Reference number : GC-2017-Q1-03357, amendment number : , agreement type : G, recipient legal name : Kudla, Stephen (University of Toronto), 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 : Imagine a crystal as a lattice of atoms arranged in space according to a regular repeating pattern. Theta functions, the mathematical objects which encode the locations of the lattice points (atoms) as one moves outward from a fixed point, have many remarkable properties and have been studied since the 19th century. Recently, much more complicated theta functions have been introduced, for example in the study of lattice points inside or outside the light cone Minkowski space. Still more exotic ones occur in the study of arithmetic geometry -- the theory of whole number solutions to polynomial equations. Theta functions are special cases of a wider class of functions, modular forms and automorphic forms. The goal of this research is to develop new types of theta functions and automorphic forms and to investigate their applications in number theory and their connections to physics, in particular, to the counting functions which arise in string theory., program purpose french : Imagine a crystal as a lattice of atoms arranged in space according to a regular repeating pattern. Theta functions, the mathematical objects which encode the locations of the lattice points (atoms) as one moves outward from a fixed point, have many remarkable properties and have been studied since the 19th century. Recently, much more complicated theta functions have been introduced, for example in the study of lattice points inside or outside the light cone Minkowski space. Still more exotic ones occur in the study of arithmetic geometry -- the theory of whole number solutions to polynomial equations. Theta functions are special cases of a wider class of functions, modular forms and automorphic forms. The goal of this research is to develop new types of theta functions and automorphic forms and to investigate their applications in number theory and their connections to physics, in particular, to the counting functions which arise in string theory., agreement title english : Modular forms and arithmetic geometry, agreement title french : Modular forms and arithmetic geometry, agreement number : RGPIN, agreement value : 215000.0, 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