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Centre for Computational and Discrete Geometry Department of Mathematics & Statistics University of Calgary Fejes Tóth Lecture – Winter 2015
Simplices, Bodies and Vertices of Polyhedra
Speaker: Prof. Endre Boros Friday March 27, 2015 (2:00pm), MS 319 The Winter 2015 Fejes Tóth Lecture will be delivered by Professor Endre Boros of
the Rutgers University, New Brunswick, NJ.
Abstract: Monotone generation problems are pervasive and are the underlying
reason for the efficiencies or inefficiencies of many of the “large data” related
tasks. Many of these problems have natural geometric representations, and lead
to interesting and sometimes surprising connections. In this talk, we survey the
complexities of generation problems and related geometric questions: given a
finite set of points in an Euclidean space, what are the minimal subsets that
contain a given point in their convex hull (simplices), in the interior of their convex
hull (bodies), or the maximal counterparts of these. Analogously, given a set of
linear inequalities, what are the minimal infeasible subsystems, or what are the
maximal feasible subsystems? Both of these types of problems have close
relations to the problem of generating the vertices of polyhedra represented as
finite systems of linear inequalities, as well as to some problems on graphs and
directed graphs. In this talk we survey these results and problems, their
connections, and recall some open problems.
About the speaker:
Prof.
Endre
Boros
is
a
Hungarian-American
mathematician, a Distinguished Professor at Rutgers
University in New Brunswick, New Jersey, and the Director
of the Center for Operations Research (RUTCOR). He is
the author of 15 book chapters and edited volumes, and
165 research papers. He is Associate Editor of the Annals
of Mathematics and Artificial Intelligence, and Editor-inChief of both the Annals of Operations Research and
Discrete Applied Mathematics.