This school is the 8th of a series of summer schools to take place in Colombia, taking place every other year since July 1999. The topics of these schools lie on the border line between geometry, topology and algebra quantum field theory, and they offer courses addressed to both physicists and mathematicians with a master’s level in either of the fields. The school will take place in Villa de Leyva, from July 15 to July 27; a total of 13 days during which the lecturers (leaders in their own areas) will give both mini-courses and specialized talks on their fields of expertise for students at the masters and PhD levels. The length of each course will range from 5 to 7 hours and they will serve as introductions to active areas of research these days. The lecture notes will be posted on the school's web site and then published in a proceedings volume, as were the lectures given at the past schools. There will be the opportunity for participants to present their research which may, eventually, be considered for publication in the proceedings prior the approval of a referee. Also, there will be poster sessions where students will be able to present their masters work or their partial results on their Ph.D. work. Last but not least, due to the fact that the village of Villa de Leyva is small enough, there has been plenty of scientific interaction between professors and participants in the past. We expect the same to happen in this forthcoming opportunity.
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