Titlebook: European Congress of Mathematics; Barcelona, July 10–1 Carles Casacuberta,Rosa Maria Miró-Roig,Sebastià X Conference proceedings 2001 Sprin

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0743-1643 second volume collects articles by prize winners and speakers of the mini-symposia..This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician..978-3-0348-9496-8978-3-0348-8266-8Series ISSN 0743-1643 Series E-ISSN 2296-505X

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https://doi.org/10.1007/978-3-8349-9532-2. I will present a couple of examples which underline the fact that computer algebra systems provide easy access to powerful computing tools. And, I will quote from and refer to a couple of survey papers, textbooks and web-pages which I recommend for further reading.

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https://doi.org/10.1007/978-3-642-47538-2fields with small root discriminant improving Martinet’s record. We show that allowing wild ramification to limited depth leads to asymptoti-cally good towers. However, we demonstrate also that the investigation of the infinitude of these towers involves difficulties absent in the tame case.

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Towards a Microscopic Theory of Phase Coexistencel. We illustrate this in the context of the Ising model in the phase coexistence regime: the most likely shapes of macroscopic droplets of one pure phase floating in the other pure phase are close to the Wulff crystal of the model. Furthermore, the law of configurations at equilibrium is governed by

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Constructing Compact 8-Manifolds with Holonomy Spin(7) from Calabi—Yau Orbifolds/F. This paper describes a new construction of compact 8-manifolds with holonomy Spin(.). We start with a Calabi—Yau 4-orbifold Y with isolated singularities of a special kind. We divide by an antiholomorphic involution . of Y to get a real 8-orbifold . Y/(a). Then we resolve the singularities of .

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