
Intercity number theory seminarFebruary 5, Leiden. Room 40512:1513:00  Peter Bruin, Computing in Picard groups of projective curves over finite fields, part 1 Abstract. Following the work of K. KhuriMakdisi (Math. Comp. 73 (2004) and 76
(2006)), I will describe a way of representing a smooth projective
curve over a field, and of divisors on it, that allows fast
computation of group operations in the Picard group. This is
especially interesting in the case of modular curves, where such a
representation can be computed from spaces of modular forms. If the
base field is finite, there are additional operations such as choosing
uniformly random elements of the Picard group and computing Frobenius
maps, Frey–Rück pairings and (for modular curves) Hecke
operators. I will explain how these operations can be done
efficiently in the setting of KhuriMakdisi's representation of the
curve.Some of this material was explained in the Intercity seminar of 12
December 2008 by Arjen Stolk and myself, but knowledge of this will
not be assumed.  14:0014:45  Peter Bruin, Part 2  15:0015:45  Lenny Taelman (EPFL Lausanne), Towards a characteristic p analogue of the class number formula, part 1 Abstract. The class number formula gives an expression for the residue
at s=1 of the Dedekind zeta function of a number field K in terms of
the class number and other arithmetic invariants of K. In this talk I
will discuss an analogue of the Dedekind zeta function, which is
associated to a characteristic p function field and which takes values
in characteristic p. I will formulate a conjecture that expresses the
value of this function at "s=1" in terms of arithmetic invariants of
the function field and present evidence towards it. Crucial to the
formulation of the conjecture is the Carlitz module, which is a
function field analogue of the multiplicative group, and most of the
talk will in fact serve as an introduction to the Carlitz module and
its arithmetic properties. (More info: http://arxiv.org/abs/0910.3142)
 16:0016:45  Lenny Taelman (EPFL Lausanne), Part 2 

Intercity number theory seminarMarch 5, Utrecht. Buys Ballot Lab, room 205. There will be tea at 15:20.11:3012:20  Oliver Lorscheid (Bonn), Geometry over the field with one element: an introduction Abstract. While the elusive object F_{1}, the socalled field with one element,
lurks around in mathematical concepts for more than half a century, in
recent years F_{1}geometry became a buzzword for a whole collection of
approaches that try to generalize algebraic geometry as invented by
Grothendieck.In this talk, we will review the philosophy of F_{1}, in particular Tits
idea on Chevalley groups over F_{1} and how to prove the Riemann
hypothesis with F_{1}geometry. We will give an overview of the various
attempts towards F_{1}, and, to present some mathematics, we will sketch
how to use ConnesConsani's F_{1}schemes resp. torified varieties to
realize Tits' idea.  13:3014:20  Nikolas Akerblom (NIKHEF), Solitons and generalized elliptic functions Abstract. Solitons are studied in physics as mathematical models of various natural phenomena, such as "solitary waves" and vortices in superconductors. One particular field theory
in physics is the JackiwPi model. The solitonic solutions of the JackiwPi model are determined by the Liouville equation, dating to the year 1853.
In this talk, I explain recent progress on obtaining all such JackiwPi solitons in the case where "space" is a torusthat is, in the case where the solitons assemble themselves
in a periodic pattern in the plane, also referred to as "vortex condensation".
In fact, I present an explicit, formulaic classification of all these soliton solutions in terms of a class of generalized elliptic functions and discuss some of their physical
properties.
 14:3015:20  Guyan Robertson (Newcastle), Building centralizers in A_{2}~ groups Abstract. I will give a brief overview of buildings, followed by some calculations, and I will end with a question to the audience on zeta functions.
 15:4016:30  Dajano Tossici (Scuola Normale Superiore di Pisa), On the essential dimension of group schemes in positive characteristic Abstract. After an introduction to the essential dimension of functors we will focus on the essential dimension of group schemes. Then I will talk about some recent results I
obtained in a joint work with A. Vistoli. We give a general lower bound and a general upper bound for group schemes in positive characteristic. We will also show how to compute,
with these two bounds, the essential dimension of some classes of group schemes.


Intercity number theory seminarMarch 19, Groningen. Room 267 Bernoulliborg11:4512:45  Bas Heijne (Groningen), Elliptic Delsarte surfaces Abstract. In 1986 T. Shioda published a method for computing the rank of
the group of sections of a class elliptic surfaces which admit
an abelian cover by a Fermat surface.
