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752 Xiangyu Zhou[11] Al. Jarnicki, P.Pflug: On the extended tube conjecture. Manuscripta Math.,89 (1996), no. 4, 461-470.[12] R. Jost: The general theory of quantized fields. Amer. Alath. Soc, Providence,R. I., 1965.[13] David Kazhdan: Introduction to QFT . in Quantum fields and strings: acourse for mathematicians. Vol. 1, 2. pp.377-418 American AlathematicalSociety, Providence, RI; Institute for Advanced Study (IAS), Princeton, NJ,1999.[14] CO. Kiselman: The partial Legendre transformation for plurisubharmonicfunctions. Invent. Math. 49, 137-148 (1978).[15] CO. Kiselman: Plurisubharmonic functions and potential theory in severalcomplex variables, in "Developments of Mathematics 1950-2000", ed. by J.-P.Pier, pp.655-714, Birkhauser-verlag, 2000.[16] AI. Lassalle: Séries de Laurent des fonctions holomorphes dans la complexificationd'un espace symétrique compact. (French) Ann. Sci. école Norm. Sup.(4) 11 (1978), no. 2, 167-210.[17] J.J. Loeb: Pseudo-convexite des ouverts invariants et convexité geodesiquedans certains espaces symétriques.Sern. Lelong-Skoda, Lect. Notes inMath.1198, 172-190.[18] J.J. Loeb: Action d'une forme réele sur un groupe de Lie complexe. Ann. Inst.Fourier, fasse 4, t.35(1985).[19] Qikeng Lu: Classical manifolds and classical domains (in Chinese), ShanghaiScientific and Technical Press, 1963.[20] D. Luna: Slices étales. Bull. Soc. Math. France. Alem 33, 81-105(1973).[21] A.G. Sergeev: Around the extended future tube conjecture, Lect. Notes inMath., v.1574, Springer-Verlag, 1994.[22] A. G. Sergeev, P. Heinzner: The extended matrix disk is a domain of holomorphy.Math. USSR Izvestija, Vol.38(1992), no.3.[23] A. G. Sergeev, V.S. Vladimirov: Complex analysis in the future tube, inEncyclopedia of Math. Sci., Vol.8 (Several Complex Variables, II), Springer-Verlag, 1994.[24] A.G. Sergeev, X.Y. Zhou: On invariant domains of holomorphy (in Russian).Proc. of Steklov Math. Institute, Tom 203, 159-172, 1994.[25] A.G. Sergeev, X.Y. Zhou: Extended future tube conjecture. Proc. of SteklovMath. Institute, Tom 228, 32-51, 2000.[26] Y.-T. Siu: Pseudoconvexity and the problem of Levi. Bull. Amer. Math. Soc.84 (1978), no. 4, 481-512.[27] D. Al. Snow: Reductive Group Actions on Stein Spaces. Math. Ann. 259,79-97 (1982).[28] R. F. Streater, A.S. WightmamPCT, Spin and statistics, and all that. Benjamin,Reading, Alass, 1964.[29] V. S. Vladimirov: Analytic functions of several complex variables and quantumfield theory. Proc. of the Steklov Inst, of Math. 1978, Issue 1, 69-81.[30] V. S. Vladimirov: Several complex variables in mathematical physics. Sem.Lelong-Skoda, Lecture Notes in Math., Vol.919, 1982, 358-386.
