Professor Roger Plymen

Page contents:

• Research interests
• Teaching
• Publications
• Co-workers
• Recent students
• Professional affiliations
• K-theory Days
• DipABRSM

Research interests

Noncommutative geometry, Representation Theory

The interface between noncommutative geometry and representation theory, especially the local Langlands correspondence; K-theory and periodic cyclic homology; a recent geometric conjecture in representation theory; Plancherel measure; Skewes number.

Teaching

• MATH20122: Metric Spaces
• MATH31022: Number Theory: The Riemann Zeta Function

Publications

Books

• p-Adic Methods and Their Applications. Edited by A.J. Baker and R.J. Plymen. Oxford Science Publications 1992.
• Spinors in Hilbert Space. With P.L. Robinson. Cambridge Tract in Mathematics 114 (1994).

(2001-2010)

• Artin-Schreier theory and L-packets in the principal series of SL_2(F_2((x))). With S. Mendes. Submitted.
• K-theory and the connection index. With T Kamran. Submitted.
• Geometric structure in the principal series of the p-adic group G_2. With Anne-Marie Aubert and Paul Baum. Accepted (subject to minor revision) for the Representation Theory journal of the AMS.
• R-groups and geometric structure in the representation theory of SL(N). With Jamila Jawdat. J. Noncommutative Geometry 4 (2010) to appear.
• Base change and K-theory for GL(n,R). With S. Mendes. Submitted.
• A new bound for the smallest x with \pi(x) > li(x). With K.F. Chao. Int. J. Number Theory 6 (2010), to appear. Skewes' number.
• Noncommutative Fourier analysis. In: Analysis on Noncommutative Spaces, LMS Lecture Note Series. Co-authors Brodzki et al. (2010) to appear.
• Geometric structure in the representation theory of p-adic groups. With A.-M. Aubert and P. Baum. C. R. Acad. Sci. Paris, Ser. I, 345 (2007) 573-578. Online published version.
• Base change and K-theory for GL(n). With S. Mendes. J. Noncommutative Geometry 1 (2007) 311-331. Online published version.
• The Hecke algebra of a reductive p-adic group: a geometric conjecture. With A.-M. Aubert and P. Baum, Aspects of Mathematics 37, Vieweg Verlag (2006) 1-34.
• Cycles in the chamber homology of GL(3). With A-M Aubert and S. Hasan. K-Theory 37 (2006) 341-377. Online published version.
• Entire cyclic cohomology of Schatten ideals. With J. Brodzki. Homology, Homotopy and Applications, 7(3) (2005) 37-52.
• Plancherel measure for GL(n,F) and GL(m,D): explicit formulas and Bernstein decomposition. With A-M. Aubert. J. Number Theory, 112 (2005) 26-66. Online published version.
• Explicit Plancherel formula for the p-adic group GL(n). With A-M. Aubert. C.R. Acad. Sci. Paris, Ser. I, 338 (2004) 843-848. Online published version.
• Local-global principle for the Baum-Connes conjecture with coefficients. With P. Baum and S. Millington. K-theory, 28 (2003) 1-18. Online published version
• Complex structure on the smooth dual of GL(n). With J. Brodzki. Documenta Math 7 (2002) 91-112.
• Reduced C*-algebra of the p-adic group GL(n) II, J. Functional Analysis, 196 (2002) 119-134. Online published version.
• Chern character for the Schwartz algebra of GL(n). With J. Brodzki. Bulletin London Math. Soc. 34 (2002) 219-228. Online published version.
• Proof of the Baum-Connes conjecture for reductive adelic groups. With P. Baum and S. Millington. C.R. Acad. Sci. Paris. 332 (2001) 195-201. Online published version.