In this talk we describe this class explicitly in terms of
Newton polygons of plane curves, and we compute ranks for these
surfaces.
 13:3014:30  Jan Draisma, A tropical proof of the BrillNoether theorem Abstract. We give an explicit sequence of BrillNoether general graphs
in every genus, confirming a conjecture of Baker
and giving a new characteristic independent proof of
the BrillNoether Theorem, due to Griffiths and Harris,
on nonexistence of special divisors on general curves.
Joint work with Filip Cools, Elina Robeva, and Sam Payne.
 14:4515:45  Jaap Top, Legendre elliptic curves over finite fields Abstract. Two aspects of the wellknown Legendre family of elliptic curves
will be discussed. The first is their relation to the family
of plane quartic curves admitting S_{4} as automorphism group.
The second aspect concerns the sets of pairwise isogenous
Legendre elliptic curves over a given finite field.
 16:0017:00  Mirjam Dür, On the cones of completely positive and doubly nonnegative matrices and their use in optimization Abstract. The convex cone of completely positive matrices and its dual cone of
copositive matrices arise in several areas of applied mathematics. In
particular, these cones have recently attracted interest in
mathematical
optimization, since it has been shown that many combinatorial and
quadratic binary problems can be reformulated as linear problems over
these cones.Both cones are related to the cones of positive semidefinite and
entrywise nonnegative matrices: every completely positive matrix is
doubly nonnegative , i.e., positive semidefinite and componentwise
nonnegative, and it is known that up to dimension 4 the reverse
statement also holds true. Therefore, the case of 5x5 matrices is of
special interest. The talk will give an overview on the role of all mentioned matrix
cones
in mathematical programming, and provide some new results about the
5x5
completely positive and doubly nonnegative matrices.


Intercity number theory seminarApril 16, Leiden. Room 40911:1512:00  Ronald van Luijk, Computing Picard groups Abstract. In general it is hard to find the Picard group of a given surface
defined over a number field. I will start by describing a method from
2004 that computes at least the rank in many cases. We will also
describe various improvements that have been made to this method and
conclude with the latest related trick, by Shioda and Schuett, which
allows us to find not only the rank, but also generators for the
Picard group.  12:1513:00  Bart de Smit, Deformation rings of group representations Abstract. For a representation V of a finite group G over the prime field F_{p} one may wonder if V lifts to a representation over Z_{p}, or over other complete local rings A with residue field F_{p}. It turns out that such a lift to A exists if and only if A contains a quotient of the socalled deformation ring R_{V} of V. In this talk we address the question which local Z_{p}algebras can occur as the deformation ring of some pair (G,V). In particular we will see that not all deformation rings are complete intersections, which answers a question of Matthias Flach. This is joint work with Ted Chinburg and Frauke Bleher.  14:0014:45  Michiel Kosters (Leiden), Tameness and rings of integers Abstract. Let K be a number field.
An important problem in algebraic number theory is to find the integral closure O of Z in K.
In general one is given an order A in K and one can ask for a prime p in Z if p divides the index (O:A).
We will give an easy criterion for this if A is `tame at p'.  15:0015:45  Sep Thijssen (Nijmegen), Recognizing radical extensions of prime degree Abstract. Let K/F be a proper extension of infinite fields, with multiplicative groups K^{*} and F^{*}. Brandis proved in 1965 that the quotient K^{*}/F^{*} is not finitely generated. The situation is much clearer for the torsion subgroup of K^{*}/F^{*}. Due to van Tieghem we know that the torsion subgroup of K^{*}/F^{*} is finite when K and F are number fields. Furthermore there is a polynomial time algorithm that constructs all elements of this group.Elements of K^{*} that are torsion over F^{*} are radicals. So it is not surprising that the algorithm uses techniques to recognize radical extensions. A well known theorem in Galois theory states that a cyclic extension is a radical extension when the ground field contains sufficient roots of unity. Many text books contain a proof that is based on Hilbert 90. The theorem itself originates from ideas of Lagrange and his resolving equations. In the talk I shall present a way to construct radicals without the condition of roots of unity in case of an extension of prime degree.  16:1517:00  Peter Stevenhagen, Primitive roots and arithmetic progressions 

