Reference number : GC-2017-Q1-03214, amendment number : , agreement type : G, recipient legal name : Mezo, Paul (Carleton University), recipient country : CA, recipient province : nan, recipient city : Ontario, recipient postal code : nan, program name english : Discovery Grants Program - Individual, program name french : Programme de subventions à la découverte - individuelles, program purpose english : My proposed research makes connections in two areas of mathematics: group theory, and number theory. In mathematical language a group is an object that encodes symmetry. For instance there is a specific group describing the symmetry we see in the maple leaf on the Canadian flag. On the other hand, number theory is the name mathematicians give to arguments that ultimately tell us about the laws governing the whole numbers 1,2,3, etc. A particular area of number theory is focused on prime numbers, numbers like 5 which can only be divided by 1 and themselves to give whole numbers. Surprisingly, there are complicated laws of prime numbers which can be expressed as some form of symmetry--that is expressed in the language of group theory. This is my proposed area of research. 
 
This area of research is of interest mainly to the global mathematical community. It is a continuation of humanity's interest in numbers for their own sake, and reveals their mysterious structure. My research represents some of Canada's expertise in this venerable and vigorous tradition., program purpose french : My proposed research makes connections in two areas of mathematics: group theory, and number theory. In mathematical language a group is an object that encodes symmetry. For instance there is a specific group describing the symmetry we see in the maple leaf on the Canadian flag. On the other hand, number theory is the name mathematicians give to arguments that ultimately tell us about the laws governing the whole numbers 1,2,3, etc. A particular area of number theory is focused on prime numbers, numbers like 5 which can only be divided by 1 and themselves to give whole numbers. Surprisingly, there are complicated laws of prime numbers which can be expressed as some form of symmetry--that is expressed in the language of group theory. This is my proposed area of research. 
 
This area of research is of interest mainly to the global mathematical community. It is a continuation of humanity's interest in numbers for their own sake, and reveals their mysterious structure. My research represents some of Canada's expertise in this venerable and vigorous tradition., agreement title english : Twisted endoscopy from the sheaf-theoretic perspective, agreement title french : Twisted endoscopy from the sheaf-theoretic perspective, agreement number : RGPIN, agreement value : 80000.0, 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