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I shall try to outline the program started 4.5 decades ago that focuses on approximating particular in a certain sense “badly approximable” functions leading to unexpectedly exciting problems in mathematical physics. So called free boundary problems. For example, studying the approximations of  ̄z by analytic functions in various norms lead to the isoperimetric inequality, J. Serrin’s problem in hydrodynamics, equilibrium shape of electrified droplets, St. Venant’s inequality for torsional rigidity, etc. Many simply stated open questions, that still remain open in spite of the recent progress in the last decades, will be mentioned. This lecture should be accessible to undergraduates. 

 

 

Location

Kusch Auditorium (FN 2.102), FN 2.102

Natural Sciences & Mathematics

#Math

Viswanath Ramakrishna
Email

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  • Mubashir Ali

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