Nolan R

Nolan R. Wallach

Curriculum Vitae

Personal

Address: University of California, San Diego

Department of Mathematics

La Jolla, California 92093-0112

(619) 534-2645

Date of Birth: August 3, 1940

Citizenship: U.S.A.

Degrees B.S. University of Maryland 1962

M.A. Washington University 1963

Ph.D. Washington University 1966

Professional

1989- Professor of Mathematics, Above Scale

University of California, San Diego

1986-1989 Hermann Weyl Professor of Mathematics

1972-1986 Professor of Mathematics

1970-1972 Associate Professor of Mathematics

1969-1970 Assistant Professor of Mathematics

Rutgers University

1968-1969 Lecturer of Mathematics

1966-1968 Instructor of Mathematics

University of California, Berkeley

Major addresses

• Hour Address, Annual meeting of the AMS, January, 1975.

• Invited Address, International Congress of Mathematicians, Helsinki, August, 1978.

• Hour Address, Joint MAA-AMS session, Annual meeting of the AMS, January, 1990.

• Plenary Address, Japan Mathematical Society, Annual meeting, September, 1990.

Major Professional Activity

• Member, National Mathematics Committee, 1985-1992

• Member, Editorial Boards Committee of the AMS (Chair 1992), 1991-1993

• NSF-Postdoctoral Selection Committee (Chair 1994), 1992-1994

• NYI-Selection Committee, 1993

• Editor, RES Section, Bulletin of the AMS, 1995-1996

• Associate Editor, Bulletin of the AMS, 1996-1998

• Associate Editor, Annals of Mathematics, 1997-

Prizes and Fellowships

• Alfred Sloan Fellowship 1972-1974

• Linback Award for Research Excellence, 1977

• Honorary Professor, University of Cordoba, Argentina, 1989

Publications of Nolan R. Wallach


1.	N. R. Wallach: "On maximal subsystems of root systems," Canad. J. Math., 20 (1968), 555-574.

2.	N. R. Wallach: "Induced representation of Lie algebras and a theorem of Borel Weil," Trans. AMS, 136 (1969), 181-187.

3.	N. R. Wallach: "Induced representations of Lie algebras II," Proc. AMS, 21 (1969), 161-166.

4.	N. R. Wallach and M. do Carmo: "Minimal immersions of spheres into spheres," Proc. Natl. Academy of Sci., 63 (3) (1969), 640-642.
5.	N. R. Wallach and M. Do Carmo: "Minimal immersions of sphere bundles over spheres," Proc. of Brazilian Acad. Sci., 42 (1) (1970), 5-9.

6.	N. R. Wallach: "Extension of locally defined minimal immersions into spheres," Archiv der Math., XXI (1970), 209-213.
7.	N. R. Wallach and M. Cahen: "Lorentzian symmetric spaces," Bull. AMS, 76 (3) (1970), 585-591.

8.	N. R. Wallach: "Homogeneous positively pinched Riemannian manifolds," Bull. AMS, 76 (1970), 783-386.

9.	N. R. Wallach and M. do Carmo: "Representations of compact groups and minimal immersions into spheres," J. Diff. Geom., 4 (1970), 91-104.

10.	N. R. Wallach and f. Warner: "Curvature forms on 2-manifolds," Proc. AMS, 25 (3) (1970), 712-713.

11.	N. R. Wallach: "Cyclic vectors and irreducibility for principal series representations," Trans. AMS, 158 (1971), 107-113.

12.	N. R. Wallach: "Application of the higher osculating spaces to the spherical principal series," J. Diff. Geom., 5 (1971), 405-413.

13.	N. R. Wallach and M. do Carmo: "Minimal immersions of spheres into spheres," Annals of Math., 93 (1971), 43-62.

14.	N. R. Wallach and S. Greenfield: "Extendability properties of submanifolds of C²," Proc. of 1970 Carolina Conf. on Holomorphic Mappings and Minimal Surfaces, (1971), 77-85.
15.	N. R. Wallach and S. Greenfield: "The Hilbert ball and bi-ball are holomorphically inequivalent," Bull. AMS, 77 (2) (1971), 261-263.
16.	N. R. Wallach: "Symmetric spaces," Marcel Dekker Series of Pure and Applied Math., 8 (1972), 1-40.

