A major component of this class will be student presentation of
papers. Each student taking the class must do 3 presentations.
Presentations (and projects) will be done in groups of 1-3 students.
Students should provide either lecture note or slides for their
presentations and should mail these out to the class mailing list at
least 24 hours before their presentation (remember pictures are
extremely helpful in presentations). Each student in the group should
do approximately 1 hour of lecture time per presentation (i.e. 3 hours
of presentation for the entire class) but it's fine to break up this
time over multiple days.
Presentations should demonstrate some careful and deep thought about
the papers presented. In particular, you are expected not only to
present the results in the paper and describe interesting and useful
mathematical tools used to achieve these results, but you are also
expected to critique the paper. How important/realistic are the
results? What is the weakest part of the paper? How could the
results in the paper be improved? What are the major open problems in
the paper? What major questions does the paper raise? Do you have
any ideas on how to approach these open problems/questions? Answering
these questions in your presentations should form the basis for your
Your presentation grade will depend both on written material (slides
and/or notes) and your oral presentation. Possible papers to present
are listed below. Remember for slides that a rough rule of thumb is
to spend 2 minutes on each slide also try to avoid ever putting more
than 4 bullets or 4 sentences on a slide. Pictures are better than
words for slides. Examples are also very helpful.
If you're very interested in an area or a paper that is not listed
below, please talk to me about adding it.
Dynamic Graphs and Dynamic Processes
Q: How do dynamic processes (e.g. worms and viruses) behave on static
graphs and dynamic graphs? What are the properties that determine
rate of spread on static and dynamic networks? How can we efficiently detect an epidemic process?
Fairness and Sperner's Lemma
Q: How can we ensure fair division of resources even with cheating players?
Quantum Computations and Security
Q: How we can use the power of quantum computation to break old security protocols or to build new ones?
Game Theory and Auctions
Q: How can we make auctions robust to coalitions of cheating players?
How can we design auctions and mechanisms that ensure there is no incentive for side
Worms and Viruses
Q: How can we automatically detect and contain worms and viruses?
There are many papers in this area on graphs like buttefly and
multibutterfly network. If you're interested in this topic, please
come talk to me - a reasonable place to start out would be looking at
the papers and bibliographies on my web page.
Q: How can we ensure privacy of information in a large scale network? What is the cost of preserving privacy?
There are many interesting mathematical topics here including: secret
sharing, public key cryptography, zero-knowledge proofs. Listed below
are just some sources for material for lectures.
Q: How can we use eigenvectors and eigenvalues to enhance robustness or to find information?