Mathematical Physics
Seminar
December Schedule
- Speaker- J.P. Solovej, University of Copenhagen
- Time/Place- Thursday 12/4/03, 11:30am in Hill 423
- Title-The Ionization Conjecture and the Size of Atoms
- Abstract- It is an experimental fact that the maximal
negative ionization an atom can sustain is one or at most two
electrons. One possible mathematical forumlation of this ionization
conjecture states that the maximal negative ionization of an atom
satisfies an upper bound independent of the atomic number (allowing
for atomic numbers tending to inifinity in non-relativistic quantum
mechanics). A related conjecture states that the radius of atoms
(properly defined) satisfies upper and lower bounds independent of the
atomic number. These conjectures are still open in the full
Schrodinger formulation, but have been proved in the approximating
Hartree-Fock theory. I will explain some of the ideas in the proof and
compare with some experimental data.
Please note there will be a brown bag lunch between the 2
seminars this morning.
Bring your
sandwich.
Coffee and homemade cookies will be
available.
Speaker- E. Sontag, Rutgers University
Title-Interconnections of Monotone Systems with
Steady-State Characteristics
Time/place-Thursday 12/4/03, 1:30pm in Hill 423
Abstract-One of the key ideas in control theory is that of
viewing a complex dynamical
system as an interconnection of simpler subsystems, thus deriving
conclusions
regarding the complete system from the properties of its building
blocks.
Following this paradigm, and mainly motivated by questions in
eukaryotic cell
signal transduction modeling, we have recently developed with
D. Angeli
(Florence) an approach based on components which are monotone systems
with
respect to partial orders in state and signal spaces and have
well-defined
steady-state characteristics. We will present a brief exposition of
recent
results, with an emphasis on small gain theorems for negative feedback
and on
the emergence of multi-stability and associated hysteresis effects
under
positive feedback. We will also discuss how one would apply these
theorems in
practical experimental situations, and in particular to a MAPK cascade
model
discussed in our recent work with Ferrell (Stanford).
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SPECIAL SEMINAR
Speaker- A. Soshnikov, University of California, Davis
Title-Janossy Densities in Determinantal and
Pfaffian Ensembles of Random Matrices
Time-Wednesday 12/10/03, 3:00pm
Place-TBA
Abstract-In the first part of the talk I plan to give an introduction to
detertminantal random point process and discuss some examples. The second
part of the talk is devoted to the problem of the calculation of the
Janossy densities in some special ensembles of random matrices, including
the Laguerre (Wishart) ensemble.