Wednesday, May 9, 2012
R. M. Hutchins Distinguished Service Professor
University of Chicago
associated to configuration spaces,
fundamental groups, . . .
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
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.
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.