants of Rosen fractions and Hurwitz constants of Hecke groups Abstract. In work with C. Kraaikamp and H. Nakada, we complete a program of
J. Lehner using continued fractions to determine the bounds on best
Diophantine approximation by the orbit of infinity under each of a
family of matrix groups. Lehner began this work in the 1980s,
using the continued fractions introduced by his Ph.D. student D.
Rosen in the 1950s. A. Haas and C. Series determined the bounds,
but using hyperbolic geometry. In fact, work of Nakada shows that
it is insufficient to use the Rosen fractions  we thus turn to a
means to interpolate this approximating sequences, the mediant
maps. A key point in the proof is to show that an ergodic theoretic
constant (known as the Lenstra constant) is equal to a certain number
theoretic constant.  13:3014:30  Michel Dekking, Algebraic differences of random Cantor sets Abstract. The study of the algebraic difference F_{2}  F_{1} = {y  x: x ∈F_{1}; y ∈F_{2}} of two dynamically defined Cantor sets F_{1}, F_{2}, was motivated by the
research of Palis and Takens in regards with the unfolding of homoclinic tangency in some oneparameter families of surface diffeomorphisms. Palis conjectured that if dimH F_{1} + dimH F_{2} > 1, then generically it should be true that F_{2} F_{1}
contains an interval. For generic dynamically generated nonlinear Cantor sets this was proved in 2001 by de Moreira and Yoccoz. The problem is open for generic linear Cantor sets. In this talk I will speak about related results for random Cantor sets.
 15:0016:00  Dieter Mayer , The transfer operator approach to Selberg`s zeta function for Hecke triangle groups G_{q} Abstract. By using the HurwitzNakada continued fractions generated by the interval
map f_{q}: I_{q}→I_{q} defined by f_{q} (x)=1/x[1/(x
λ_{q}) +1/2] λ_{q} with
I_{q}=[λ_{q}/2,λ_{q}/2] and
λ_{q}=2cos(π/q), q=3,4,... we derive a symbolic
dynamics for the geodesic flow on the Hecke surfaces G_{q} \ H. This allows us to construct a transfer operator
L_{β} whose Fredholm determinant det(1L_{β})
is closely related to the Selberg zeta function for the Fuchsian group
G_{q}.
This is common work with T.Muehlenbruch and F. Stroemberg (see also J. of
Modern Dynamics vol 2, No. 4, 2008, 349).
 16:0017:00  Charlene Kalle, Expansions and Tilings Abstract. The transformation Tx = βx (mod 1) for any real β>1 can be used
to generate number expansions in base β and with integers between 0 and
the floor of β as digits. If β is a certain kind of algebraic
integer, then this transformation is linked to a tiling of a Euclidean
space. Properties of the number expansions can be obtained from the tiling
and vice versa. We will discuss the construction of this tiling and
generalizations of it to a more general class of expansion generating
transformations. 

March 20, Utrecht. Program of four lectures by Spencer Bloch, Rob de Jeu, Alex Quintero Velez, Dmitri Orlov. 
Hendrik Lenstra's sixtieth birthdayApril 24, Leiden. A special day at the occasion of Hendrik Lenstra's sixtieth birthday will be held on April 24 in Leiden. The morning program contains two
mathematical talks and is part of the workshop
Counting
Points on Varieties. The afternoon will feature more personal
talks by friends and colleagues of Hendrik Lenstra. Everybody is
welcome to attend. Morning program in the De Sitterzaal, Oort building:
 9:15: coffee
 9:45: opening
 9:50  10:40: Carl Pomerance (Dartmouth)
 10:50 11:40: Manjul Bhargava (Princeton)
Afternoon program in the Lorentzzaal (A144)
Kamerlingh Onnes Gebouw, Steenschuur 25, Leiden.
 14:00  14:25: Ed Schaefer (Santa Clara)
 14:30  14:55: Everett Howe (San Diego)
 15:00: coffee
 15:30  15:55: Johannes Buchmann (Darmstadt)
 16:00  16:25: Richard Groenewegen (London)
 16:30: closing and drinks
Organisers: Ronald van Luijk, Bart de Smit, Peter Stevenhagen, Lenny Taelman. 09:5010:40  Carl Pomerance, Sociable numbers Abstract. Consider iterating the function which sends a natural number
to the sum of its proper divisors. A fixed point for this system,
such as 6 or 28, is called perfect, while a number belonging to a
cycle of length 2, such as 220 or 284, is called amicable. Known to
Euclid and Pythagoras, some scholars have even found allusions
to perfect and amicable numbers in the Old Testament. Sociable
numbers are the natural generalization of perfect and amicable
numbers to cycles of arbitrary length  they are mere
youngsters, having been studied for only a century! This talk
will describe the colorful history of the problem (with more
connections to Hendrik Lenstra than you might imagine) and
report on some recent results on the distribution of sociable
numbers within the natural numbers.
 10:5011:40  Manjul Bhargava, Galois closure for rings Abstract. Abstract: We all learn the notion of "Galois closure" or "normal
closure" for a finite extension of fields. But what might we mean by
the "Galois closure" of an extension of rings?
(joint work with Matthew Satriano; based on conversations with Hendrik Lenstra, JeanPierre Serre, Bart de Smit, and Kiran Kedlaya)  14:0014:25  Ed Schaefer, I started feeling sorry for the problem.  14:3014:55  Everett Howe, Channeling your advisor  15:3015:55  Johannes Buchmann, Hendrik Lenstra and cryptography  16:0016:25  Richard Groenewegen, A sense of reality 

