Events
Workshop on Geometry and Computation

MPI für Mathematik in den Naturwissenschaften Leipzig

A3 01 (Sophus-Lie room)

conference

21.01.06

Workshop on Geometry and Computation

conference

21.01.06

Workshop on Geometry and Computation

Program

10:00 - 10:45	Armin Uhlmann (Universität Leipzig) On convex (concave) roofs Given a function g on the exrtremal points of a convex compact set K, one may ask for the largest convex extension $g^{\cup}$ of $g$ on $K$ . Similar the smallest concave extension $g^{\cap}$ ist defined. Entanglement of formation, entanglement of assistance, some concurrences belong to these classes of functions. If the extreme boundary of K is also compact and g is continuous, then a remarkable phenomenon takes place: $K$ is covered by convex subsets on each of which the extension, say $g^{\cup}$ , is affine, and every one of these subsets is convexly generated by some extremal points of $K$ . Because of this I have called $g^{\cup}$ and $g^{\cap}$ "roofs" . I try to explain how to use this as a tool and I show the structure of some of the known examples, with and without bifurcations.
10:45 - 11:30	Shao-Ming Fei (MPI MiS) Theory of Quantum Entanglement: Measure and Local Equivalence We introduce some recent results on quantum entanglement (which plays key roles in quantum information processing): in particular, the derivation of the measure of entanglement: Entanglement of Formation and Concurrence for mixed bipartite quantum states; the classification of quantum states under local unitary transformations: nonlocal properties and local invariants, geometry and dimensions of the orbits.
11:30 - 11:45	Coffee break
11:45 - 12:30	Sabine Jansen (Technische Universität Berlin) The adiabatic theorem and quantum adiabatic computing The quantum adiabatic approximation has a long history. Recently, the realization that the adiabatic approximation could be used as the basis for a method of quantum computing has generated a resurgence of interest in this topic. We present a simple proof of the theorem with explicit error bounds and sketch the application of the bounds to Grovers algorithm.
12:30 - 14:30	Lunch
14:30 - 15:30	Markus Müller (Technische Universität Berlin) Stationary algorithmic probability The randomness of finite words can be measured in terms of Kolmogorov complexity and algorithmic probability. Nevertheless, both notions depend on the arbitrary choice of an underlying universal computer U. We propose a machine-independent approach to algorithmic probability, resulting from a Markov process that describes computers that randomly simulate each other.
15:30 - 16:00	Stephan Weis (Universität Erlangen) Curvature of exponential families and ruled surfaces The state space of two bits contains the exponential family of product states. This family forms a surface of second order and is also a ruled surface. For the latter, there exists a geometrically motivated parametrization that implies an easy curvature formula. Which of these structures may be extended to exponential families of a more general type?
16:00 - 16:15	Coffee break
16:15 - 17:00	Nihat Ay (MPI MiS) On the affine structure of exponential families A natural geometric approach to dual structures will be presented. In particular exponential families will be discussed within the context of Stephan Weis' talk.
17:30 - 18:30	Dinner at "Brasserie Augustus", Augustusplatz 14 (à la carte and on the basis of individual payment): (à la carte and on the basis of individual payment)

Organizers

Nihat Ay

Max Planck Institute for Mathematics in the Sciences

Administrative Contact

Antje Vandenberg

Max-Planck-Institut für Mathematik in den Naturwissenschaften Contact via Mail