Sharp functional inequalities in geometry and PDEs


Friday, January 12, 2024 - 09:00 to 09:50




Speaker:Dr. Joshua Flynn (McGill University)

Title: Sharp functional inequalities in geometry and PDEs


Many important functional inequalities, namely inequalities relating integral norms of a function and its derivatives, are often geometric in spirit and intimately tied to PDE problems. Pertaining to my mathematical work, some such inequalities (and related PDEs) are listed as follows: Sobolev (Yamabe equation), trace Sobolev (Caffarelli-Silvestre extension problem), Hardy and Hardy-Sobolev-Maz'ya (Schrodinger operators) and isoperimetric (geometric flow equations). Many of my works are in different geometric settings (e.g., symmetric spaces and CR and conformal geometry). In this talk I will survey some of my recent work on sharp functional inequalities and related PDEs.


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