Intercity number theory seminarMay 21, Utrecht. Buys Ballot Lab, room BBL 06511:3012:20  Noriko Yui (Queens), The modularity of certain K3fibered CalabiYau threefolds over Q Abstract. We consider certain K3fibered CalabiYau threefolds defined
over Q. We will discuss their modularity (automorphicity). Some of the
CalabiYau threefolds considered here are shown to be of CM type. We
establish the modularity of such CalabiYau threefolds, and their mirror partners (if exist) in the sense of Arthur and Clozel. Several explicit examples are discussed. This reports on a joint work in progress with Y. Goto and R. Livne.  13:3014:20  Esther Bod (Utrecht), Algebraicity of the AppellLauricella and Horn functions Abstract. The AppellLauricella and Horn functions are generalizations of the
Gauss hypergeometric function. In 1873, Schwarz found a list of all rational
parameters such that the Gauss function is algebraic over C(z). In 2006,
Beukers proved a combinatorial criterion for algebraicity of general
GKZhypergeometric functions. In this talk, I will explain some basic concepts
of GKZhypergeometric functions and show how we can use Beukers' criterion to
extend Schwarz's list to all AppellLauricella and Horn functions.  14:3015:20  Bart de Smit, The covering spectrum of Riemannian manifolds Abstract. The Galois configurations of nonisomorphic number fields with the same zeta functions can also be used to make nonisomorphic Riemannian manifolds with the same Laplace spectrum. In this talk we give a group theoretic criterion
for two Riemannian manifolds to have the same covering spectrum, and we show
by group theoretic means that the covering spectrum is not a spectral invariant. This is joint work with Ruth Gornet and Craig Sutton.  15:4016:30  Gunther Cornelissen, Some Dirichlet series in Riemannian geometry Abstract. It is known that the spectrum of the LaplaceBeltrami operator doesn't
necessarily determine a RIemannian manifold up to isometry. Knowing the spectrum
is the same as knowing the zeta function of the manifold. I will define more
general Dirichlet series on closed Riemannian manifolds that do capture the
manifold up to isometry. This allows one to define a "length" of a homeomorphism
of Riemannian manifolds. 

Intercity number theory seminarJune 11, Leiden. Part of the workshop on numeration at the Lorentz CenterSpeakers: Boris Adamczewski, Vilmos Komornik, Mike Keane and Mark Pollicott. 09:3010:30  Mark Pollicott, Dynamical Zeta Functions Revisited Abstract. Dynamical zeta functions are complex functions which are used, amongst other things, to asymptotically count dynamical quantities for either discrete maps or flows (e.g., closed orbits). The basic philosophy is that the more you know about the domain of zeta function the more you know about the properties of the dynamical system.i) Extending the Domain of zeta functions: In these lectures we will describe different approaches to extending zeta functions, culminating in recent progress on extending Ruelle zeta functions for Anosov diffeomorphisms and flows using operator theoretic methods, and their applications. ii) Special Values of zeta functions: Once a zeta function (or the closely related Lfunction) has an extension to a larger domain it is a natural question to ask what is the significance of the locations of the zeros, the poles and their residues, and the value of the function at specific values. Frequently, these provide interesting global information about the system. We will describe a number of results of this type. iii) Dynamical zeta functions and counting: One of the historical motivations for studying (dynamical) zeta functions was to obtain asymptotic estimates, particularly on the number of closed orbits. We will describe both classical results and recent results. Throughout we will motivate the work by drawing analogies with classical results in number theory.  11:0012:00  Mike Keane (Wesleyan), Numeration dynamincs Abstract. Using an idea I developed some time ago, I explain how to
write the usual continued fraction transformation on the unit interval
as a transformation acting on coefficients of quadratic polynomials,
instead of as a mapping on [0,1]. This leads to a geometric picture of
this transformation in terms of a socalled baker's transformation,
from which the ergodic nature of the transformation can be easily
deduced. As a byproduct I obtain a derivation of the wellknown
invariant distribution discovered by Gauss and documented in his
notebooks and in a letter to Laplace. Then, according to an idea of
Allouche, I use this representation to sketch a simple proof of
Lagrange's theorem on the periodicity of continued fractions for
quadratic irrationals. Finally, I shall discuss an up to now
unsuccessful attempt to use these ideas to prove that the classical
Cantor middlethird set does not contain any quadratic irrationals.
