Date  Time  Lecture 

May 31st, 2007  9:4510:00 am  Opening 
May 31st, 2007  10:0011:00 am  Karl Rubin Euler systems in number theory Abstract: Euler systems were introduced about 20 years ago by Kolyvagin, and have become one of the best tools available for relating special values of zeta functions to arithmetic. Euler systems have been used successfully to prove analytic class number formulas, and to make progress on the Birch and SwinnertonDyer conjecture for elliptic curves. In this talk we will describe the basic examples and applications of Euler systems, and explain why an Euler system should be viewed as the algebraic incarnation of a zeta function. 
May 31st, 2007  11:30 am12:30 pm  Pierre Deligne Multizeta values, from the 1740's to now Abstract: Euler introduced multizeta values, and proved identities relating them to zeta values, possibly with the hope of shedding light on the values of the zeta fucntions at odd integers. The modern interpretation of multizeta values as "periods" gives a framework to understand which algebraic relations they should satisfy, but still lacks effectiveness. 
May 31st, 2007  2:303:30 pm  Eberhard Zeidler Euler and the Mathematical Principles of Modern Natural Philosophy Abstract: In 1744 Euler founded the calculus of variations. This is a basic tool for describing the four fundamental forces in nature: strong, weak, electromagnetic, and gravitative interaction. In the 20th century it was discovered that the principle of local symmetry is basic for formulating both the standard model in cosmology and the standard model in elementary particle physics. It is the challenge for the mathematics and physics of the 21th century to create a rigorous unified theory for the fundamental forces acting in nature. 
May 31st, 2007  4:305:30 pm  Stefan Müller Rigidity, Geometry and Elastica Abstract: One of Euler's beautiful contributions to mechanics and analysis is his theory of elastica, onedimensional objects which are unstretchable but bendable. A fundamental problem is to relate Euler's and other theories of thin elastic objects to threedimensional nonlinear elasticity. While since Euler there has been an enormous amount of heuristic ansatzbased derivations of large variety of theories, a mathematical understanding has been suprisingly difficult. In this talk I will discuss a new approach to the rigorous derivation of lowerdimensional theories. The key ingredient is a new geometric rigidity estimate which generalizes Fritz John's work on rotation and strain and can be seen as a quantative version of the classical fact a map from ndimensional Euclidean space to itself whose differential is a rotation (almost) everywhere is already a rigid motion. 
May 31st, 2007  8:159:15 pm  Craig Fraser Leonhard Euler and the History of Mathematics: Changing Perspectives Abstract: Euler has always been recognized as the preeminent figure of eighteenthcentury analysis, rivaled only by Lagrange in his place in the history of the subject. In traditional history this view of Euler's greatness has been combined with a more critical assessment of his understanding of fundamental principles. Euler is seen as someone who was an enormously energetic and resourceful pragmatist with a fairly limited grasp of foundational conceptions. In 1947 Rudolph Langer wrote of Euler's "naive faith in the infallibility of formulas and the results of manipulations upon them." In 1970 Imre Lakatos characterized Euler as a "naive inductivist" who possessed a somewhat uncritical view of foundational matters. In the view of these historians basic conceptions remained undeveloped by him and would only receive a proper formulation in the writings of such nineteenthcentury mathematicians as Cauchy and Weierstrass. 
June 1st, 2007  10:0011:00 am  Ronald J. Stern Euler, Polyhedron, and Smooth 4 dimensional Manifolds Abstract: We will discuss Euler's interest in polyhedra, the open problem of whether every closed manifold of dimension greater than 4 is a polyhedron, and how this leads us to the study of smooth 4dimensional manifolds. We will then discuss our current (lack of) understanding of smooth 4manifolds with an emphasis on those with small Euler characteristic. 
June 1st, 2007  11:30 am12:30 pm  Günter M. Ziegler Euler's Polyhedron Formula  at the starting point of today's Polytope Theory Abstract: The Euler Polyhedron Formula, known as e  k + f = 2 (as shown on the poster), or in modern scientific notation as

June 1st, 2007  2:003:00 pm  Alfio Quarteroni Mathematical Modelling for Environment, Medicine, and Sport: Euler's Legacy Abstract: In this talk I will review some classical mathematical models to describe complex phenomena in continuum mechanics. Applications will concern environmental problems, cardiovascular flow problems, and problems arising from sport competition. 
June 1st, 2007  3:304:30 pm  Anthony Tromba VARIATIONS AND SINGULARITIES Abstract: Euler and Lagrange initiated the study of the first variation of nonlinear integral functionals and Legendre, Jacobi, Weierstrass and H.A. Schwarz the second variation. Schwarz also studied the second variation associated to The Plateau Problem. We will discuss how one can now calculate Nth order variations associated to Plateau's Problem and how these variations are related to the existence or non existence of singularities of minimal immersions. 
June 1st, 2007  5:006:00 pm  Roger Penrose Euler's Profound Influence on Twistor Theory Abstract: Twistor theory provides a scheme whereby spacetime notions are reformulated in terms of complex analysis and geometry. Spacetime points are regarded as secondary entities, to be constructed from spining massless elements (like photons). It owes a great debt to Euler in a number of basic respects. Some of the most striking have to do with twistor diagram theory (the twistor formulation of quantum field theory), where Euler's summing of a divergent series plays a crucial role. 
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