Invited Speakers
Titles and Abstracts
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Manuel Kauers
Johannes Kepler University, Austria 
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D-Finiteness: A Success StoryAbstract: A considerable portion of the work on special functions in computer algebra during the past decades was focused on D-finite functions. This focus was chosen for good reasons, as the concept of D-finiteness has proven to provide a fairly good compromise between, on the one hand, covering as many functions as possible, and on the other hand, keeping the class of functions restricted enough that computations stay reasonably efficient. In the talk, we will illustrate how questions about D-finite functions naturally arise in applications and how computer algebra is nowadays routinely used to answer such questions. |
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Teresa Krick
Universidad de Buenos Aires, Argentina 
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Effective bounds for polynomial systems defined over the rationalsAbstract: Given some computer algebra problems described by polynomials with rational coefficients, I will present tools that help measure the complexity of the problem by describing bounds for the degrees and heights (i.e. bit-sizes) of the output solution in terms of those of the input data. I will focus on the case of finite common roots, detailing an arithmetic Bézout inequality and some consequences, including an arithmetic shape lemma. I will also present an arithmetic Nullstellensatz and an arithmetic Perron's theorem for algebraic dependence equations. |
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Sergio Rajsbaum
Universidad Nacional Autonoma de Mexico, Mexico 
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An introduction to distributed computing and the combinatorial topology approachAbstract:
Modern computer systems are becoming more and more concurrent. Nearly every activity in our society
depends on the Internet, where distributed databases communicate with one another and with human
beings. When a customer asks to withdraw money from an automatic teller machine, the banking system must either both
provide the money and debit that account or do neither, all in the presence of failures and unpredictable
communication delays. Concurrency is not limited to wide-area networks. As transistor sizes shrink,
manufacturers have focused on making processors more parallel.
Shared-memory multiprocessors are systems that concurrently execute multiple threads
of computation which communicate and synchronize through data structures in shared
memory. The efficiency of these concurrent data structures is crucial to performance, yet they are far more difficult to design than sequential
ones because threads executing concurrently may interleave their steps in many ways, each with a different and potentially unexpected outcome. |
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J. Rafael Sendra
CUNEF, Spain 
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Symbolic and Algebraic Manipulation of Parametric Algebraic Curves and SurfacesAbstract: With the emerging development of symbolic computation, and more specifically of computer algebra, there appeared a clear interest, in the theory of algebraic curves and surfaces, in the development of symbolic algorithms and the algebraic manipu- lation of this type of mathematical objects. On the other hand, progress in the field of applications, such as computer aided design, brought with it the raising of new computational issues, in our case related to the parametric representation of curves and algebraic surfaces. These questions of applied origin, which probably would not have been raised naturally from the more theoretical field, were translated into true theoretical and algorithmic challenges that immediately captured the interest of the computer algebra communitity. As a consequence, an active field of research emerged that is still alive and full of challenges today. In this talk we will give a panoramic view of the state of the art, and describe some of the main challenges. |