Analysis group. Joel Feinstein. School of Mathematical Sciences University of Nottingham

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1 Analysis group Joel Feinstein School of Mathematical Sciences University of Nottingham Joel Feinstein (University of Nottingham) Analysis group / 8

2 Permanent staff in analysis Professor Jim Langley (Complex Analysis) Joel Feinstein (University of Nottingham) Analysis group / 8

3 Permanent staff in analysis Professor Jim Langley (Complex Analysis) Dr. Joel Feinstein (Functional Analysis) Joel Feinstein (University of Nottingham) Analysis group / 8

4 Permanent staff in analysis Professor Jim Langley (Complex Analysis) Dr. Joel Feinstein (Functional Analysis) Dr. Joachim Zacharias (Functional Analysis) Joel Feinstein (University of Nottingham) Analysis group / 8

5 Permanent staff in analysis Professor Jim Langley (Complex Analysis) Dr. Joel Feinstein (Functional Analysis) Dr. Joachim Zacharias (Functional Analysis) We hope to have a new permanent member of staff in analysis by next year. Joel Feinstein (University of Nottingham) Analysis group / 8

6 Complex Analysis Professor Langley s research is on functions of a complex variable Joel Feinstein (University of Nottingham) Analysis group / 8

7 Complex Analysis Professor Langley s research is on functions of a complex variable The starting point is Picard s theorem. Joel Feinstein (University of Nottingham) Analysis group / 8

8 Complex Analysis Professor Langley s research is on functions of a complex variable The starting point is Picard s theorem. Theorem (Picard s Theorem) Any function which is analytic on C and which omits two values must be constant. Joel Feinstein (University of Nottingham) Analysis group / 8

9 Complex Analysis Professor Langley s research is on functions of a complex variable The starting point is Picard s theorem. Theorem (Picard s Theorem) Any function which is analytic on C and which omits two values must be constant. This is sharp, because the function e z omits one value (namely 0). Joel Feinstein (University of Nottingham) Analysis group / 8

10 Complex Analysis Professor Langley s research is on functions of a complex variable The starting point is Picard s theorem. Theorem (Picard s Theorem) Any function which is analytic on C and which omits two values must be constant. This is sharp, because the function e z omits one value (namely 0). Since 1996, Professor Langley has had six students who have graduated with a Ph.D. in this area. Joel Feinstein (University of Nottingham) Analysis group / 8

11 Complex Analysis Group Two current Ph.D. students Joel Feinstein (University of Nottingham) Analysis group / 8

12 Complex Analysis Group Two current Ph.D. students Two postdoctoral researchers (from Warwick, Berlin) Joel Feinstein (University of Nottingham) Analysis group / 8

13 Complex Analysis Group Two current Ph.D. students Two postdoctoral researchers (from Warwick, Berlin) Weekly PG seminars Joel Feinstein (University of Nottingham) Analysis group / 8

14 Complex Analysis Group Two current Ph.D. students Two postdoctoral researchers (from Warwick, Berlin) Weekly PG seminars Occasional joint seminars with integrable systems group at Loughborough. Joel Feinstein (University of Nottingham) Analysis group / 8

15 Complex Analysis Group Two current Ph.D. students Two postdoctoral researchers (from Warwick, Berlin) Weekly PG seminars Occasional joint seminars with integrable systems group at Loughborough. For (lots of) details see Joel Feinstein (University of Nottingham) Analysis group / 8

16 Dr Feinstein (Functional Analysis) Dr Feinstein s main interests are in Banach algebras of complex-valued functions. Joel Feinstein (University of Nottingham) Analysis group / 8

17 Dr Feinstein (Functional Analysis) Dr Feinstein s main interests are in Banach algebras of complex-valued functions. Research projects include the following Joel Feinstein (University of Nottingham) Analysis group / 8

18 Dr Feinstein (Functional Analysis) Dr Feinstein s main interests are in Banach algebras of complex-valued functions. Research projects include the following Regularity conditions Joel Feinstein (University of Nottingham) Analysis group / 8

19 Dr Feinstein (Functional Analysis) Dr Feinstein s main interests are in Banach algebras of complex-valued functions. Research projects include the following Regularity conditions Rational and polynomial approximation Joel Feinstein (University of Nottingham) Analysis group / 8

20 Dr Feinstein (Functional Analysis) Dr Feinstein s main interests are in Banach algebras of complex-valued functions. Research projects include the following Regularity conditions Rational and polynomial approximation Classification of endomorphisms and derivations Joel Feinstein (University of Nottingham) Analysis group / 8

21 Dr Feinstein (Functional Analysis) Dr Feinstein s main interests are in Banach algebras of complex-valued functions. Research projects include the following Regularity conditions Rational and polynomial approximation Classification of endomorphisms and derivations Algebraic extensions of commutative Banach algebras. Joel Feinstein (University of Nottingham) Analysis group / 8

