University of Toronto
                  PDE/Applied Math/Analysis Seminar
                      Friday April 7, 12:10-1pm
                          2135 Bahen Center      



SPEAKER:  Prof. Stanislav Molchanov (UNCC)

TITLE:    Transition from a network of thin waveguides to a 
          quantum graph

ABSTRACT: The concept of a quantum graph is popular today not 
          only in Applied Physics (optical fiber networks), 
          but also in Mathematics (Differential Geometry, 
          Spectral Theory). One important problem here is the 
          justification of the transition from the Helmholtz 
          equation in a system of branching cylinders with some 
          boundary conditions (usually, Dirichlet BC) to 
          differential equations on the limiting graph with 
          appropriate "gluing condition" at the vertices of the 
          graph. Is this transition always possible, how can we 
          describe the "gluing conditions",  what are spectral 
          properties of the quantum graph? The talk will have 
          several recent results in this direction 
          (Molchanov, Vainberg).


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University of Toronto PDE/Applied Math/Analysis Seminar 
http://www.math.toronto.edu/appmath/

2005-2006 organizers:
          Pieter Blue           pblue@ math.toronto.edu
          Almut Burchard        almut@ math.toronto.edu
          Bob Jerrard           rjerrard@ math.toronto.edu
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