 13:0014:00  Vilmos Komornik, Expansions in noninteger bases Abstract. Expansions in noninteger bases often appear in number theory and probability theory, and they are closely connected to ergodic theory, measure theory and topology. Seemingly innocent questions lead to surprisingly deep problems many of which are still open. Starting with a discussion of Renyi's greedy or betaexpansions, we give an overview of various results concerning the number of expansions of some given real number in a given base. Most of the early results in this field are due to P. Erd\H os and his collaborators. Next we concentrate ourselves to the case of unique expansions and we clarify the rich combinatorial, topological and fractal nature of the set of such bases and real numbers. Finally, we study the existence of socalled universal expansions and their relationship to problems of Diophantine approximation.  14:3015:30  Boris Adamczweski, Automata in Number Theory Abstract. Among infinite sequences or infinite sets of integers, some have a rigid structure, such as periodic sequences or arithmetic progressions, whereas others, such as random sequences or random sets, are totally unordered and could not be described in a simple way. Finite automata are one of the most basic model of computation and thus take place at the bottom of the hierarchy associated with Turing machines. Such machines can naturally be used at once to generate sequences with values over a finite set, and as a device to recognize some sets of integers. One of the main interest of these automatic sequences/sets comes from the fact that they are highly ordered without necessarily being trivial. One can thus consider that they lie somewhere between order and chaos, even if, in most respects, they appear to have a rigid structure. In these lectures, I will survey some of the connections between automatic sequences/sets and number theory. Several substantial advances have recently been made in this area and I will try to give an overview of some of these new results. This will possibly includes discussions about prime numbers, the decimal expansion of algebraic numbers, the search for an analogue of the SkolemMahlerLech theorem in positive characteristic and the study of some Diophantine equations that generalize the famous Sunit equations over fields of positive characteristic.  15:3016:30  Shigeki Akiyama, What is the Pisot conjecture? Abstract. In this talk, I wish to give a rathor personal account on Pisot conjecture of substitutive
dynamical systems. This conjecture contains many interesting aspects: ergodic, analytic,
combinatorial and number theoretical nature. Moreover it can also be understood as a problem of
numeration on Pisot number base, which is called DumontThomas number system. In the end, I wish to
talk on a possible generalization in higher dimension 

Intercity number theory seminarSeptember 3, Leiden. Room 17411:3012:30  Lenny Taelman, Mass formulas for finite pgroups Abstract. Fix a positive integer n. We will study the function which
associates to a prime number p the mass of the category of groups of
order p^{n}. This mass is defined to be the rational number ∑_{G}
1/#Aut(G), where G runs over the set of isomorphism classes of groups
of order p^{n}.We will make use of the correspondence between nilpotent groups and
Lie algebras due to Lazard, and a result coming from the theory of
motivic integration due to Denef and Loeser. No prior knowledge of
these techniques will be assumed.  13:3015:30  Andrea Lucchini (Padova), The probabilistic zetafunction of finite and profinite groups Abstract. See PDF  15:4516:45  Hendrik Lenstra, Radical Galois groups Abstract. Given a field K with separable closure K_{sep}, let L be the
field obtained by adjoining to K all elements x of K_{sep} for
which there is a positive integer n such that x^{n} belongs
to K. The lecture is concerned with describing the Galois
group Gal(L/K) as well as the kernel of the restriction
map of Gal(K_{sep}/K) to Gal(L/K). 

Intercity number theory seminarSeptember 17, Eindhoven. DIAMANT seminar room (HG 9.41).
Tea and cookies will be served at 15:1511:4512:30  Wouter Zomervrucht (Leiden), The complexity of Buchberger's algorithm Abstract. Thomas Dubé (1990) proved the existence of a Gröbner basis of a multivariate polynomial ideal with an explicit upper bound for the degree of its polynomials; this bound is doubly exponential in the number of variables. Similar lower bounds are known.
These results, however, do not apply to the complexity of Buchberger's algorithm  the standard algorithm for the construction of Gröbner bases.
For this algorithm, no general complexity bound appears to be proved
in the literature. We will prove such a bound, given in terms of the
Ackermann function.  13:3014:15  Jan Draisma, Gröbner bases in infinitely many variables, or equations for the 2factor model Abstract. In 1928, educational psychologist Truman Lee Kelley
published "Crossroads in the Mind of Man", which contained a new
"pentad test" for Gaussian factor analysis with two factors. Pentads
are degree5 polynomials that vanishes on all symmetric nxnmatrices
that can be expressed as a rank2 matrix plus a diagonal matrix. In
their recent algebraic approach to factor analysis, Drton, Sturmfels,
and Sullivant raise the problem of determining all such polynomials. I
will report on a finite computation that determines a generating set
of polynomials for all n. While the result is very satisfactory, the
methodGröbner bases in infinitely many variablesis likely to
have even more striking applications in the future. This is joint work with Andries
Brouwer.