[31[32[33[34'[35[36[37[38;[39[4o;[41Some Results Related to Group Actions in Several Complex Variables 753V. S. Vladimirov, V. V. Zharinov: Analytic methods in mathematicial physics.Proc. of the Steklov Inst, of Math. 1988, Issue 2, 117-137.A. S. Wightman: Quantum field theory and analytic function of several complexvariables, J. Indian Math. Soc. (N.S.) 24(1960/1961), 625-677.B. I. Zav'yalov, V.B.Trushin: On the extended n-point tube, Teoret. Mat. Fiz.27, 1(1976), 3-15.X.Y. Zhou: On matrix Reinhardt domains. Math.Ann. 287, 35-46(1990).X.Y. Zhou: On orbit convexity of certain torus invariant domain of holomorphy.Dokl. AN SSSR, T.322, N.2, 1992, 262-267.X.Y. Zhou: On orbit connectedness, orbit convexity, and envelopes of holomorphy.Izvestiya Ross.Akad.Nauk, Series Alath. T.58, N.2, 1994, 196-205.X.Y. Zhou: On invariant domains in certain homogeneous spaces. Ann. LTnst.Fourier, T.47, N.4, 1997, 1101-1115.X.Y. Zhou: A proof of the extended future tube conjecture(in Russian).Izvestiya Ross.Akad.Nauk, Series Alath. T.62, N.l, 1998, 211-224.X.Y. Zhou: The extended future tube is a domain of holomorphy. Math.Research Letters 5, 185-190(1998).X.Y. Zhou: Quotients, invariant version of Cartan's lemma, and the minimumprinciple. Proc. of first ICCM., 335-343, Amer. Alath. Soc. and InternationalPress, 2001.X.Y. Zhou: Invariant version of Cartan's lemma and complexicification ofinvariant domains (in Russian). Dokl. Ross. Akad. Nauk, vol.366, no.5, 1999,608-612.
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Beijing 2002August 20-28Proceedings
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ContentsSection 1. LogicE. Bouscare
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R. Pandharipande: Three Questions i
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Section 1. LogicE. Bouscaren: Group
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4 E. Bouscaren2. Different notions
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6 E. BouscarenWe now consider an al
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8 E. Bouscarendimension would need
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10 E. Bouscaren1. Either G is not o
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12 E. Bouscaren[7] E. Bouscaren & F
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14 J. Denef F. Loeserthis theory to
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16 J. Denef F. Loeserwill require m
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18 J. Denef F. Loeserseries P P (T)
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20 J. Denef F. Loeserfor all m> n.
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22 J. Denef F. Loeseri > 1. One ver
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ICM 2002 • Vol. II • 25-33Autom
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Automorphism Groups of Saturated St
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ICM 2002 • Vol. II • 37-45Repre
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3. The Blanchfield pairingRepresent
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Representations of Braid Groups 41n
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Representations of Braid Groups 43A
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Representations of Braid Groups 45T
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48 A.Bondal D.Orlovis believed to b
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50 A.Bondal D.OrlovDefinition 4 [BK
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52 A.Bondal D.OrlovLet Y be a smoot
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54 A.Bondal D.OrlovIn particular, w
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56 A.Bondal D.Orlov[BVdB] Bondal A.
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58 M. Levine(PB) Let £ be a rank r
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60 M. Levine2. Let 1Z d%m (X) be th
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62 M. LevineNow, if P = P(ci,. •
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64 M. LevineProof. For CH*, this us
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66 M. Levineis an isomorphism. Sinc
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68 Cheryl E. Praegeranalysis. Analo
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70 Cheryl E. Praegers-arc-transitiv
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72 Cheryl E. Praegercase a good kno
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74 Cheryl E. Praeger5. Simple group
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76 Cheryl E. Praeger[15] C. H. Li,
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78 Markus Rost1. Norm varietiesAll
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80 Markus RostWe apply the degree f
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82 Markus Rost4. Hubert's 90 for sy
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84 Markus RostFor n = 2 one can tak
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ICM 2002 • Vol. II • 87^92Dioph
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Diophantine Geometry over Groups an
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Diophantine Geometry over Groups an
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ICM 2002 • Vol. II • 93^103None
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Noncommutative Projective Geometry
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106 Dimitri Tamarkinalgebra and def
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108 Dimitri TamarkinThe product on
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110 Dimitri TamarkinProof. Let F =
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112 Dimitri Tamarkin2.5.9.Similarly
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114 Dimitri TamarkinComputeJ2,jl(a
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116 Dimitri Tamarkin3.2.1.To descri
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ICM 2002 • Vol. II • 119-128Con
