2007 Bowen Lectures
The Twenty-Seventh Annual Bowen Lectures will be delivered by Michael Freedman on October 9, 10 and 11.
The Bowen lectures are supported by an anonymous donor, who was an undergraduate student of Professor Bowen.
Department of Mathematics, University of California, Berkeley, presents
The 2007 Bowen Lectures
Michael Freedman
Fields Medalist
Microsoft Research
Quantum Information, Quantum Physics, and Quantum Topology
Abstract:
Much of modern (quantum) topology is descended from the Jones
polynomial, but the Jones polynomial turns out to be (merely) the
"calculus" for certain physical systems that can now be produced in
laboratories. These physical systems "realize" the mathematical
abstraction of quantum topology. It is almost as if the Navier Stokes
equation was discovered BEFORE water. Some of these physical systems are
thought to be universal quantum computers if only we can harness them. I
will talk about how this might be done, and more abstractly, on what
constraints topology enforces on quantum mechanical systems in 2+1 and
3+1 dimensions.
Lecture I: How topology will save Moore's law: quantum computation via exotic states of matter
Tuesday, October 9
Sibley Auditorium, Bechtel Hall - 4:10pm-5:00pm
Abstract: Einstein wrote, "God integrates empirically, he
is not concerned with our mathematical difficulties." A quantum computer
will allow us (as well) to integrate the Shrodinger equation. Like the
microscope before it, the quantum computer will peer into an unseen
space. It is difficult to believe that this space, once illuminated,
will be less interesting or less germane than the "space" of a living
cell.
"Building" a quantum computer appears to be a nearly impossible task,
however we may expect to "find" natural quantum computers through the
study of 2-dimensional systems of interacting electrons. These natural
computers are topological states of matter exhibiting "nonabelian
statistics." For background one may read: ["Computing with Quantum
Knots" - Scientific American, April 2006] and ["Topological quantum
computation" - Physics Today, July 2006.]
Reception in 1015 Evans at 5:15 pm following Tuesday's lecture.
Lecture II: Topological phases of matter in 2+1 dimensions
Wednesday, October 10
Room 105, North Gate - 4:10pm-5:00pm
Abstract: I will attempt to explain the Fractional
Quantum Hall Effect (FQHE) in mathematical terms, and how we hope to
manipulate FQHE systems as quantum computers. This will include the Idea
of braiding quasiparticles (anyons), and also a more recent idea:
"topological, measurement-only, quantum computation". This latter topic
may have some philosophical implications related to the paradox of the
(apparent) existence of the classical world. I will touch on this.
Lecture III: Positivity of Three Manifold Pairings
Thursday, October 11
Sibley Auditorium, Bechtel Hall - 4:10-5:00pm
Abstract: Since Milnor built the exotic 7-spheres in 1956 by gluing together two copies of S3 x D4,
gluing has played a key role in manifold topology. In this talk, I will
borrow and idea from quantum mechanics and consider gluing
superpositions of manifolds. It turns out that there is a dramatic
difference according to dimension. The natural pairings induced by
gluing have null vectors when the manifold dimension is 4 or higher, in
contrast the pairings are positive when the dimension is 3 or lower.
This difference has a profound implication for what topological features
can be captured within the physics of a d-dimensional quantum
mechanical system; it gives another perspective on the fact that the
known topological phases of matter are 2+1 dimensional.
The last two lectures will be accessible to both mathematicians and theoretical physicists.