1. Math 557 Research Interests Overview Name: Major/Degree program/Year in Program: Research Group Name/Advisor: (leave blank if none) Summary of Research Interests: (or academic interests – be sure to list interests for which you might apply probability)

2. Specific Example Indicate applications – try to include a picture or specific example of one of your interests to which probabilistic combinatorics could be applied. You might be using a random model (random sensor network), a random algorithm, or attempting to find a combinatorial structure with desired properties. You might look at a random feasible solution and check its properties, a random coloring of the integers, etc.

3. Possible Avenues of Exploration Brainstorm areas of your interest to which probability might be applied, that you would consider pursuing as a project in this course. List one or more major references for this effort.