Before 2001

• Geometry of the smooth dual of GL(n). With J. Brodzki. C.R. Acad. Sci. Paris 331 (2000) 213 - 218. Online published version.
• Representation theory of p-adic groups : a view from operator algebras. With P. Baum & N. Higson. The mathematical legacy of Harish-Chandra : a celebration of representation theory & harmonic analysis. Proc. Symp. Pure Math. 68 (2000) 111--149.
• Periodic cyclic homology of certain nuclear algebras. With J. Brodzki. C.R. Acad. Sci. Paris 329 (1999) 671 - 676. Online published version.
• Proof of the Baum-Connes conjecture for p-adic GL(n). With P. Baum & N. Higson. C.R. Acad. Sci. Paris 325 (1997) 171--176. Online published version.
• The representation theory of p-adic GL(n) and Deligne-Langlands parameters. With J.E. Hodgins."Analysis, Geometry and Probability", edited by R. Bhatia. Hindustan Book Agency, Texts and Readings in Mathematics 10 (1996) 54 - 72.
• Universal example for S-arithmetic groups. With J.E. Hodgins. Expo. Math. 15 (1997) 149 -- 159.
• Equivariant homology for SL(2) of a p-adic field. With P. Baum & N. Higson. Contemporary Math 148 (1993) 1-18.
• K-theory and elliptic representations of SL(l). Houston J. Math. (Herrero Memorial Issue) 18 (1992) 25-32.
• Coupling constants for p-adic groups, in ``p-Adic Methods and Their Applications'', edited by A.J. Baker & R.J. Plymen, Oxford Science Publications, Oxford University Press, 1992, p. 63-72.
• L2-Fourier transform for reductive p-adic groups. With C.W. Leung. Bull. London Math. Soc. 23 (1991) 146-152.
• Arithmetic aspect of operator algebras. With C.W. Leung. Compositio Math. 77 (1991) 293-311.
• Equivalence bimodules in the representation theory of reductive groups. Proc. Symp. Pure Math. 51 (1990) 267-272.
• Reduced C*-algebra for reductive p-adic groups. J. Functional Analysis 88 (1990) 251-266.
• Complex conformal rescaling and spin-structure. With B.W. Westbury. Bull. London Math. Soc. 19 (1987) 363-370.
• The reduced C*-algebra of the p-adic group GL(n). J. Functional Analysis 72 (1987) 1-12.
• Strong Morita equivalence, spinors and symplectic spinors. J. Operator Theory 16 (1986) 305-324.
• K-theory of the reduced C*-algebra of SL(2,Q_p), in ``Operator algebras and their connections with topology and ergodic theory'', Lecture Notes in Mathematics 1132 (1985) 409-420.
• The Dirac operator and the principal series for complex semisimple Lie groups. With M.G. Penington. J. Functional Analysis 53 (1983) 269-286.
• The Weyl bundle. J. Functional Analysis 49 (1982) 186-197.
• Cyclotomic integers and the inner invariant of Connes. J. London Math. Soc. 22 (1980) 14-20.
• On the outer and inner invariants of Connes. With K.R. Parthasarathy. J. Functional Analysis 38 (1980) 1-15.
• The Laplacian and the Dirac operator in infinitely many variables. Compositio Math 41 (1980) 137-152.
• Automorphic group representations: the hyperfinite II_1 factor and the Weyl algebra, in "Algébres d'opérateurs", Lecture Notes in Mathematics 725 (1979) 291-306.
• Automorphic group representations: a new proof of Blattner's theorem. With de la Harpe. J. London Math. Soc. 19 (1979) 509-522.
• Some recent results on infinite-dimensional spin groups. Advances in Math., supplementary study 6 (1979) 159-171.
• Projective representations of the infinite orthogonal group. Mathematika 24 (1977) 115-121.
• Spinors in Hilbert space. Math. Proc. Camb. Phil. Soc. 80 (1976) 337-347.
• A variant of the fundamental theorem of projective geometry. With C.M. Williams. Mathematika 23 (1976) 89-93.
• On the Weyl character formula for SU(n). Int. J. Theor. Phys. 15 (1976) 201-206.
• A model of the universal covering group of SO(E)_2. With R.F. Streater. Bull. Lond. Math. Soc. 7 (1975) 283-288.
• On the spin algebra of a real Hilbert space. J. London Math. Soc. With R.M.G. Young. 9 (1974) 286-292.
• Two-state systems and the two-sphere. Nuovo Cimento 13B (1973) 55-58.
• Dispersion-free normal states. Nuovo Cimento 54A (1968) 862-870.
• A modification of Piron's axioms. Helv. Phys. Acta 41 (1968) 69-74.
• C*-algebras and Mackey's axioms. Commun. Math. Phys. 8 (1968) 132 - 146.
• A model of the arithmetic of alephs in the equation calculus. Math. Logic Quarterly 7 (1961) 257 - 258.

Unpublished

• Fourier algebra of a compact Lie group, arXiv:math.FA/0104018.

For MathSciNet, please click here.

Co-workers

• P. Baum (Penn State)
• J. Brodzki (Southampton)
• Anne-Marie Aubert (CNRS)

Recent Students

• Christine Lee
• K. F. Chao
• J. Jawdat
• S. Mendes

Professional affiliations

• London Mathematical Society
• American Mathematical Society
• European Mathematical Society
• EPSRC College

K-theory Days

These are sponsored by the London Mathematical Society and take place 4 times each year. For details of programmes past and present, please click here.

DipABRSM

I have a Diploma in Music Performance (Piano). This is a DipABRSM (Diploma of the Associated Board of the Royal Schools of Music). The requirements for this are a Quick Study, Viva Voce and Recital. Here is my recital programme.

• Vingt Regards I, Regard du P\`{e}re, Olivier Messiaen (1908--1992)
• Prelude and Fugue, Book 1, no. 16 in G minor, J.S. Bach (1685--1750)
• Mazurka in C# minor, Op. 50 no. 3, F. Chopin (1810--1849)
• Suite Pour le Piano : 2nd movt, Sarabande, Claude Debussy (1862--1918)
• Two preludes: no. 9 in E, no. 20 in C minor, Op. 11, Alexander Scriabin (1872--1915)
• In the Mists II and III, Leos Jan\'{a}cek (1854--1928)