17.	N. R. Wallach and S. Greenfield: "Global hypoellipticity and Liouville numbers," Proc. AMS, 31 (1) (1972), 112-114.

18.	N. R. Wallach and S. Greenfield: "Automorphism groups of bounded domains in Banach spaces," Trans. AMS, 166 (1972), 45-57.

19.	N. R. Wallach: "Three new examples of compact manifolds admitting Riemannian structures of positive curvature," Bull. AMS, 78 (1972), 55-56.
20.	N. R. Wallach: "Cyclic vectors and irreducibility for non-unitary principal series representations," Trans. AMS, 164 (1972), 389-396.

21.	N. R. Wallach: "Compact homogeneous Riemannian manifolds with strictly positive curvature," Annals Math., 96 (1972), 277-295.

22.	N. R. Wallach and K. Johnson: "Composition series and intertwining operators for the spherical principal series," Bull. AMS, 78 (1972), 1053-1059.

23.	N. R. Wallach: "Harmonic analysis on homogeneous spaces," Marcel Dekker, New York, 1973.
24.	N. R. Wallach and J. Lepowsky: "Finite dimensional and infinite dimensional representations of linear Lie groups," Trans. AMS, 184 (1973), 223-246.

25.	N. R. Wallach and S. Greenfield: "Remarks on global hypoellipticity," Trans. AMS, 183 (1973), 153-164.

26.	N. R. Wallach and S. Greenfield: "Globally hypoelliptic vector fields," Topology, 12 (1973), 247-253.

27.	N. R. Wallach: "Kostants P and R matrices and intertwining integrals," Proc. Symp. in Pure Math., XXVI AMS, Providence, RI (1973), 269-275.

28.	N. R. Wallach: "On Harish-Chandra's C-function," Amer. J. Math., 97 (1975), 386-403.

29.	N. R. Wallach and R. Hotta: "On Matsushima's formula for the Betti numbers of a locally symmetric space," Osaka J. Math., 12 (1975), 419-431.
30.	N. R. Wallach and S. Aloff: "An infinite family of 7-manifolds admitting positively curved Riemannian structures," Bull. AMS, 81 (1975), 93-97.
31.	N. R. Wallach: "On the unitarizability of representations with highest weights," Proceedings of Conference at Luminy of 1974 (1975).

32.	N. R. Wallach: "On an asymptotic formula of Gelfand and Gangolli for the spectrum of \G," J. Diff. Geom., 11 (1976), 171-195.

33.	N. R. Wallach: "On the Selberg trace formula in the case of compact quotient," Bull. AMS, 82 (1976), 171-195.

34.	N. R. Wallach: "On the Enright-Varadarjan modules: A construction of the discrete series," Ann. Ec. Norm. Sup., 9 (1976), 810-102.

35.	N. R. Wallach and A. Knapp: "Szego kernels associated with the discrete series," Inventiones Math., 34 (1976), 163-200.

36.	N. R. Wallach and K. Johnson: "Composition series and intertwining operators or the spherical principal series,I," Trans. AMS, 229 (1977), 137-173.
37.	N. R. Wallach: "Symplectic Geometry and Fourier Analysis," Math. Sci. Press, 1977.

38.	N. R. Wallach: "Representations of semi-simple Lie groups and Lie algebras," Lie Theories and Their Applications, Proceedings 1977 Canadian Math. Congress, 143-246.
39.	N. R. Wallach and D. DeGeorge: "Limit formulas for multiplicities in L²( \G)," Ann. Math., 107 (1978), 133-150.

40.	N. R. Wallach and T. J. Enright: "The fundamental series for a semi-simple Lie algebra," Acta Math., 140 (1978), 1-32.