Intercity number theory seminarMay 8, Groningen. Room 267, Bernoulliborg11:4512:30  Steve Meagher (Freiburg), Equations for Abelian varieties with a prescribed number of points over a finite field. Abstract. This talk is about ongoing work with Robert Carls. We
describe equations for a zerodimensional subvariety of the moduli space
of Abelian varieties whose points correspond to an Abelian variety with a
given Lfunction. We also explain potential
algorithmic applications to curves of very small genus.
 13:1514:00  Vivija Ceprkalo, Elliptic curves in Edwards form Abstract. This is a survey on the Edwards form, which is a
particular type of quartic equations for describing elliptic curves.
 14:1515:00  Cecilia Salgado, On the rank of the fibres of rational elliptic surfaces. Abstract. We compare the generic and the special ranks of rational
elliptic surfaces over number fields. We show that, for a big class of
rational elliptic surfaces, there are infinitely many fibres with rank
at least equal to the generic rank plus two. If time allows we will
discuss the same type of problem for some K3 elliptic surfaces.  15:1516:00  Marius van der Put, Painlevé differential equations Abstract. The classical work of Painlevé, Gambier, Garnier et al. on
nonlinear ordinary differential equations was ended by the
1930's. New interest and new ideas in the subject came in
the 1980's by Jimbo, Miwa, Ueno, Okamato and others.
We present a historical survey and some new joint results
with MasaHiko Saito.
 16:1517:00  René Pannekoek, Parametrizations over Q of cubic surfaces Abstract. Given any smooth cubic surface S defined over a number field K,
it is a wellknown fact that there exists a birational map f: S →P^{2}.
If we pose the additional requirement that f be defined over K, however,
the assertion may no longer be true. In the 1970s, Manin and
SwinnertonDyer formulated a necessary and sufficient criterion for S to
allow a birational map to P^{2} over K. First, I will discuss their
criterion and show that it is a pretty strong restriction on S. Also, I
will give several examples of cubic surfaces in order to give some idea
which cases actually occur. After this, I will elaborate on the fact
that there are several cases in which a special sort of birational map
can be found; I will show how these cases overlap and that they do not
exhaust the class of all birationally trivial cubic surfaces. Finally, I
will give examples of explicit birational and rational maps that I have
been able to construct. 

