Patrick U. Speissegger
Canada Research Chair in Model Theory
Tier 2 - 2003-06-01 Renewed: 2008-06-01
COMING TO CANADA FROMUniversity of Wisconsin - Madison, USA
RESEARCH INVOLVESThe discovery and study of new o-minimal structures; applications to real analytic geometry and differential equations.
RESEARCH RELEVANCEDevelopment of new insights and methods in the study of real analytic geometry and dynamical systems, with applications to the study of hybrid systems and learning theory.
SHARPENING THE TOOLS OF LOGICMathematical logic has long played a role in delineating between what is formally possible and impossible. For example, in his well-known incompleteness theorem, Czech-born mathematician Kurt Gödel demonstrated that within any given branch of mathematics there would always be some propositions that could not be proven either true or false using the rules and axioms of that mathematical branch itself. You might be able to prove every conceivable statement about numbers within a system by going outside the system in order to come up with new rules and axioms, but by doing so you would only create a larger system with its own unprovable statements. Given this limit on the scope of what is formally knowable in mathematics, model theorists have devised simple properties of structures that fall under the formally knowable framework and still give rise to a rich collection of definable sets.
One of the most successful of these properties is called o-minimality, which has proven its usefulness by providing key insights into the foundations of dynamical and hybrid systems, and learning theory, and helped to settle some significant open problems in real algebraic geometry.
Dr. Patrick Speissegger is considered one of the world's leading theorists in o-minimality and is widely regarded as an innovative researcher able to address complex problems across a wide range of mathematical disciplines.
His research program at McMaster University aims to discover rich, new o-minimal structures, provide detailed analysis of these structures, study the effective nature of existing constructions, and investigate the possible generalizations of o-minimality.
One of the existing problems that Dr. Speissegger's work will address is German mathematician David Hilbert's famous 16th problem on limit cycles of plane vector fields, which was one of 23 problems Hilbert outlined in his hugely influential address of 1900 to the International Congress of Mathematicians.