Description and Organization

Main axiom of this RFG: Everyone is welcome to attend! Especially students! No prior knowledge will be assumed, questions are encouraged!!

This RFG will focus on how other fields helped combinatorics evolved and how combinatorics later became useful in return. It aims to broaden the mathematical knowledge and interests of students. Historically there have been several success stories in which the solution of a difficult problem required the intervention of a novel point of view and connecting together fields that appeared to be wide apart. Examples include commutative algebra methods in combinatorics, which were introduced by Richard Stanley was to solve various problems about f-vectors of simplicial complexes using rings and algebraic geometry. Another famous example is the use of probabilistic techniques to solve problems of existence in combinatorics, a method pioneered by Erdos and Turan in the 1940's. A third example is how computer tools have come to affect research and proofs in combinatorial research; this is exemplified by the proof of the 4-color theorem by Appel and Haken in 1977 and by the Wilf-Zeilberger algorithm used to deduced combinatorial identities.

This RFG will open in the Fall with a Math 280 course teaching topological tools that have been used to solve various problems in combinatorics. Later during the Winter and Spring quarters, the idea will be to run academic seminars/ guest lectures that highlight diverse methodologies that are used when solving combinatorial problems, including at least algebraic, analytic, computational, geometric, probabilistic, topological, etc. We hope several methods will be demonstrated with examples of successful research done with them, so that students see the importance of the interaction of mathematical fields and breadth of knowledge.

We will invite many guest lecturers from among graduate students, postdocs, and faculty. Student participants will be asked to present papers during the reading seminar, and students who wish to earn more than one credit for the course will be required to make a presentation during the reading seminar. In addition, we plan to invite speakers from UC Berkeley, Stanford, MSRI, and the University of Washington to give special lectures. We intend to follow the nice tradition of having the seminar speaker present another seminar just for graduate students where they can learn and prepare for a more technical lecture.

Postdocs Steve Klee (co-lead), Andrew Berget, Amitabh Basu, Arvind Ayyer.

Graduate students: Yvonne Kemper, Katherine Glaeser, Andrew Hermann, Mark Junod, Brandon Dutra, Alex Lang, Robert Hildebrand, Matthew Stamps, Chelsea Weaver.

Undergraduate Students: Sara Cohen, Katherine Pannell, and Greg Pinto.