Skip to main content
MathOverflow

Return to Question

Post Closed as "Needs more focus" by Daniel Moskovich, Alexey Ustinov, Andreas Thom, Ian Morris, Yemon Choi
Post Made Community Wiki by S. Carnahan♦
added 7 characters in body; edited title
Source Link
No One
No One
  • 1.6k
  • 11
  • 21

Applications of functional analysis beyond analysis(totowards algebra, geometry, number theory...)

So far, We have seen the applications of functional analysis in PDE, probability and many areas in applied mathematics. On the other hand, methods of algebraic topology are introduced to functional analysis via operator K-theory.

From the mathematical research point of view, (as a crazy fan of pure math) I wonder if functional analysis(theory of Banach and Hilbert spaces and operator algebras), as a well-built theory in mathematics, has any applications to the areas in pure math like algebraic topology, algebraic geometry and number theory, solving problems for which purely algebraic or geometric methods areseem to be powerless.

Applications of functional analysis beyond analysis(to algebra, geometry, number theory...)

So far, We have seen the applications of functional analysis in PDE, probability and many areas in applied mathematics. On the other hand, methods of algebraic topology are introduced to functional analysis via operator K-theory.

From the mathematical research point of view, (as a crazy fan of pure math) I wonder if functional analysis(theory of Banach and Hilbert spaces and operator algebras), as a well-built theory in mathematics, has any applications to the areas like algebraic topology, algebraic geometry and number theory, solving problems for which purely algebraic or geometric methods are powerless.

Applications of functional analysis beyond analysis(towards algebra, geometry, number theory...)

So far, We have seen the applications of functional analysis in PDE, probability and many areas in applied mathematics. On the other hand, methods of algebraic topology are introduced to functional analysis via operator K-theory.

From the mathematical research point of view, (as a crazy fan of pure math) I wonder if functional analysis(theory of Banach and Hilbert spaces and operator algebras), as a well-built theory in mathematics, has any applications to the areas in pure math like algebraic topology, algebraic geometry and number theory, solving problems for which purely algebraic or geometric methods seem to be powerless.

Source Link
No One
No One
  • 1.6k
  • 11
  • 21

Applications of functional analysis beyond analysis(to algebra, geometry, number theory...)

So far, We have seen the applications of functional analysis in PDE, probability and many areas in applied mathematics. On the other hand, methods of algebraic topology are introduced to functional analysis via operator K-theory.

From the mathematical research point of view, (as a crazy fan of pure math) I wonder if functional analysis(theory of Banach and Hilbert spaces and operator algebras), as a well-built theory in mathematics, has any applications to the areas like algebraic topology, algebraic geometry and number theory, solving problems for which purely algebraic or geometric methods are powerless.