Intercity number theory seminarMay 15, Eindhoven. DIAMANT seminar room (HG 9.41)
We will have coffee served in the seminar room at 11:00 and tea at 15:00.11:1512:15  Ben Kane, Equidistribution of Heegner points and quadratic forms Abstract. In this talk we will investigate a relationship between supersingular
reduction of Heegner points and representations by quadratic forms. Using
equidistribution for representations by quadratic forms, we will establish
a certain corresponding equidistribution result for the reduction map.
 13:0013:55  Ted Chinburg, Lifts of group actions on curves from characteristic p to characteristic 0 Abstract. This talk is about lifts to characteristic 0 of faithful actions of a
finite group G on smooth projective curves in characteristic p.
One can ask for which G every such action lifts, and for which G at least one such
action lifts. I will survey some recent results concerning
these questions, including joint work with David Harbater and Bob
Guralnick.  14:0515:00  Ted Chinburg, Katz Gabber covers with extra automorphisms Abstract. It is an old problem to write down explicit automorphisms of order p^{2}
of a power series ring k[[t]] over a perfect field k of characteristic p.
I will describe some positive and negative results concerning
this problem which are based on a classification of Katz Gabber covers
of the projective line which have large automorphism groups. This
is joint work with Frauke Bleher, Peter Symonds, Bjorn Poonen
and Florian Pop.  15:2016:20  Shabnam Akhtari, Representation of integers by binary forms Abstract. Suppose F(x,y) is an irreducible binary form with integral
coefficients, degree n ≥3 and discriminant D_{F} ≠0. Let
h be an integer. The equation F(x,y) = h has finitely many
solutions in integers x and y. I shall discuss some different
approaches to the problem of counting the number of integral solutions
to such equations. I will give upper bounds upon the number of
solutions to the Thue equation F(x,y) = h. These upper bounds are
derived by combining methods from classical analysis and geometry of
numbers. The theory of linear forms in logarithms plays an essential
rule in this study.


RISC/Intercity number theory seminarMay 20, Leiden. Room 174. This extra Intercity/RISC seminar on a wednesday will feature talks by the Kloosterman professor Ted Chinburg, Gabriele Dalla Torre, and Chaoping Xing.11:3012:30  Gabriele Dalla Torre, The unitresidue group of an algebraic number field Abstract. Given a positive integer m and a local field F which
contains a primitive mth root ζ_{m} of unity, it is possible to
define the normresidue symbol, a bilinear map of F^{*} ×F^{*}
into the group ⟨ζ_{m} ⟩. This definition can be
extended to ideles of any number field K which contains a primitive
mth root of unity. We will study the ``unitresidue group", a
quotient of the group of unit ideles which naturally arises in this
setting, with special care to the structure deriving from the
normresidue symbol. Finally, we will give some examples and a
complete description in the case of quadratic number fields.
 13:2014:15  Ted Chinburg, Deformations of complexes of modules for a profinite group Abstract. This talk is about a new finiteness problem concerning deformations
of complexes of Galois modules arising from arithmetic geometry.
The main question is whether the associated versal deformations
can be represented by bounded complexes of finitely generated
modules over the versal deformation ring. This is joint work
with F. Bleher, with key ideas from Luc Illusie and Ofer Gabber.  14:2515:20  Ted Chinburg, Rationality of Euler characteristics Abstract. This talk is about characterizing those finite groups G which have the
following property.
Whenever G acts faithfully on a smooth projective irreducible
curve C in characteristic 0, the action of G on the holomorphic
differentials of C defines a character of G having only rational values.
We will find all such G, using Dirichlet Lfunctions to determine
when certain cyclotomic algebraic integers are rational. This
is joint work with Amy Ksir.  15:3016:25  Chaoping Xing, Construction of algebraic curves over finite fields from linear codes and vice versa Abstract. The interrelationship between error correcting codes and
algebraic curves over finite fields with many rational points was
discovered as early as the 1980s with the invention of Goppa geometric
codes.In this talk, we present yet another method to show how linear codes and
algebraic curves are intertwined. More precisely, by using upper bound on
linear codes, we can show existence of algebraic curves over finite fields
with many rational points. On the other hand, by using upper bounds on
algebraic curves, we can construct good linear codes.