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Converse Theorems, Functoriality, a
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Constructing and Counting Number Fi
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ICM 2002 • Vol. II • 139-148Ana
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Analyse p-adique et Représentation
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ICM 2002 • Vol. II • 149-162Equ
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Equiv. Bloch-Kato Conjecture and No
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[17;[is;[19;[20;[21[22[23;[24;[25;[
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ICM 2002 • Vol. II • 163-171Tam
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Tamagawa Number Conjecture for zeta
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174 S. S. Kudlaseries with represen
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t.176 S. S. Kudlais the exponential
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178 S. S. Kudlawhere Z = J2ì n ìP
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180 S. S. Kudla(ii) T £ Sym 2 (Z)>
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182 S. S. KudlaTheorem 6. ([13], [9
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Elliptic Curves and Class Field The
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198 E. UllmoSoit X une variété al
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200 E. UllmoThéorème 2.4 Soit X u
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202 E. UllmoQuestion 4.1 Soit x n =
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204 E. UllmoNotons que cet énoncé
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206 E. Ullmo[17] H. Oh. Uniform Poi
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208 T. D. WooleyWaring's problem as
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210 T. D. Wooleycircumstances one h
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212 T. D. Wooleywith 1 < z,w < F, M
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214 T. D. Wooleyand also byl f \K(a
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216 T. D. Wooleytions involving nor
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Section 4. Differential GeometryB.
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222 B. Andrewspotentially applicabl
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224 B. Andrewssurface can look metr
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226 B. Andrewsboundary of the set {
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228 B. Andrewseach t > 0, to either
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230 B. AndrewsUSSR Izv. 20 (1983).[
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232 Robert Bartnikprovides an impor
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234 Robert BartnikTheorem 2 If (M,
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236 Robert BartnikThe horizon condi
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238 Robert BartnikTheorem 8 Suppose
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240 Robert BartnikPhysics, LNP 212.
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242 P. Biran2. Various intersection
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244 P. BiranTheorem E'. Let (M,oj)
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246 P. Biransymplectic packings in
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248 P. Birangroup of Hamiltonian di
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250 P. Birannumber of steps it take
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252 P. Biranbe used to obtain many
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254 P. Biran[6] P. Biran, A stabili
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ICM 2002 • Vol. II • 257-271Bla
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Black Holes and the Penrose Inequal
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[23;[24;[25;[26;[27[28;[29'[30^Blac
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274 Xiuxiong ChenFor simplicity, in
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276 Xiuxiong ChenTheorem 0.1. [14]
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278 Xiuxiong ChenQuestion 0.6. (Don
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280 Xiuxiong Chencurvature in S 2 c
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282 Xiuxiong Chen[12] X. X. Chen an
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284 Weiyue DingSehrödinger flows a
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286 Weiyue DingIn order to prove Th
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288 Weiyue DingFor the first term i
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290 Weiyue Dingwhich satisfies the
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ICM 2002 • Vol. II • 293^302Dif
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Differential Geometry via Harmonic
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then eitherorDifferential Geometry
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ICM 2002 • Vol. II • 303-313Ind
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Index Iteration Theory for Symplect
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316 Anton PetruninTheorem A. Given
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318 Anton PetruninRiemannian manifo
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320 Anton Petruninspace. In the cas
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ICM 2002 • Vol. II • 323-338Col
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Collapsed Riemannian Manifolds with
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ICM 2002 • Vol. II • 339-349Com
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Complex Hyperbolic Triangle Groups
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352 Paul Seideldeformation spaces.
