### May 28,2008 - 3:30 pm (Bahen 1180)

*The spectral characterization of manifolds*

### May 29,2008 - 3:30 pm (Bahen 1130)

*A CKM invariant in Riemannian geometry*

May 30,2008 - 3:30 pm (Bahen 1130)

*About the field with one element*

I will show that the first five axioms I had given in 96 on spectral
triples suffice in the commutative case to characterize smooth compact
manifolds. I will also define a new invariant in Riemannian geometry,
which when combined with the spectrum of the Dirac operator is a
complete invariant of the geometry. It is an analogue of the CKM
mixing matrix of the Standard model. In the last lecture I shall
describe joint work with C. Consani and M. Marcolli which shows
how the inductive structure of the algebraic closure of the mysterious
"field with one element" gives rise to the quantum statistical
mechanical system known to give, after passing to the dual system,
a spectral realization of the zeros of the Riemann zeta function,
as well as a trace formula interpretation of the Riemann-Weil explicit
formulas."

Born in France in 1947, Connes entered the École Normale Supérieure
in Paris in 1966, and graduated in 1970. He became a researcher at
the Centre National de la Recherche Scientifique where he completed
his thesis on von Neumann algebras under Jacques Dixmier in 1973.
He was elected to the Académie des Sciences in 1982 and he
was awarded the Fields Medal in 1982. He has contributed to the theory
of operator algebras, including the general classification and structure
theorem of factors of type III and applications of the theory of C*-algebras
to foliations and differential geometry which led to the development
of the new field of non-commutative geometry. He was awarded the Crafoord
Prize in 2001

Speakers in the Distinguished Lecture Series (DLS) have made outstanding
contributions to their field of mathematics. The DLS consists of
a series of three one-hour lectures.

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