 14:3015:15  Christiane Peters, Wild McEliece Abstract. We propose using the McEliece publickey cryptosystem with ``wild Goppa codes''.
These are subfield codes over small F_{q} that have an increase
in errorcorrecting capability by a factor of about q/(q1).
McEliece's construction using binary Goppa
codes is the special case q=2 of our construction.
The advantage of considering the case q>2 is that larger finite
fields allow to use smaller keys at the same security level.
We explain how to use wild Goppa codes in the McEliece cryptosystem and
how to correct ⌊ qt/2 ⌋ errors
where previous proposals corrected only ⌊ (q1)t/2⌋ errors.
We also present a listdecoding algorithm that allows even more errors.
This is joint work with Daniel J. Bernstein and Tanja Lange.
http://eprint.iacr.org/2010/410
 15:4516:30  Yael Fleischmann (Eindhoven), Questions of rationality in Ruan's conjecture on crepant resolutions Abstract. After he gave an new definition of a cohomology of orbifolds, Y. Ruan conjectured in 2002 that the cohomology ring of a
complex orbifold [Y] and the cohomology ring of a crepant resolution of the underlying space Y are isomorphic, if such a
crepant resolution exists. In 2007, J. Bryan and T. Graber gave a conjecture describing this isomorphism. In my
talk I will give an overview of my diploma thesis where I proved Ruans conjecture restricted to the 2dimensional complex
case and ADE singularities using Bryans and Grabers results. 

Intercity number theory seminarOctober 1, Nijmegen. The first talk will be in room HG00.086 and the last two talks in room
HG00.071. This is also the day of the Wiskundetoernooi.14:3015:15  Cecilia Salgado, Zariski density of rational points on del Pezzo surfaces of low degree Abstract. Let k be a nonalgebraically closed field and X be a surface defined over k. An interesting problem is to know
whether the set of krational points X(k) is Zariski dense in X. A lot of research is done in this field but, surprisingly, this
problem is not completely solved for the simplest class of surfaces, the rational, where one expects a positive answer. In this lecture I
will define del Pezzo surfaces, a important subclass of rational surfaces. I will talk about the cases already treated (mainly by Manin),
as well as the two cases left open, the del Pezzo surfaces of degrees one and two, presenting recent results (in progress) in the field.
 15:3016:15  Rajender Adibhatla (Essen), Higher congruence companion forms Abstract. This talk will discuss the local splitting behaviour of ordinary,
modular Galois representations and relate them to companion forms and
complex multiplication. Two modular forms (specifically pordinary,
normalised eigenforms) are said to be "companions" if the Galois
representations attached to them satisfy a certain congruence property.
Companion forms modulo p play a role in the weight optimisation part of
(the recently established) Serre's Modularity Conjecture. Companion
formsmodulo p^{n} can be used to reformulate a question of Greenberg
about when a
normalised eigenform has CM.  16:3017:15  David Gruenewald , Explicit Complex Multiplication in Genus 2 Abstract. In this talk we make explicit the Galois action on the CM moduli for genus 2
Jacobians. By using recently computed (3,3)isogeny relations, we demonstrate
how this can be used to improve the CRT algorithm for computing Igusa class
polynomials, providing some examples. This is joint work with Reinier
Bröker and Kristin Lauter. 

Stieltjes afternoonOctober 8, Leiden. An afternoon with presentations on the work of John Tate. 
Intercity number theory seminarOctober 15, CWI Amsterdam. Room L01714:0014:45  Alexander Kruppa (CWI), The factorization of RSA768 Abstract. The factorization of the RSA challenge number RSA768 of 232 digits (768
bits) with the General Number Field Sieve by an international team on
December 12th, 2009, set a new record for the factorization of hard,
general integers. This talk gives a brief introduction to the Number
Field Sieve, describing the different steps of the algorithm, how they
were carried out in the case of RSA768 using computing resources
distributed over various countries, some of the difficulties that arose
and how they were solved.  15:0015:45  Florian Luca, Multiperfect repdigits Abstract. For a positive integer n, let σ(n) denote the sum of
divisors of n.
Positive integers n such that σ(n)/n is an integer are called
multiperfect. These include the perfect numbers n (for
which the
above ratio is 2) as well as others such as n=120 for which
σ(120)/120=3.