Intercity number theory seminarJune 12, Nijmegen. room HG00.307 (Huygens Gebouw), Heyendaalseweg 13513:0014:00  Sander Zwegers, Mock modular forms: an introduction Abstract. The main motivation for the theory of mock modular forms comes from the
desire to provide a framework to understand the mysterious and intriguing
mock theta functions, defined by Ramanujan in 1920, as well as related
functions.In this talk, we will describe the nature of the modularity of the original
mock theta functions, formulate a general definition of mock modular forms,
and consider some further examples. Time permitting, we will also consider
a generalization to higher depth mock modular forms.
 14:3015:30  Oliver Lorscheid, Toroidal Eisenstein series and double Dirichlet series Abstract. A formula of Erich Hecke in an article from 1917 laid a connection between
a sum of values of an Eisenstein series E(,s) with the value ζ(s) of
the zeta function ζ. We call an automorphic form toroidal if the
corresponding sum (or integral in its adelic formulation) vanishes for all
right translates. The importance of this definition lies in a reformulation
of the Riemann hypothesis in terms of the space of toroidal automorphic
forms as observed by Don Zagier. Namely, the Eisenstein series E(,s) lies
in a tempered
representation if and only if s has real part 1/2, and by Hecke's formula,
E(,s) is toroidal if s is a zero of the zeta functions. In order to
reverse the latter statement, nonvanishing results has to be shown for the
factors occuring in Hecke's formula. In a joint work with Gunther
Cornelissen, double Dirichlet series are used for this purpose.In this talk, we will introduce into the theory of (toroidal) automorphic
forms and give an overview over results in this direction. Then we will
explain how to use double Dirichlet series to show nonvanishing results.
 16:0017:00  Dimitar Jetchev, Global divisibility of Heegner points and Tamagawa numbers Abstract. We improve Kolyvagin's upper bound on the order of the pprimary part of
the ShafarevichTate group of an elliptic curve of rank one over a
quadratic imaginary field. In many cases, our bound is precisely the one
predicted by the Birch and SwinnertonDyer conjectural formula.


Intercity Number Theory Seminar at the Woudschoten conference on automorphic forms.June 19, Woudschoten. See the conference webpage.
Speakers:
1011 Henryk Iwaniec (Rutgers): Some features of spectral summation formulas
1112 Akshay Venkatesh (Stanford): Torsion in homology of arithmetic groups
1213 Lunch
1314 Emmanuel Kowalski (ETHZ): Families of Cusp Forms and Lfunctions

Intercity number theory seminarSeptember 4, Leiden. Room 402  René Schoof, padic representations and (φ, Γ)modules Abstract. In this lecture we discuss padic representations of padic fields. We explain Fontaine's description in terms of (φ, Γ)modules.  14:0015:00  JanHendrik Evertse, Complexity of algebraic numbers Abstract. Given an integer b>1, any real number from (0,1) can be expressed
uniquely as
d_{1}b^{1}+d_{2}b^{2}+... with bary digits
d_{1}, d_{2}, ... from {0,...,b1}.
It is generally believed that the sequence of bary digits of an algebraic
irrational number from (0,1) should behave like a random sequence, but up
to know only some weak results in this direction
have been obtained.
We discuss some work of Adamczewski and Bugeaud, and of Bugeaud and the
speaker,
on the distribution of the bary digits of an algebraic number.
 15:1516:15  Hendrik Lenstra, Finding the ring of integers in a number field Abstract. A classical algorithmic problem in algebraic number theory is to
find the ring of integers of a given algebraic number field. The
lecture is devoted to a new technique for solving this problem.
It does not always work, but if it does, then it writes down the
answer in one stroke.


Intercity number theory seminarSeptember 18, Eindhoven. DIAMANT seminar room (HG 9.41). There will be coffee and tea at 12:00 and 14:45.  René Schoof, Curves over finite fields  12:1513:00  Ronald van Luijk, Unfaking the fake Selmer group Abstract. Let C be a smooth projective curve over a global field k
with Jacobian J. Then the MordellWeil group J(k) of krational
points on J is finitely generated. Knowing the torsion subgroup,
which is usually relatively easy to find, the rank of J(k) can be
read off from the size of the finite group J(k)/2J(k). This quotient
injects into the so called Selmer group, which is abstractly defined
as a certain subgroup of the cohomology group H^{1}(k,J[2]). The
Selmer group is finite, so the image of J(k)/2J(k) in it can be
determined by deciding for each element of the Selmer group separately
whether or not it is in the image of J(k)/2J(k). Unfortunately, the
abstract definition of the Selmer group is not very amenable to
explicit computations, which are in practice done with the fake Selmer
group instead. In general the fake Selmer group is isomorphic to a
quotient of the Selmer group by a subgroup of order 1 or 2. In
this talk we will define all the groups just mentioned and we will
introduce a new group, equally amenable to explicit computations as
the fake Selmer group, that is always isomorphic to the Selmer group.
This is joint work with
Michael Stoll.
 14:0014:45  David Freeman, Pairingfriendly hyperelliptic curves and Weil restriction Abstract. A "pairingfriendly curve" is a curve C over a finite field F_{q} such that
(a) the Jacobian of C has a subgroup of large prime order r, and (b) the
rth roots of unity are contained in an extension field F_{qk} for some
small value of k.Pairingfriendly curves have found many uses in cryptography. For such
applications one wants to control the extension degree k, known as the
"embedding degree," while keeping the field size q as small as possible
relative to the subgroup size r. We describe a construction of pairingfriendly genus 2 curves that, for
certain embedding degrees k, achieves the smallest known ratio log q/log r
for simple, nonsupersingular abelian surfaces. The proof that these curves
have the desired properties relates them to Weil restrictions of elliptic
curves. We also describe some experimental results suggesting that our construction
fails in certain cases. Finding alternative constructions for these cases
is an open problem. This is joint work with Takakazu Satoh (Tokyo Institute of Technology).
 15:0015:45  Bart de Smit, The valuation criterion for normal bases Abstract. For a finite Galois extension L/K of local fields we consider the question whether there is an integer d so that all elements x of L of valuation d
have the property that the Galois conjugates of x form a basis of L as
a vector space over K. This is joint work with Lara Thomas (Lausanne) and
Mathieu Florence (Paris). 

