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 Saito, Alexander 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"
Winter
2005:
Spring
2005:
For suggestions or
questions please contact Roman Vershynin.