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 project proposal. 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 deals?

Worms and Viruses

Q: How can we automatically detect and contain worms and viruses?

Robust Graphs

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.

Spectral Methods

Q: How can we use eigenvectors and eigenvalues to enhance robustness or to find information?