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Distinguished
Lecture Series 2011 - 2012
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Noga Alon
Tel Aviv University /
Institute for Advanced Study, Princeton
Noga Alon is an Israeli mathematician
noted for his contributions to
combinatorics and theoretical computer
science, having authored hundreds of
papers.
Source: Wikipedia
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Probabilistic Methods in
Combinatorics
First Lecture: The
Probabilistic Method
The discovery that deterministic
statements can be proved by probabilistic
reasoning led already more than fifty
years ago to several striking results in
various mathematical disciplines. It
soon became clear that the method, which
is now called the probabilistic method, is
a very powerful tool for proving results
in Discrete Mathematics.
I will describe several applications of
probabilistic ideas in the proofs of
combinatorial statements. The main
theme is that a probabilistic point of
view may be very helpful even when we are
interested only in purely deterministic
algorithms, or in purely deterministic
mathematical statements.
Second Lecture: The
structure of large graphs
A property of graphs is hereditary if it
is closed under deleting vertices. Many
interesting properties of graphs are
hereditary, and their study reveals some
unexpected phenomena. This study is
heavily based on probabilistic ideas
together with combinatorial, geometric and
analytic tools, including Szemeredi's
Regularity Lemma and Grothendieck's
Inequality, and leads to interesting
extremal and algorithmic applications.
I will survey the topic focusing on
several recent results and questions.
Third
Lecture: Random Cayley graphs
The study of random Cayley graphs of
finite groups is related to the
investigation of expanders and to problems
in combinatorial number theory. I will
discuss this topic, focusing on the
question of estimating the chromatic
number of a random Cayley graph of a given
group with a prescribed number of
generators.
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Lectures
- November 15, 2011 - Tuesday @ 2:00 -
3:00 pm in MS 6627
- November 16, 2011 - Wednesday @ 2:00
- 3:00 pm in MS 6627
- November 17, 2011 - Thursday @ 3:00
- 4:00 pm in MS 6627
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