41.	N. R. Wallach: "The spectrum of compact quotients of semi-simple Lie groups," Int. Congr. of Math., 1978.

42.	N. R. Wallach: "The analytic continuation of the discrete series, II," Trans. AMS, 251 (1979), 19-37.

43.	N. R. Wallach: "The analytic continuation of the discrete series, I," Trans. AMS, 251 (1979), 1-17.

44.	N. R. Wallach and D. DeGeorge: "Limit formulas for multiplicities in L²( \G), II" Ann. Math., 109 (1979), 477-495.

45.	N. R. Wallach: "Representations of reductive Lie groups, Part I," Proc. Symp. in Pure Math., 33 (1979), 71-86.
46.	N. R. Wallach and A. Borel: "Continuous cohomology, discrete subgroups and representations of reductive groups," Annals of Math. Studies, 94 (1980).

47.	N. R. Wallach and R. Goodman: "Conical vectors and Whittaker vectors," J. Functional Analysis, 39 (1980), 199-279.

48.	N. R. Wallach and T. J. Enright: "Homological algebra and group representations," Duke Math. Journal 47 (1980), 1-15.
49.	N. R. Wallach: "Restriction of Whittaker modules to certain parabolic subalgebras," Proc. AMS, 81 (1981), 181-188.

50.	N. R. Wallach and J. T. Stafford: "Restriction of admissible representations to certain parabolic subalgebras," Trans. AMS, 272 (1982), 333-350.

51.	N. R. Wallach and R. Goodman: "Classical and quantum-mechanical systems of Toda lattice type, I," Comm. Math. Phys., 83 (1982), 355-386.
52.	N. R. Wallach and A. Rocha-Caridi: "Projective modules over graded Lie algebras, I," Math. Zeit., 180 (1982), 151-172.

53.	N. R. Wallach: "On the constant term of an L²-automorphic form," Rumanian International Conference.

54.	N. R. Wallach, T. J. Enright, and R. Howe: "A classification of unitary highest weight modules," Proceedings of Utah Conference, 1982, Birkhauser, New York (1983).
55.	N. R. Wallach: "Highest weight modules over graded Lie algebras: Resolutions, filtrations and character formulas," Trans. AMS, 277 (1983), 133-162.

56.	N. R. Wallach and A. Rocha-Caridi: "Characters of irreducible representations of the Lie algebra of vector fields on the circle," Invent. Math., 72 (1983), 57-76.
57.	N. R. Wallach: "Asymptotic expansions of generalized matrix entries," Springer-Verlag Lecture Notes in Math, 1024 (1983), 287-369.
58.	N. R. Wallach and J. Wolf: "Poincare series associated with L¹-discrete series," Proceedings of Utah Conference, 1982, Birkhauser, New York (1983).
59.	N. R. Wallach, T. J. Enright, V. Parthasarathy and J. Wolf: "Unitarizability of a class of derived functor modules," Proc.Nat. Acad. Sci., 80 (1983), 7047-7050.

60.	N. R. Wallach: "L² - Automorphic forms and cohomology classes on arithmetic quotients of SU(p.q.)," Math. Annalen, 266 (1984), 261-278.
61.	N. R. Wallach and R. Goodman: "The structure and projective unitary representations of loop groups and the group of diffeomorphisms of the circle," J. Reine Angew. Math., 347 (1984), 69-133.

62.	N. R. Wallach and A. Rocha-Caridi: "Characters of irreducible representations of the Verasoro algebra, Math. Zeit., 185 (1984), 1-21.

63.	N. R. Wallach: "Asymptotic behavior of holomorphic representations," Memoirs of the French Math. Soc., 2e Serie, 15 (1984), 291-305.
64.	N. R. Wallach and Roe Goodman: "Classical and quantum- mechanical systems of Toda lattice type, II," Comm. Math., Phys., 94 (1984), 177-217.
65.	N. R. Wallach: "On unitarizable derived functor modules," Inv. Math., 78 (1984), 131-141.

