By A.C.M. Ran, Herman te Riele, Jan Wiegerinck

The eu Congress of arithmetic, held each 4 years, has proven itself as a big foreign mathematical occasion. Following these in Paris (1992), Budapest (1996), Barcelona (2000), and Stockholm (2004), the 5th eu Congress of arithmetic (5ECM) happened in Amsterdam, The Netherlands, July 14-18, 2008, with approximately one thousand contributors from sixty eight diversified nations. Ten plenary and thirty-three invited lectures have been brought. 3 technology lectures defined purposes of arithmetic in different sciences: weather switch, quantum info conception, and inhabitants dynamics. As within the 4 previous EMS congresses, ten EMS prizes have been granted to very promising younger mathematicians. moreover, the Felix Klein Prize used to be provided, for the second one time, for an program of arithmetic to a concrete and hard commercial challenge. there have been twenty-two minisymposia, unfold over the entire mathematical quarter. around desk conferences have been prepared: one on business arithmetic and one on arithmetic and constructing international locations. As a part of the forty fourth Nederlands Mathematisch Congres, which was once embedded in 5ECM, the so-called Brouwer lecture used to be awarded. it's the Netherland's such a lot prestigious award in arithmetic, geared up each 3 years by way of the Royal Dutch Mathematical Society. information regarding Brouwer used to be given in an invited ancient lecture in the course of the congress. those court cases include a variety of the contributions to the congress, offering an everlasting checklist of the easiest of what arithmetic bargains at the present time. A ebook of the ecu Mathematical Society (EMS). dispensed in the Americas through the yankee Mathematical Society.

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Math. Biol. 68 (2006), no. 7, 1601–1623. 16 J. A. Carrillo and J. Rosado [31] G. Toscani, One-dimensional kinetic models of granular flows. RAIRO Modél. Math. Anal. Numér. 34 (2000), no. 6, 1277–1291. [32] C. Villani, Topics in optimal transportation. Grad. Stud. Math. 58, Amer. Math. , Providence, RI, 2003. [33] C. Villani, Optimal transport, old and new. Grundlehren Math. Wiss. 338, Springer-Verlag, Berlin, 2009. [34] V. I. Yudovich, Non-stationary flow of an incompressible liquid. Zh. Vychisl.

Carrillo and Jesús Rosado Abstract. We show how to extend the method used in [22] to prove uniqueness of solutions to a family of several nonlocal equations containing aggregation terms and aggregation/diffusion competition. They contain several mathematical biology models proposed in macroscopic descriptions of swarming and chemotaxis for the evolution of mass densities of individuals or cells. Uniqueness is shown for bounded nonnegative mass-preserving weak solutions without diffusion. In diffusive cases, we use a coupling method [16], [33], and thus we need a stochastic representation of the solution to hold.

2, for m 2 N given together with its factorisation into primes, the number of elements x of the Leech lattice with kxk2 D 2m can be computed in time polynomial in log m. This will be explained in Section 5. 2. p/ is the trace of the Frobenius conjugacy class. We make this more explicit. K` =Q/,! F` /; uniquely determined by the modular form by the following conditions. , irreducible, or the direct sum of two 1-dimensional representations). Secondly, the extension Q ! K` is unramified at all primes p ¤ `.