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354 Paul Seidelforgetting all the p
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356 Paul SeidelTheorem 3. Si,...,S
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358 Paul Seidelwhich must be of ord
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360 Paul Seidel[10] E. Getzler, Bat
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362 Weiping Zhang(iii) The heat ker
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364 Weiping Zhang3. The index theor
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366 Weiping Zhangwhere ch(g) is the
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- T p ( P d M , > 0 , 9 P d M , > 0
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Section 5. TopologyMladen Bestvina:
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374 Mladen Bestvinaof Out(F n ) coc
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376 Mladen Bestvina3. Culler-Vogtma
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378 Mladen BestvinaDefinition 8. A
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380 Mladen Bestvinaand then gluing
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382 Mladen BestvinaAnal. 10 (2000),
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384 Mladen Bestvina63 John R. Stall
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386 Yu. V. Chekanovplu I,Figure 1:
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388 Yu. V. Chekanovwithout loss of
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390 Yu. V. ChekanovFigure 2: Lagran
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392 Yu. V. ChekanovFigure 5: Local
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394 Yu. V. Chekanovderived from the
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396 M. Furatadimensional vector spa
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398 M. FurataHowever in the Seiberg
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400 M. Furata6. Seiberg-Witten-Floe
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402 M. Furata[14] K. Fukaya & K. On
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ICM 2002 • Vol. II • 405-114Gé
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Géométrie de Contact 407- la sph
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Géométrie de Contact 4093) chaque
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412 E. Giroux- en tout point p où
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414 E. Giroux[EU] Y. ELIASHBERG, Cl
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416 L. Hesselholt1. Algebraic üC-t
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418 L. Hesselholt(i) a pro-log diff
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420 L. HesselholtThe canonical map
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422 L. Hesselholttogether with a mu
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424 L. Hesselholtwhere \'- GK —^
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ICM 2002 • Vol. II • 427-436Sym
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Symplectic Sums and Gromov-Witten I
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ICM 2002 • Vol. II • 437-146Kno
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Knots, von Neumann Signatures, and
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ICM 2002 • Vol. II • 447-156Str
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Strings and the Stable Cohomology o
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ICM 2002 • Vol. II • 457-168Non
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Non-zero Degree Maps between 3-Mani
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Section 6. Algebraic and Complex Ge
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472 Hélène Esnaultto ^klX)/k carr
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474 Hélène Esnaultf*c 2 (E, V) is
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476 Hélène EsnaultTheorem 3.1 ([5
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478 Hélène Esnaultno longer the c
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480 Hélène EsnaultQuestion 5.4. W
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ICM 2002 • Vol. II • 483-494Hil
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Hilbert Schemes of Points on Surfac
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and use this to define operatorsHil
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ICM 2002 • Vol. II • 495-502Vec
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Vector Bundles on a K3 Surface 497s
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Vector Bundles on a K3 Surface 499A
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Vector Bundles on a K3 Surface 501a
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ICM 2002 • Vol. II • 503-512Thr
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Three Questions in Gromov-Witten Th
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ICM 2002 • Vol. II • 513^524Upd
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Update on 3-folds 515in the hyperbo
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Update on 3-folds 517In many contex
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Update on 3-folds 5193.3. Explicit
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Update on 3-folds 521The modem view
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Update on 3-folds 523is entertainin
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ICM 2002 • Vol. II • 525-532Sur
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Sur les Algèbres Vertex Attachées
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ICM 2002 • Vol. II • 533-541Top
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Topology of Singular Algebraic Vari
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ICM 2002 • Vol. II • 545-554Har
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Harmonie Analysis on Real Reductive
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[BS3][BS4][Be]Harmonie Analysis on
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ICM 2002 • Vol. II • 555-570On
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On the Dynamical Yang-Baxter Equati
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ICM 2002 • Vol. II • 571-582Geo
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Geometrie Langlands Correspondence
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ICM 2002 • Vol. II • 583-597On
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On the Local Langlands Corresponden
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600 A. KlyachkoAmong commonly known
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602 A. KlyachkoBy Theorem 2.3 this
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604 A. Klyachkois stable iff for ev
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606 A. KlyachkoUnitary spectral pro
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608 A. Klyachkospectra. By Metha-Se
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610 A. KlyachkoAgain our experience
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612 A. Klyachko[9] G. Faltings, Mum
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ICAl 2002 • Vol. II • 615-627Br
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Branching Problems of Unitary Repre
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630 Vikram Bhagvandas AlehtaDefinit
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632 Vikram Bhagvandas Alehtais in t
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634 Vikram Bhagvandas AlehtaTheorem
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ICAl 2002 • Vol. II • 637^642Cl
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Clifford Algebras and the Duflo Iso
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Clifford Algebras and the Duflo Iso
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ICAl 2002 • Vol. II • 643^654Re
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Representations of Yangians 6451.2.
