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Quasirandomness and Regularity (WS 2005/2006)
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News:
The lecture will be given in english. |
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Dozent:
Dr. Joshua Cooper 
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Zeit und Ort:
Dienstag 14.00 -16.00 Uhr und Mittwoch 11.00 -12.00 Uhr (Vorlesung) / Mittwoch 10.00 - 11.00 Uhr (Übung)
Vorlesungsbeginn ist am 25.10.2005, und die Vorlesungen dauern bis 21.12.2005.
Die mündliche
Prüfung ist am 22. Dezember
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Inhalt:
We will introduce and discuss the areas of quasirandomness and
regularity, the intimate connections between them, and applications.
Both subjects have been very active areas in the past ten years, and
there are many open problems and topics of study still to be addressed.
This course will focus on developing "working knowledge" of
quasirandomness and regularity for several classes of combinatorial
objects: graphs, permutations, Abelian groups, hypergraphs, and others
as time permits. We will spend the first half of the course studying
the definitions and basic theorems in these contexts, beginning with
the series of discoveries by Chung and Graham in the early 1990's. The
second half will consist of more in-depth topics, including
applications to number theory, the seminal work of Simonovits-Sos, and
recent developments in hypergraph regularity. |
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Übungsblätter:
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Voraussetzung:
Recommended background is knowledge of basic combinatorics and graph
theory, and some familiarity with the probabilistic method. However,
the presentation will be self-contained, and so previous experience in
these areas is not strictly necessary.
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Lecture Notes
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Literatur:
Komlós, János; Shokoufandeh, Ali; Simonovits,
Miklós; Szemerédi, Endre; The regularity lemma and its
applications in graph theory.
Theoretical aspects of computer science (Tehran, 2000),
84--112, Lecture Notes in Comput. Sci., 2292, Springer, Berlin, 2002.
- Alon, Noga; Spencer, Joel H. The probabilistic method.
Second edition.
With an appendix on the life and work of Paul Erdös.
Wiley-Interscience Series in Discrete Mathematics and Optimization. Wiley-Interscience [John Wiley & Sons], New York, 2000.
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Links:
Komlós, Simonovits, Szemeredi's Regularity Lemma and its Applications in Graph Theory.
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