66.	N. R. Wallach: "Classical invariant theory and the Verasoro algebra," in Vertex Operators in Mathematics and Physics, Springer-Verlag, 1984.
67.	N. R. Wallach, T. J. Enright, V. Parthasarathy and J. Wolf: "Unitarizable derived functor modules with small spectrum," Acta Mathematica, 154 (1985), 105-136.
68.	N. R. Wallach and Roe Goodman: "Projective unitary positive energy representations of Diff(S¹)," J. Funct. Anal., 63 (1985), 299-321.

69.	N. R. Wallach and Roe Goodman: "Classical and quantum- mechanical systems of Toda lattice type, III, " Comm. Math. Phys., 105 (1986), 473-509.
70.	N. R. Wallach: "A class of non-standard modules for affine Lie algebras," Math. Zeit., 196 (1987), 303-313.

71.	N. R. Wallach: "On the irreducibility and inequivalence of unitary representations of gauge groups," Comp. Math., 64 (1987), 3-29.
72.	N. R. Wallach: "Real Reductive Groups, I," Academic Press Pure and Applied Mathematics, Boston, 132 (1988).

73.	N. R. Wallach: "Lie algebra cohomology and the analytic continuation of generalized Jacquet integrals," Advanced Studies in Pure Mathematics, 14 (1988), 123-151.

74.	N. R. Wallach and R. Miatello: "Automorphic forms constructed from Whittaker vectors," J. Func. Analysis, 86 (1989), 411-487.
75.	N. R. Wallach and R. Goodman: "Higher order Sugawara operators for affine Lie algebras," Trans. AMS, 315 (1989), 1-55.
76.	N. R. Wallach: "Limit multiplicities in L²( \G), Lecture Notes in Mathematics 1447, Springer-Verlag (1989), 31-56.

77.	N. R. Wallach and D. Vogan: "Intertwining operators for real reductive groups," Advances in Math., 82 (1990), 203-242.

78.	N. R. Wallach and R. Miatello: "Kuznetsov formulas for real rank one groups," J. Func. Analysis, 93 (1990), 171-205.

79.	N. R. Wallach and R. Miatello: "Kuznetsov Formulas for Product Groups of R-rank One," Israeli Mathematical Conference Proceedings, 31 (1990), 305-320.
80.	N. R. Wallach: "The powers of the resolvent on a locally symmetric space," Bull. Soc. Math. Belg. 42 (1990), 777-795.

81.	N. R. Wallach: "Polynomial differential operators associated with a Hermitian symmetric space," RepresentationTheory of Lie Groups and Lie Algebras, World Scientific, Singapore, 1992, 76-95.
82.	N. R. Wallach: "Real Reductive Groups II," Academic Press, Boston, 1992.

83.	N. R. Wallach with J. Tirao (co-editors): "New Developments in Lie Theory and Their Applications," Progress in Mathematics, Birkäuser, Boston, 1992.
84.	N. R. Wallach: "Automorphic Forms," in New Developments in Lie Theory and Their Applications, Birkhäuser, Boston (1992), 1-25.

85.	N. R. Wallach and R. Miatello: "The resolvent of the Laplacian on locally symmetric spaces," J. Diff. Geom. 36 (1992), 663-698.

86.	N. R. Wallach: "Invariant differential operators on a reductive Lie algebra and Weyl group representations," J. A.M.S 6 (1993), 779-816.
87.	P. J. Sally, Jr. and N. R. Wallach (Editors): “Representation Theory and Automorphic Forms,” Reprints from the Bulletin of AMS 2 (1993).
88.	B. H. Gross and N. R. Wallach: "A distinguished family of unitary representations for the exceptional groups of real rank 4," Lie Theory and Geometry, C. Kostant, Volume 1, Birkhäuser, Boston (1994), 289-304.
89.	N. R. Wallach: “Transfer of unitary representations between real forms,” Contemp. Math. 177 (1994), 181-216.