Given an integer g>1, a {\it base g repdigit} is a positive
integer N whose
base g representation consists of a string of identical digits d. Such a
base g repdigit is therefore of the form N=d(g^{m}1)/(g1), where
d∈\{1,ldots,g1\} is the repeated digit and m is the number of
base g digits of N.
In this talk, I will show that in any fixed base g>1, there are only
finitely many repdigits N which are multiperfect. When g=10, the only
such is N=6.  16:0016:30  Herman te Riele, Rules for construction of amicable pairs Abstract. Amicable pairs are pairs of positive integers (m,n), m<n, satisfying
σ(m)m=n and σ(n)n=m, where σ is the sumofdivisors
function. Smallest example: (220,284). Many ``rules'' for finding
amicable
pairs are known and these rules have played a major role in the
construction
of the
current list of almost twelve million known amicable pairs.
Still, it has not yet been proved
that the number of amicable pairs is infinite.
In this talk some rules will be discussed, including a rule of Erdős,
to find amicable pairs, and implications for a possible proof of the
existence
of infinitely many amicable pairs.  16:4517:30  Gabriele Dalla Torre, Digits and powers of two Abstract. Consider the sequence of powers of two written in base 10. Does the
sum of the digits in 2^{n} tend to infinity? Is it eventually
increasing? Are there infinitely many powers of 2 with more digits 4 than
digits 8? These and other similar questions will be discussed in the talk. 

RISC/Intercity Number Theory SeminarNovember 18, CWI Amsterdam. Special two day seminar on towers of function fields including lectures
of Garcia and Stichtenoth. 
DIAMANT SymposiumNovember 26, Lunteren. Two day workshop with a special session on the ABC conjecture on Friday afternoon. Speakers: Masser, Oesterlé, Palenstijn. 
Intercity number theory seminarDecember 10, Groningen. Room 293 Bernoulliborg,
Speakers: Monique van Beek, Peter Dickinson, Florian Hess, Claus
Diem11:4512:45  Monique van Beek (Groningen), The rank of elliptic curves admitting a 3isogeny Abstract. In the sixties John Tate presented an elementary account on
how
one might succeed in calculating the rank of an elliptic curve over the
rational numbers, in case the curve admits a rational isogeny of degree
2.
In my master's thesis I do the same for elliptic curves admitting a
rational
isogeny of degree 3. The talk discusses some aspects of this.
 13:3014:30  Claus Diem, On the discrete logarithm problem in elliptic curves. Abstract. It is well known that the classical discrete logarithm
problem (the problem to compute indices modulo prime numbers) can be
solved in
subexponential expected time.
In contrast, it is not known whether the discrete logarithm problem in
the groups of rational points of elliptic curves over finite fields
(the elliptic curve discrete logarithm problem) can be solved in
subexponential expected time. Indeed, it was the lack of an obvious
algorithm for this computational problem which was faster than
"generic" algorithms which lead Miller and Koblitz to suggest the use
of the problem for cryptographic applications.
In 2004 Gaudry gave a randomized algorithm with which one can  under
some heuristic assumptions  solve the elliptic curve discrete
logarithm problem over all finite fields with a fixed extension degree
at least 3 faster than with generic algorithms. Based on this work, in
an article which is going to be published in Compositio Mathematica, I
have shown that there exists a sequence of finite fields (of strictly
increasing cardinality) over which the elliptic curve discrete
logarithm problem can be solved in subexponential time.
In this talk I want to explain how my previous result can be extended
such that over more families of finite fields the elliptic curve
discrete logarithm problem can be solved in expected subexponential
time.
 14:4515:45  Peter Dickinson, Lineartime checking of sparse matrices for complete positivity Abstract. The cone of completely positive matrices and its dual, the
cone of copositive matrices, are useful in optimisation, especially in
providing convex formulations of NPcomplete problems. It has been
proven that telling if a matrix is copositive is a coNPcomplete
problem and it is widely expected that telling if a matrix is
completely positive is an NPcomplete problem. In this talk we study
how to check sparse matrices for complete positivity. We present
lineartime methods for preprocessing a sparse matrix in order to
reduce the problem. For some types of matrices these methods do not
just reduce the problem but in fact solve it in lineartime.  16:0017:00  Florian Hess, The TateLichtenbaum pairing and applications Abstract. Pairings on elliptic curves over finite fields have been in the focus
of
one of the most active and important research areas in cryptography
during
the last ten years. The main objectives are their use in cryptographic
primitives and number theoretic, algorithmic issues. We want to discuss
some of these aspects with a view towards class field theory.