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Representations of Yangians 6478 9
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Representations of Yangians 6492. T
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Representations of Yangians 651irre
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Representations of Yangians 6532.4.
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ICAl 2002 • Vol. II • 655-666Au
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Automorphic L-functions and Functor
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ICAl 2002 • Vol. II • 667^677Mo
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Modular Representations 669(l.b.2)
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Modular Representations 671e) Any p
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Modular Representations 673conjugac
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Modular Representations 675A genera
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Modular Representations 677^-repres
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ICAl 2002 • Vol. II • 681-690Va
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Value Distribution and Potential Th
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ICAl 2002 • Vol. II • 691-700Th
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The Branch Set of a Quasiregular Al
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Page 676 and 677: Harmonie Aleasure and "Locally Flat
Page 684 and 685: 712 N. Lerner1. From Hans Lewy to N
Page 686 and 687: 714 N. Lernergood cases in (1.5) (w
Page 688 and 689: 716 N. Lerner2. Counting the loss o
Page 690 and 691: 718 N. LernerSolvability with loss
Page 692 and 693: 720 N. Lerner6] L.Hörmander, On th
Page 694 and 695: 722 C. ThieleA basic point of singu
Page 696 and 697: 724 C. ThieleFigure 1: "Cone"< en I
Page 698 and 699: 726 C. Thieleis negative. If all of
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Page 704 and 705: 732 C. Thiele[6] Gilbert J., Nahmod
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Page 710 and 711: 738 S. Zelditchfor U C
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Page 714 and 715: 742 S. Zelditch[11] V. F. Lazutkin,
Page 716 and 717: 744 Xiangyu Zhou+00 at the boundary
Page 718 and 719: 746 Xiangyu Zhouconnected component
Page 720 and 721: 748 Xiangyu ZhouWightman [32], Jost
Page 722 and 723: 750 Xiangyu ZhouBrief proof is as f
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Page 728 and 729: 758 Semyon Alesker0.1.1 Definition,
Page 730 and 731: 760 Semyon Alesker2. Translation in
Page 732 and 733: 762 Semyon Alesker2.3. Valuations i
Page 734 and 735: 764 Semyon AleskerReferences[1] Ale
Page 736 and 737: 766 P. Bianewith classical cumulant
Page 738 and 739: 768 P. BianeObserve thatr(ai ... a
Page 740 and 741: 770 P. Biane4. Noncrossing cumulant
Page 742 and 743: 772 P. Bianethis gives the order of
Page 744 and 745: 774 P. Biane[20] R. Speicher, Combi
Page 746 and 747: 776 D. Bischsubfactors has develope
Page 748 and 749: 778 D. Bisch(for all k > 0), where
Page 750 and 751: 780 D. BischObserve that by constru
Page 752 and 753: 782 D. BischIt should be evident th
Page 754 and 755: 784 D. Bisch[4] D. Bisch, Bimodules
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Page 758 and 759: Free Probability, Free Entropy and
Page 764 and 765: ICAl 2002 • Vol. II • 795^812Ba
Page 766 and 767: Banach KK-theory and the Baum-Conne
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Banach KK-theory and the Baum-Conne
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ICAl 2002 • Vol. II • 813-822On
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On Some Inequalities for Gaussian A
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Author IndexAlesker, Semyon 757Andr
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