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Leonidas Alaoglu Memorial Lecture
in Mathematics
Wednesday, May 9, 2012

4:00 p.m.  151 Sloan

Spencer Bloch
R. M. Hutchins Distinguished Service Professor
University of Chicago

Motives associated to configuration spaces,
fundamental groups, . . .

Abstract: Roughly speaking, a motive is a cohomology group of an algebraic variety, or more generally a diagram of algebraic varieties. Motives carry a great deal of interesting arithmetic structure: complex periods, l-adic galois representations, p-adic frobenius modules, etc. I will discuss a class of examples which include configuration spaces and motives associated to fundamental groups of algebraic varieties.

The discussion will focus on basic combinatorial properties, e.g. relations between Euler characteristics of motives and chromatic polynomials of graphs. I will also discuss periods; e.g. multiple zeta values, multiple polylogarithms, and multiple elliptic polylogarithms. Work of Ceyhan-Marcolli shows that Feynman amplitudes in position space are analogous to periods of such motives.

The talk will not use methods beyond elementary topology and complex manifold theory.

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Spencer Bloch, the Robert M. Hutchins Distinguished Service Professor in Mathematics at the University of Chicago, focuses his research on arithmetic algebraic geometry. He looks for unifying properties of certain numbers called periods (pi, for example, is a period), which arise in geometry and arithmetic. Currently, he is looking at periods coming from quantum field theory in physics. Bloch has served as editor of several mathematics journals, including the American Journal of Mathematics, the Bulletin of the American Mathematical Society, Compositio Mathematica, the Journal of Algebraic Geometry and Communications in Algebra, K-Theory, Mathematical Research Letters. An elected member of the National Academy of Sciences, he also has received fellowships from the Alfred P. Sloan Foundation, the North Atlantic Treaty Organization and France’s National Center for Scientific Research. His other honors include receiving the Alexander von Humboldt Prize and being named the Takagi Lecturer in Kyoto.

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The Leonidas Alaoglu Memorial Lecture was established by friends and family of the late Leonidas Alaoglu in recognition of his great talents, distinguished contributions to mathematics, and long friendship with Caltech. The Institute is privileged to honor his memory with a lecture each year by an outstanding mathematician.

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