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Functional Analysis Notes by Prof. Sylvia Serfaty
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Functional Analysis Notes written by Sylvia Serfaty
These notes are for Serfaty at the Courant Institute of Mathematical Science, New York University. The course was largely based on Haim Brezis Analyse fonctionnelle, thorie et applications and Michael Reed's and Barry Simon's Methods of modern mathematical physics vol 1. The geometric versions of the Hahn Banach Theorem were taken almost entirely out of Brezis and the section on Spectral Theory was based entirely on Reed and Simon.
Book Detail :-
Title: Functional Analysis Notes
Author(s): Sylvia Serfaty
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About Author :-
Author Prof. Sylvia Serfaty (born 1975) is a French mathematician. She start her teaching career in Paris but later he worked in the United States. She won the 2004 European Mathematical Society Prize for her contributions to the Ginzburg–Landau theory, the Henri Poincaré Prize in 2012, and the Mergier–Bourdeix Prize [fr] of the French Academy of Sciences in 2013.
Serfaty was born and raised in Paris. She was interested in mathematics since high school. Serfaty earned her PhD from Paris-Sud 11 University in 1999, under supervision of Fabrice Bethuel. She then held a teaching position (agrégé préparateur) at the École Normale Supérieure de Cachan. She joined as a full professor at the Courant Institute of Mathematical Sciences of New York University since 2007.
Her research work and interest was in the field of partial differential equations, statistical mechanics and mathematical physics. Her work particularly focuses on the Ginzburg-Landau model of superconductivity and quantum vortexes in the Ginzburg–Landau theory. In 2007 she published a book on the Ginzburg-Landau theory with Étienne Sandier, Vortices in the Magnetic Ginzburg-Landau Model. She was elected to the American Academy of Arts and Sciences in 2019. She is one of the editors-in-chief of the scientific journal Probability and Mathematical Physics.
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Book Contents :-
Functional Analysis Notes written by Sylvia Serfaty cover the following topics.
1. Hahn-Banach Theorems and Introduction to Convex Conjugation
2. Baire Category Theorem and Its Applications
3. Weak Topology
4. Bounded (Linear) Operators and Spectral Theory
5. Compact and Fredholm Operators
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