VIGRE Research Focus Group 2004-2005:

Probabilistic Aspects of Convexity and Combinatorics


The mistery, as well as the glory, of mathematics lies not so much in the
fact that abstract theories do turn out to be useful in solving problems
but in that wonder of wonders, the fact that a theory meant for solving one type
of problem is often the only way of solving problems of entirely different kinds,
problems for which the theory was not intended. These coincidences occur
so frequently that they must belong to the essence of mathematics.

Gian-Carlo Rota


Welcome to this RFG, which is the crossroads of probability, combinatorics and convexity. We will study the most powerful probabilistic method (aimed at proving existence of various structures by a random choice) and its use in existential combinatorics, convex and discrete geometry, analysis and in applications to computer science (randomized algorithms and derandomization).



Participants

Faculty:
Janko Gravner, Greg Kuperberg, Jesus DeLoera, Anne Schilling, Naoki SaitoAlexander Soshnikov, Thomas Strohmer, Monica Vazirani, Roman Vershynin (lead faculty), Roger Wets
Postdocs, Graduate students,Undergraduate Students are welcome

Activities

Fall 2004:
         
Preliminary Exam Workshop: "Linear Algebra"
280: Special Topics Class: "Probability and Convexity"
290: Reading seminar:
"The Probabilistic Method in Combinatorics"

Winter 2005:
290: Reading seminar: "Randomized Algorithms"

Spring 2005:
290: Study Group in Geometric Functional Analysis
Bay Area Discrete Mathematics Day


For suggestions or questions please contact Roman Vershynin.