[Turkmath:6975] April 16 (Friday), 2010 - 14:00, Szilard Szabo (Budapest University of Technology and Economics), The minimal number and algebraic construction of apparent singularities of logarithmic connections

[Kursat Aker]

TUBITAK <http://www.tubitak.gov.tr>Feza Gursey Institute 
<http://www.gursey.gov.tr/>BOUN <http://www.boun.edu.tr>

April 16 (Friday), 2010 - 14:00
*Szilard Szabo* (Budapest University of Technology and Economics)
*The minimal number and algebraic construction of apparent singularities 
of logarithmic connections*

*Abstract :* It is classical to associate a linear first-order system of 
differential equations to a higher-order scalar valued linear equation 
over a complex domain. Conversely, one may ask whether any system over 
the Riemann sphere can be represented in a suitable sense by a 
higher-order equation. The answer to this question is known to be 
affirmative, at least over the complement of a finite subset, whose 
points are called apparent singularities. In this talk, we will 
determine the minimal cardinality of this subset, and give an algebraic 
method to find a representative with this number of apparent 
singularities. This induces rational maps from the moduli space of 
logarithmic connections to projective space. We also spell out the 
choices on which are construction depends, and raise a few open questions.

Poster <http://www.gursey.gov.tr/autoposter/posters/47.pdf>
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