90.	N. R. Wallach and M. Hunziker: “On the Harish-Chandra homomorphism of invariant differential operators on a reductive Lie algebra,” Contemp. Math. 191 (1995), 223-243.
91.	N. R. Wallach: “On a theorem of Milnor and Thom,” Progress in Nonlinear Differential Equations, 20 (1996), 331-348.

92.	J.S. Huang, T. Oshima, N. R. Wallach: “Dimensions of spaces of generalized spherical functions,” Amer. J. Math. 118 (1996), 637-652.
93.	B. Gross and N. R. Wallach: "On quaternionic discrete series representations, and their continuations," J. reine angew. Math., 481 (1996), 73-123

94.	T. Enright and N. R. Wallach: "Embeddings of Unitary Highest Representations and Generalized Dirac Operators," Math. Annalen., 307 (1997), 627-646
95.	R. Goodman and N. R. Wallach: "Representations and invariants of the classical groups," Cambridge University Press., Encyclopedia of Mathematics and its applications 68, Cambridge, (1998).

96.	N.R. Wallach: "C^∞ vectors, Representations of Lie groups and quantum groups," (Trento 1993), 205-270, Confman Sci. Tech., Harlow, (1994).

97.	N. R. Wallach: "A variety of solutions to the Yang-Baxter equation," Advances in Geometry, 391-399.

98.	H. Kraft, L.W. Small, N.R. Wallach: "Hereditary properties of direct summands of Algebras," Mathematical Research Letter, 6 (1999), 371-375

99.	A. Borel and N.R. Wallach: "Continuous cohomology, discrete subgroups and representations of reductive groups," 2^nd. Ed., Mathematical Surveys and Monographs, 67, American Mathematical Society, RI (2000).

100.	R.W. Bruggeman, R.W. Miatello, N. R. Wallach: "Resolvant and lattice points on symmetric spaces of strictly negative curvature," Math. Ann. 315 (1999), 617-639.

101.	N.R. Wallach and J. Willenbring: "On Some q-analogs of a theorem of Kostant-Rallis," Canad. J. Math., 52 (2000), 438-448.

102.	N.R. Wallach: "An Unentangled Gleason's theorem" to appear Contemp. Math. Volume in Quantum Computing, quant. - ph/002058

103.	B. Gross and N. Wallach: "Restriction of small discrete series representations to symmetric subgroups," Proceedings of Symposia in Pure Mathematics, Volume 68 (2000), 255-272.

104.	H. Kraft, L.W. Small and N. Wallach: "Properties and Examples of FCR-Algebras," Manuscripta Math. 104(2001), 443-450.

105	David A. Meyer and Nolan Wallach, ``Invariants for multiple qubits: the case of 3 qubits'',in Ranee K. Brylinski and Goong Chen, eds.,The Mathematics of Quantum Computation(Boca Raton: CRC Press 2002) 77-97.

106	David A. Meyer and Nolan R. Wallach, ``Global entanglement in multiparticle systems'', quant-ph/0108104, to appear in Jour. Math. Phys.

107	Generalized Whittaker vectors for holomorphic and quaternionic representatios, to appear Commentarii Math. Helv.

	Unpublished distributed preprints

1.	N. R. Wallach: "An elementary approach to theorems of Paley-Wiener type on semi-simple Lie groups of split rank 1," distributed preprint.

2.	N. R. Wallach and T. J. Enright: "The fundamental series of semi-simple Lie algebras and Lie groups," distributed preprint.

David A. Meyer and Nolan Wallach, ``Invariants for multiple qubits: the case of 3 qubits'',in Ranee K. Brylinski and Goong Chen, eds.,The Mathematics of Quantum Computation(Boca Raton: CRC Press 2002) 77-97.

David A. Meyer and Nolan Wallach,
``Invariants for multiple qubits: the case of 3 qubits'',in Ranee K. Brylinski and Goong Chen, eds.,The Mathematics of Quantum Computation(Boca Raton: CRC Press 2002) 77-97.