Reference number : GC-2017-Q1-03144, amendment number : , agreement type : G, recipient legal name : Ivrii, Victor (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 : During the first two years I plan to finish the project, spanning over 35 years and which in its current form is " Sharp Spectral Asymptotics and their Applications to Mathematical Physics ". To wrap it I plan to revisit the problem of the asymptotics of the ground state energy for atoms heavy molecules in the ultra-strong magnetic field, and also consider the case when magnetic field includes self-generated component (all other parts of the project are done). It will result in the releasing my research monograph of over 3,000 pages (with the same name). 
 
During remaining three years I plan to switch to some new problems: 
 
Asymptotics of the Integrated Density of States with the goal to derive asymptotics with the better remainder estimates than follow directly from local spectral asymptotics. This would require further development of the micro local analysis and long term propagation of singularities. 
 Scattering Theory and the Distribution of the Resonances (Scattering Poles) ?n the complex plane. 
This would require the extension of the technique developed earlier for self-adjoint operators to dissipative operators., program purpose french : During the first two years I plan to finish the project, spanning over 35 years and which in its current form is " Sharp Spectral Asymptotics and their Applications to Mathematical Physics ". To wrap it I plan to revisit the problem of the asymptotics of the ground state energy for atoms heavy molecules in the ultra-strong magnetic field, and also consider the case when magnetic field includes self-generated component (all other parts of the project are done). It will result in the releasing my research monograph of over 3,000 pages (with the same name). 
 
During remaining three years I plan to switch to some new problems: 
 
Asymptotics of the Integrated Density of States with the goal to derive asymptotics with the better remainder estimates than follow directly from local spectral asymptotics. This would require further development of the micro local analysis and long term propagation of singularities. 
 Scattering Theory and the Distribution of the Resonances (Scattering Poles) ?n the complex plane. 
This would require the extension of the technique developed earlier for self-adjoint operators to dissipative operators., agreement title english : Microlocal Analysis and Spectral and Scattering Asymptotics, agreement title french : Microlocal Analysis and Spectral and Scattering Asymptotics, 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