Special day in honour of Wilberd van der Kallen and Joop KolkOctober 2, Utrecht. See this page 
Intercity number theory seminarOctober 30, CWI Amsterdam. Joint session with the RISC seminar in the Turingzaal (the main auditorium on the ground floor, to the left of
the main entrance).  Christine Bachoc, Secure Message Transmission with Small Public Discussion Abstract. In the problem of Secure Message Transmission in the public discussion
model (SMTPD), a Sender wants to send a message to a Receiver
privately and reliably. Sender and Receiver are connectedby n channels,
up to t<n of which may be maliciously controlled by a computationally
unbounded adversary, as well as one public channel, which is reliable but
not private.The SMTPD abstraction has been shown instrumental in achieving
secure multiparty computation on sparse networks, where a subset
of the nodes are able to realize a broadcast functionality, which
plays the role of the public channel. However, the implementation
of such public channel in pointtopoint networks is highly costly and
nontrivial, which makes minimizing the use of this resource an
intrinsically compelling issue. In this talk, after a brief introductory survey, we present the first SMTPD
protocol with sublinear (i.e., logarithmic in m, the message size)
communication on the public channel. In addition, the protocol incurs a
private
communication complexity of O(mn/(nt)), which, as we also
show, is optimal. By contrast, the best known bounds in both
public and private channels were linear. Furthermore, our protocol
has an optimal round complexity of (3,2), meaning three rounds, two of
which must invoke the public channel. Finally, we ask the question whether some of the lower bounds on
resource use for a single execution of SMTPD can be beaten on
average through amortization. In other words, if Sender and
Receiver must send several messages back and forth (where later
messages depend on earlier ones), can they do better than the
naïve solution of repeating an SMTPD protocol each time?
We show that amortization can indeed drastically reduce the use of
the public channel: it is possible to limit the total number of uses of the
public channel to two, no matter how many messages are ultimately
sent between two nodes. (Since two uses of the public channel are
required to send any reliable communication whatsoever, this is best
possible.) This is joint work with Clint Givens (UCLA) and Rafi Ostrovsky (UCLA).  11:3012:30  Andries Brouwer, The eigenvalues of the graph on the flags of a finite building, joined when in mutual general position.  13:3014:30  Heng Huat Chan, Class invariants Abstract. It is well known that values of the modular jinvariant function
evaluated at certain
imaginary quadratic integer
generates the Hilbert class fields of the corresponding imaginary quadratic
fields.
In this talk, we will replace jinvariant by some other modular functions
and examine
their behavior as class invariants.
 16:0017:00  Ronald Cramer, Towers of Algebraic Function Fields in Secure Computation 

