Reference number : GC-2017-Q1-01469, amendment number : , agreement type : G, recipient legal name : Rechnitzer, Andrew (The University of British Columbia), recipient country : CA, recipient province : nan, recipient city : British Columbia|Colombie-Britannique, recipient postal code : nan, program name english : Discovery Grants Program - Individual, program name french : Programme de subventions à la découverte - individuelles, program purpose english : Enumeration is the branch of mathematics that examines questions of the form "How many..."; it is perhaps the apparent simplicity and yet universal nature of these questions that explains their ubiquity. They arise in many different areas of mathematics and in problems at the interface between mathematics and physics, chemistry and computer science. The aim of this program is to apply different types of enumeration methods in the context of particular sets of objects - random walks and self-avoiding walks. From there, I will apply those methods, both exact and approximate, to problems such as phase transitions in polymers, random knotting and linking of curves and to questions of growth and cogrowth in an area of pure mathematics - geometric group theory. I will also undertake two number theory projects of with a computational and enumerative flavour - cataloguing elliptic curves and counting primes in arithmetic progressions., program purpose french : Enumeration is the branch of mathematics that examines questions of the form "How many..."; it is perhaps the apparent simplicity and yet universal nature of these questions that explains their ubiquity. They arise in many different areas of mathematics and in problems at the interface between mathematics and physics, chemistry and computer science. The aim of this program is to apply different types of enumeration methods in the context of particular sets of objects - random walks and self-avoiding walks. From there, I will apply those methods, both exact and approximate, to problems such as phase transitions in polymers, random knotting and linking of curves and to questions of growth and cogrowth in an area of pure mathematics - geometric group theory. I will also undertake two number theory projects of with a computational and enumerative flavour - cataloguing elliptic curves and counting primes in arithmetic progressions., agreement title english : Applications of exact and approximate enumeration, agreement title french : Applications of exact and approximate enumeration, agreement number : RGPIN, agreement value : 120000.0, agreement start date : 2017-05-10, agreement end date : nan, description english : nan, description french : nan, expected results english : nan, expected results french : nan, additional information english : Grant or Award spanning more than one fiscal year. (2017-2018 to 2022-2023), additional information french : Subvention ou bourse octroyée s'appliquant à plus d'un exercice financier. (2017-2018 à 2022-2023), owner organization : nserc-crsng, owner organization title : Natural Sciences and Engineering Research Council of Canada | Conseil de recherches en sciences naturelles et en génie du Canada