22 Dr Feinstein (Functional Analysis) Dr Feinstein s main interests are in Banach algebras of complex-valued functions. Research projects include the following Regularity conditions Rational and polynomial approximation Classification of endomorphisms and derivations Algebraic extensions of commutative Banach algebras. Since 1997, Dr Feinstein has had four students who have graduated with a Ph.D. in this area. Joel Feinstein (University of Nottingham) Analysis group / 8

23 Dr Feinstein (Functional Analysis) Dr Feinstein s main interests are in Banach algebras of complex-valued functions. Research projects include the following Regularity conditions Rational and polynomial approximation Classification of endomorphisms and derivations Algebraic extensions of commutative Banach algebras. Since 1997, Dr Feinstein has had four students who have graduated with a Ph.D. in this area. Dr Feinstein has two current research students: one just starting, one just finishing! Joel Feinstein (University of Nottingham) Analysis group / 8

24 Dr Feinstein (continued) Work in this area includes the construction of Swiss cheeses! Joel Feinstein (University of Nottingham) Analysis group / 8

25 Dr Feinstein (continued) Work in this area includes the construction of Swiss cheeses! Joel Feinstein (University of Nottingham) Analysis group / 8

26 Dr Feinstein (continued) Work in this area includes the construction of Swiss cheeses! For more details, see Joel Feinstein (University of Nottingham) Analysis group / 8

27 Dr Zacharias (Functional Analysis) Dr Zacharias s research interests mainly concern simple C*-algebras and their classification, using: Joel Feinstein (University of Nottingham) Analysis group / 8

28 Dr Zacharias (Functional Analysis) Dr Zacharias s research interests mainly concern simple C*-algebras and their classification, using: K-theory; Joel Feinstein (University of Nottingham) Analysis group / 8

29 Dr Zacharias (Functional Analysis) Dr Zacharias s research interests mainly concern simple C*-algebras and their classification, using: K-theory; semigroups of endomorphisms on von Neumann algebras (which have connections to quantum probability); Joel Feinstein (University of Nottingham) Analysis group / 8

30 Dr Zacharias (Functional Analysis) Dr Zacharias s research interests mainly concern simple C*-algebras and their classification, using: K-theory; semigroups of endomorphisms on von Neumann algebras (which have connections to quantum probability); C*-dynamical systems; Joel Feinstein (University of Nottingham) Analysis group / 8

31 Dr Zacharias (Functional Analysis) Dr Zacharias s research interests mainly concern simple C*-algebras and their classification, using: K-theory; semigroups of endomorphisms on von Neumann algebras (which have connections to quantum probability); C*-dynamical systems; tensor products of C*-algebras. Joel Feinstein (University of Nottingham) Analysis group / 8

32 Dr Zacharias (Functional Analysis) Dr Zacharias s research interests mainly concern simple C*-algebras and their classification, using: K-theory; semigroups of endomorphisms on von Neumann algebras (which have connections to quantum probability); C*-dynamical systems; tensor products of C*-algebras. Two of Dr Zacharias s research students have recently graduated with Ph.D. degrees. Joel Feinstein (University of Nottingham) Analysis group / 8

33 C*-algebras and their classification C*-algebras and their measure theoretical counterpart, von Neumann algebras, are algebras of operators on a Hilbert space which were first motivated by quantum theory and occurred in group representations and ergodic theory. Joel Feinstein (University of Nottingham) Analysis group / 8

34 C*-algebras and their classification C*-algebras and their measure theoretical counterpart, von Neumann algebras, are algebras of operators on a Hilbert space which were first motivated by quantum theory and occurred in group representations and ergodic theory. C*-algebras can also be characterised abstractly as Banach algebras by a very natural norm condition. Joel Feinstein (University of Nottingham) Analysis group / 8

35 C*-algebras and their classification C*-algebras and their measure theoretical counterpart, von Neumann algebras, are algebras of operators on a Hilbert space which were first motivated by quantum theory and occurred in group representations and ergodic theory. C*-algebras can also be characterised abstractly as Banach algebras by a very natural norm condition. C*-algebras have occurred in many other branches of mathematics. Very recently for instance they were successfully applied to essentially solve a longstanding conjecture in topology due to S.P. Novikov. Joel Feinstein (University of Nottingham) Analysis group / 8

36 C*-algebras and their classification C*-algebras and their measure theoretical counterpart, von Neumann algebras, are algebras of operators on a Hilbert space which were first motivated by quantum theory and occurred in group representations and ergodic theory. C*-algebras can also be characterised abstractly as Banach algebras by a very natural norm condition. C*-algebras have occurred in many other branches of mathematics. Very recently for instance they were successfully applied to essentially solve a longstanding conjecture in topology due to S.P. Novikov. Currently there are one research student and one postdoctoral researcher working with Dr Zacharias in this area. Joel Feinstein (University of Nottingham) Analysis group / 8