Intercity number theory seminarNovember 13, Groningen. The first lecture is in room 105 Bernoulliborg, the second in Room 5116.0116 in the Physics & Chemistry NCC
Building, and the last two in room 267 Bernoulliborg.
(The last two talks have been switched after the email announcement.)11:4512:45  Marios Magioladitis, The discrete logarithm problem on isogenous hyperelliptic curves of genus 2 Abstract. In 2005, Jao, Miller, and Venkatesan proved that
the DLP of elliptic curves with the
same endomorhism ring is random reducible under the GRH.
In this talk, we discuss a possible generalization of this result to
hyperelliptic curves of
genus 2 (and 3) defined over a finite field and show the difficulties
involved.
First, we explain the role of the endomorphism rings of the Jacobian and
the polarization.
Following the work of Jao, Miller and Venkatesan, we construct isogeny
graphs
for genus 2 curves. Specifically, we discuss the connection between
isogenies and
ideal classes in the Jacobian of these curves. This project is research in
progress and
we describe the current status of this research.
 13:3014:30  Jaap Top, Ruled quartic surfaces Abstract. In the 19th century, Cremona in a
synthetic geometric way and Cayley using analytic
geometric methods subdivided the ruled quartic surfaces
in P^{3} into twelve classes. Somewhat later, K. Rohn
wrote about the subject and moreover had models made
of such surfaces. We explain and extend some of
these classical results in more modern terms.  15:0016:00  Robin de Jong, Logarithmic equidistribution of division points on superelliptic curves Abstract. A superelliptic curve is a curve over a number field K given by an equation
y^{N}=f(x), with suitable conditions on f and N. On such curves one has the
notion of ndivision points, generalising the notion of ntorsion points on
elliptic curves. We discuss two results. First, the NeronTate height
restricted to the canonical image of X in its jacobian can be written as a
sum, over all places of K, of certain local logarithmic integrals over X.
Second, for almost all algebraic points on X these local integrals can be
computed by averaging over the ndivision points of X, and letting n tend
to infinity. For elliptic curves these results were shown by Everestní Fhlathúin and EverestWard.
 16:0517:05  Jorge Mozo Fernández, Results on analytic classification of germs of holomorphic foliations Abstract. We shall review the main known
results concerning the
analytic classification of germs of codimension one, singular
holomorphic foliations in dimension two and three. In dimension two,
we shall focus in the classical works of J. Martinet and J.P. Ramis,
in the reduced case, and in the works of Cerveau, Moussu, Meziani,
Berthier, Sad and others, in the nilpotent case. In the
quasihomogeneous case, we shall mention the work of Y. Genzmer. The
stateofart of this subject in dimension three will be explained.
We shall recall the main concepts involved: reduction of
singularities, existence of separatrices, and holonomy of the leaves,
and how they are used in order to establish the results.


DIAMANT/EIDMAsymposiumNovember 27, Lunteren. See this page 
Intercity number theory seminarDecember 4, Utrecht. Room 505 of the BBL building. Tentative list of speakers: Jeroen Sijsling, Jonathan Reynolds, Marco Streng, Gunther Cornelissen11:3012:20  Jonathan Reynolds, Power integral points on elliptic curves. Abstract. Siegel proved that there are finitely many rational points
on an elliptic curve which have an integral coordinate. I will explain
why finiteness still holds when the denominator of the coordinate is
an integer raised to a fixed nontrivial power. The effectiveness of
this result for certain families of curves will be discussed.
 13:3014:20  Jeroen Sijsling, Equations for (1;e)curves Abstract. A (1;e) curve is a special compact quotient of the upper
half plane: it has genus 1 and one elliptic (branch) point. A Shimura
curve is a quotient of the upper half plane coming from orders in
certain quaternion algebras over totally real fields. Kisao Takeuchi
classified all (1;e) curves that are naturally commensurable to
Shimura curves: there are 72 of these. This talk discusses techniques
for calculating explicit equations for Takeuchi's curves. These range
from dessins d'enfants to modularity over Q and classical modular
curves.
 14:3015:20  Marco Streng, Abelian surfaces admitting an (l,l)endomorphism Abstract. We give a classification of all principally polarized abelian
surfaces that admit an (l,l)isogeny to themselves. We make the
classification explicit in the simplest cases l=1 and l=2 and show how
to compute all abelian surfaces that occur.
This research was done during an internship of the speaker at Microsoft
Research (MSR). It is joint work with Reinier Bröker (MSR, currently
Brown University) and Kristin Lauter (MSR).  15:4016:30  Gunther Cornelissen, Arithmetic equivalence for function fields Abstract. A theorem of Tate and Turner says that global function
fields have the same zeta function if and only if the Jacobians of the
corresponding curves are isogenous. In this talk, we discuss what
happens if we replace the usual (characteristic zero) zeta function by
the positive characteristic zeta function introduced by Goss, or by a
"Teichmüller lift" of that (joint work with Aristides Kontogeorgis
and Lotte van der Zalm, arXiv:0906.4424, doi:10.1016/j.jnt.2009.08.002).



