15:15
15:15
16:30
16:30
Iteration between model and experiment in studying cardiac mechano-electric feedback: from clinics to channels, and back
Abstract
The heart can be described as an electrically driven mechanical pump. This
pump couldn't adapt to beat-by-beat changes in circulatory demand if there
was no feedback from the mechanical environment to the electrical control
processes. Cardiac mechano-electric feedback has been studied at various
levels of functional integration, from stretch-activated ion channels,
through mechanically induced changes in cardiac cells and tissue, to
clinically relevant observations in man, where mechanical stimulation of the
heart may either disturb or reinstate cardiac rhythmicity. The seminar will
illustrate the patho-physiological relevance of cardiac mechano-electric
feedback, introduce underlying mechanisms, and show the utility of iterating
between experimental research and mathematical modelling in studying this
phenomenon.
17:00
17:00
17:00
Elliptic systems, integral functionals and singular sets
Abstract
I shall give a brief overview of the partial regularity results for minima
of integral functionals and solutions to elliptic systems, concentrating my
attention on possible estimates for the Hausdorff dimension of the singular
sets; I shall also include more general variational objects called almost
minimizers or omega-minima. Open questions will be discussed at the end.
14:15
Brownian motion in tubular neighborhoods around closed Riemannian submanifolds
Abstract
We consider Brownian motion on a manifold conditioned not to leave
the tubular neighborhood of a closed riemannian submanifold up
to some fixed finite time. For small tube radii, it behaves like the
intrinsic Brownian motion on the submanifold coupled to some
effective potential that depends on geometrical properties of
the submanifold and of the embedding. This characterization
can be applied to compute the effect of constraining the motion of a
quantum particle on the ambient manifold to the submanifold.
12:00
Invariant length scale in general relativity
Abstract
Dirac-Born-Infeld Kinematics
14:15
16:30
Symmetries in semidefinite programming, and how to exploit them
Abstract
Semidefinite programming (SDP) techniques have been extremely successful
in many practical engineering design questions. In several of these
applications, the problem structure is invariant under the action of
some symmetry group, and this property is naturally inherited by the
underlying optimization. A natural question, therefore, is how to
exploit this information for faster, better conditioned, and more
reliable algorithms. To this effect, we study the associative algebra
associated with a given SDP, and show the striking advantages of a
careful use of symmetries. The results are motivated and illustrated
through applications of SDP and sum of squares techniques from networked
control theory, analysis and design of Markov chains, and quantum
information theory.
12:00