Nolan R. Wallach
Curriculum Vitae
Personal
Address:
Department of Mathematics
(858) 534-2645
Degrees B.S.
M.A.
Ph.D.
Professional
1989- Professor of Mathematics, Above Scale
1986-1989 Hermann Weyl Professor of Mathematics
1972-1986 Professor of Mathematics
1970-1972 Associate Professor of Mathematics
1969-1970 Assistant Professor of Mathematics
1968-1969 Lecturer of Mathematics
1966-1968 Instructor of Mathematics
Major addresses
• Hour Address, Annual meeting of the AMS, January, 1975.
• Invited
Address, International Congress of Mathematicians,
• 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
• Member of the committee: U.S. Mathematical Sciences Research Institutes:
Value and Need, The Board of Mathematical Sciences of the NAS 1998.
• Associate Editor,
• Council of the AMS, 1998-2001
• Science Policy committee of the AMS, 1998-2001
• Editor
Mathematics: Theory and Applications, Birkhauser,
• Science Policy committee of the AMS, 2007-
Prizes and Fellowships
• Alfred Sloan Fellowship 1972-1974
• Linback Award for Research Excellence, 1977
• Honorary
Professor,
• Elected Fellow
of the
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
15.N. R. Wallach
and
16. N. R. Wallach: “Minimal Immersions of Symmetric spaces,” Marcel Dekker Series of Pure and Applied Math., 8 (1972), 1-40.
17. N. R. Wallach
and
18. N. R. Wallach
and
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,
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
26.N. R. Wallach
and
27. N. R.
Wallach: “Kostants Pg
and Rg matrices and
intertwining integrals,” Proc. Symp. in Pure Math., XXVI AMS,
28. N. R. Wallach: “On Harish-Chandra's C-function,” Amer. J. Math., 97 (1975), 386-403.
In the paper below all results (especially Lemma 2.1) should exclude Sp(n,1) and rank 1 F_4.
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.Get PDF version
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\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\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\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,” Operator Algebras and Group
Representations.II (Momog. Stud. Math., Vol. 18), Pittman,
54. N. R.
Wallach, T. J. Enright, and R. Howe: “A
classification of unitary highest weight modules,” Proceedings of Utah
Conference, 1982,
55. N. R. Wallach and A. Rocha-Caridi, “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,
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 Virasoro 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. Get reprint,
65. N. R. Wallach: “On unitarizable derived functor modules,” Inv. Math., 78 (1984), 131-141.
66. N. R. Wallach: “Classical invariant theory and the Virasoro 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,
73. N. R. Wallach: “Lie algebra cohomology and the Holomorphicic continuation of generalized Jacquet integrals,” Advanced Studies in Pure Mathematics, 14 (1988), 123-151.Get .pdf version
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 \G), Lecture Notes in Mathematics 1447, Springer-Verlag (1989), 31-56.Paper in pdf form
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,” Representation
Theory of Lie Groups and Lie Algebras, World
82. N. R.
Wallach: Real Reductive Groups II, Academic Press,
83. N. R. Wallach
with J. Tirao (co-editors): New Developments in Lie Theory and Their
Applications, Progress in Mathematics, Birkäuser,
84. N. R.
Wallach: “Automorphic Forms,” in New Developments in Lie Theory and Their
Applications, Birkhäuser,
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, In Honor of B. 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,
96. N.R. Wallach:
“C∞vectors”, Representations
of Lie groups and quantum groups,(
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, 2nd. 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” Quantum computation and
information (
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(
106. David A. Meyer and Nolan R. Wallach, “Global entanglement in multiparticle systems”, quant-ph/0108104, Journal of Math. Phys. 43(2002),4273-4278
107. “Generalized Whittaker vectors for holomorphic and quaternionic representations”, Commentarii Math. Helv. 79(2003), 266-307.
108. H. Kraft and N. Wallach, “On the separation property of orbits in representation spaces. Special issue in celebration of Claudio Procesi's 60th birthday, J. Algebra 258 (2002), 228--254
109. A.Garsia and N. Wallach, “Qsym is free over Sym”, J. Comb. Theorey Ser. A,104 (2003), 217--263.
110. A.M. Garsia and N. R. Wallach, Sime new applications of orbit harmonics, Sem. Lothar. Combin. 50(2003/2004), Art. B50j. 47pp.
111. T.Enright, M.Hunziker and N.Wallach, “A Pieri rule for Hermitian Symmetric Spaces I”, Pacific J. Math.,214(2004),23-30.
112. J.Kuttler and N. Wallach, “Representations of SL2 and the distribution of points in Pn”, Non-commutative harmonic analysis, 355-373,Prog. Math.,220, 2004 Birkhauser Boston,
113. T. Enright and N. Wallach, “A Pieri rule for Hermitian Symmetric Spaces II”, Pacific J. Math., 216(2004), 51-61..
114. Nolan R. Wallach, The Hilbert series for measures of entanglement in 4 qubits, Acta Appl. Math. 86(2005),203-220.
115. N.R. Wallach and Chen-bo Zhu, Transfer of Unitary Representations, Asian J. Math. 8(2004), 861-879.
116. A. Garsia and Nolan Wallach, “Combinatorial Aspects of the Baker Akhieser Functions for S2”, European J. Combin. 25(2004), 1231-1262.
117. J. Bell, A. Garsia and N . Wallach, Some new methods in the theory of m-quasininvariants, Electron. J. Combin. 11(2004/2006), Research Paper 20, 32 pp.
118. Nolan R. Wallach,“Holomorphic continuation of generalized Jacquet integrals for degenerate principal series”, Represent. Theory, 10(2006), 380-396..
119. Karin Baur and Nolan Wallach, Nice parabolic subalgebras of reductive Lie algebras, Represent. Theory 9 (2005),1-29.
120. Jessica Benton, Rion Snow and Nolan Wallach, A combinatorial problem associated with nanograms, Linear Algebra Appl. 412(2006) 30-38.
121. Kostant Bertram and Nolan Wallach, Gelfand –Zeitlin theory from the perspective of classical mechanics I, Studies in Lie Theory,319-364, Progr. Math., 243, Birkhauser Boston, 2006.
121. Kostant Bertram and Nolan Wallach, Gelfand –Zeitlin theory from the perspective of classical mechanics II, The unity of mathematics, 387-364, Progr. Math., 244, Birkhauser Boston, 2006.
122. Hanspeter Kraft and Nolan R. Wallach, On the nullcone of representations of reductive groups, Pacific J. Math. 224 (2006), 119-139.
123. A. M. Garsia and N. R. Wallach, The non-degeneracy of the bilinear form of m-quasiinvariants, Adv. In Appl. Math. 37(2006), 309-359.
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.