Fall 2007 Quarter Activities:

We will organize a reading seminar, devoted to learning some techniques from modern probability on a topic which is a subject of active research. A good example are random networks, an area undergoing a rapid expansion in the amount of theory and the number of applications. Here is a short introduction. Some additional information is also available on Raissa's course web page on networks; this course will be a part of the RFG in the Winter quarter. We will read through the recent book by R. Durrett, Random Graph Dynamics, Cambridge Univ. Press, 2007 (currently available for $27.23 on Amazon, but we can probably get by with sharing a few copies). Participants will be expected to give talks and participate in the discussion.

Remco van der Hofstad has lecture notes on the web, which have a lot more introductory (and other) detail than Durrett's book.

There will also be a problem session, where speakers will present open problems. I will also ask visitors to the department to give short talks on their research. During weeks when there is an appropriate Probability Seminar or Colloquium, the participants will be expected to attend it. Part of the problem session will be devoted to the growth processes, currently the area of my primary research interest. Among other possible topics: percolation, random walks, connections to PDE.

Prerequisites: This is an opportunity to learn some advanced probability, but a participant should either have had some exposure to graduate level probability and analysis or be willing to do some extra reading when necessary.

Credit: A participant will receive from 1 unit of credit (by sitting in at least 80% of meetings and participating in the discussion) to 3 units of credit (by giving a few talks).

Fall 2007 Quarter Meetings and Topics

• Tuesday, Oct. 9.
  Reading seminar: Janko Gravner will talk on Erdos-Renyi random graphs.
  Problem seminar: Janko Gravner, "Bootstrap percolation." (Slides.)
• Tuesday, Oct. 16.
  Reading seminar: David Sivakoff will talk on diameter of the giant component of the Erdos-Renyi random graphs.
  Problem seminar: Janko Gravner, "Packard Snowflakes."
• Tuesday, Oct. 23.
  Reading seminar: David Sivakoff will talk on connectivity threshold.
  Problem seminar: Benjamin Morris.
• Tuesday, Oct. 30.
  Reading seminar: Janko Gravner will talk on fixed degree distributions. (Notes on proving Poisson convergence.
  Problem seminar: Janko Gravner, "Random perturbation of Packard Snowflakes." (Slides for both Packard snowflakes presentations.)
• Tuesday, Nov. 6.
  Reading seminar: Janko Gravner will continue to talk on fixed degree distributions.
  Problem seminar: Sebastian Schreiber from Evolution and Ecology.
• Tuesday, Nov. 13. This time we meet in MSB 3106!
  Reading seminar: Raissa D'Souza will give an overview of power laws and relevance to real-world networks.
  Problem seminar: Tim Lewis.
• Tuesday, Nov. 20.
  Reading seminar: Janko Gravner will start talking on preferential attachment (Durrett calls this Barabasi-Albert model).
  Problem seminar: Sebastian Schreiber from Evolution and Ecology.
• Two special meetings for the week of Nov. 26-Nov. 30, both mandatory for the RFG participants. This week, we do not meet at the regular time!
  Tuesday, Nov. 27, 4:10PM, 1147 MSB. Persi Diaconis, Stanford University: What do we know about the Metropolis algorithm?
  Friday, Nov. 30, 5:10pm, 2112 MSB, Special RFG talk. Sergey Gavrilets, University of Tennessee: Dynamics of Coalition Formation and the Egalitarian Revolution
• Tuesday, Dec. 4.
  Reading seminar: Janko Gravner will conclude the derivation of degree distribution in the preferential attachment model.
  This is the last meeting of this quarter. Thanks to all participants, especially the speakers!