2014年ICM上颁发的五个奖项.pdf

2014 X ICM YNSR^TV_ 2014 ICM :4 8 o 13—21 it e^ Mz 27 7 ^ %(l } (ICM). } u z ^ %(6z 5 B *FPe2(z Fields (' ;) * , Rolf Nevanlinna (-℄ ~,) *Carl Friedrich Gauss (= +) *Chern Medal Award (R|*) l Leelavati * 1. Fields W Fields *KL # “%( Nobel (9 ) *”, z 6)l%( John C. Fields (1863—1932), Fields *G:z A" 8* 4 4t^%(l}zM' u E[ xz ) L VBz%(8 *^A B 4 *ez 40 8i&!t Fields **s4 1 o 1 i q Fields * d*t 1936 4u 2010 4 P ^ 52 i%( xz Fields * *ezVB&!ab%( Fields UQ` d P ^ 4 i%( x Fields *: (ÆA&d$) ^^ P(5A" (CNRS) l v ^ h dUZ%(5A9 (IMPA) z Artur Avila, ^ E~+ l (z Manjul Bhargava, S ^u ^ (Warwick) l(z Martin Hairer l ^ +? 4 l(z 1) Maryam Mirzakhani2). a. Artur Avila Fields * Artur Avila, G. : s|Mh ~Sz O :G& y J MAhzzO^sz, 9 )z 8 ez • Avila P l 3yz s|Med:z n J AK:F?tY l5 zAe s(q Schrödinger (' K) 4>zFh A=V (flat billiards) l : - (partially) 'Y s(z' e[xz ;} • a : X zX_h40G& y zX h Avila z H J Ae s(zTEX3$:t 5 s(z H Jn℄z Feigenbaum Julia (,k1) - m zNQh4 • tqG Schrödinger 4>zFh " Avila xuzfoF l K v%F ) zA$ F#(rz Lyapunov (i0E9 1) %e=3z - D4u (M http://www.icm2014.org/en/awards/awards }[> 1) { Y vo Fields Medal Ud ( <+ 7 ( <+d1 Chern Medal Award HUdS}+ 7UdS}++—— M3 2) y3J{Maryam Mirzakhani Bjy Fields +{8 —— M3 · 274 · tA=Vh "Avila ÆzAMGhJz WaX ,|Yx (interval-exchange map) ,n z<:tn a z: - 'Y|Ml ,nzh4u[x z~mz;} • Avila zJ # Ao%(A$L • b. Manjul Bhargava * Manjul Bhargava, G. :t%z m z5A"M \AO^sz # 0;Za z z%06 SjYDzAL • Bhargava z4 k ax B g d z Gauss 5n C K zA B &##:Æz3 B -8 .zyuzb SL(2, Z)3 z ℄ vU a d z (Z u 2 z z) d 3 B H A zh GX l= z4 # xuz Gauss 5n q :5Az G5 sz ."z ℄ v; Uan d/d l qd z z ℄ v04zG^^6:/ z z z%( • Bhargava /:5A6)y z z.HF!qz.℄ g/d U ub P GL(2, Z) zJZ E \^x BÆ rz6)y;dSjYz#^ W Bhargava l :z( Arul Shankar AKZ W aG^^6 = z ℄ v%(z> S ℄6 SjYDzAL # Q [ u = X ? Y:F<ÆzX ? w 2 zF (most) OSj (hyperelliptic) Y^^h • Bhargava z H JG 4!b.z~Sh4G o% l- u4? z Æ Ak n H^ Fields c. Martin Hairer Martin Hairer, Fields * G. : a7> _ -# Wh z1\ O A/: a:z # W ayzA$ z3 Q h t B P("A Bo &;z%(mEh4x _ -# WzWG 4zMG zW a L_ -# W 7 B mE Itô (CB) t 1940 4o4 Jza>_-#WX_zh F ÆG .xu tAAT ( # W,* (tame) ) |) >xuzeIz3 ` Hairer z H Jy 8 h zx Bk # d Mattingly n J:UZ Malliavin (Æ o1Y) 94 A # (rz e7 Navier-Stokes (,e – +RR+) # Wz,n a Lyons z7L_-#WzgA#Hairer ayz7>_-#W (SPDEs) z3QzA$[ h p"tU l zfm(a^ Taylor (>a) }M B h : aIN ) 7>_ -# W1 R |M Q y4J & ya W" z6 · 275 · :Hairer B1 R trh(Iz" 7>_ -# Wd E \;4 ? z 0t f K d. Maryam Mirzakhani * Maryam Mirzakhani, G. < a Riemann (e) Y H#U z s( l m (z1 \ O • Maryam Mirzakhani t Riemann Y H#U h z5A"[xz=ez;}0t e"M TzzM8h • _ -# Wz # :t% - u # z O Y Engquist-Osher ? A TVD ? LI&ENO l WENO ? l % # z Hamilton-Jacobi ( – 0Q$) # WF?Q~ 9 )z 8 e:t) A # z O Yz)A 94Xz%A!F l ={(#) -# = beq - u mZ (G Hamilton-Jacobi # W 4z4 )A #F?t4IP _h4P(" GW U#< 4℄F?i >_ -# Wh z$F F !z5AXVzUZ%(i;b%( z w 1) TVD, total variation diminishing (C*H# ) {"Uu& $ #TVD [^5%gp Æ(Z?`.$ X{ $% $ {G0{V[u5G t)#—— M3 2) ENO, essentially non-oscillatory ("! * ({)) {"U —— M3 3) WENO, weighted ENO (^ ENO) {"U —— M3 3. Carl Friedrich Gauss 1) 2) 3) · 277 · G^ Æ AztA :Wzo\ zUZ%(z-f0O :za?>:F?V J :z%(nuz H ?" • J A B UZ%(Osher 6 D $!q Qz ? lM %(6 l % - u6=36F: [" z 9 )zn ? I l %( : 6zh4 0 E znz H G℄g B 6 4. P℄[W R|*A%(*G6F U z" ^ %(R | (1911—2004). 8 *℄ ^ %(udR|*9 } (CMF) u n t. t%(e[xF = )Az1\ VBz B ed* 2010 4tQ d x[ (Hyderabad) Ez 26 7 ^ %(l } zM' u A 4 4t ^ %(l } M' u* O\ZUQ` Phillip Griffiths R|* ^= |5Al (IAS) z Phillip Griffiths (? j ' ,), G. :a5m(On#Mal>"z }A/ :t Hodge (I) h l o%hz(G # zMa H J • Phillip Griffiths to% m _ - ml _ -# W # l:ht ;z H Jt a ℄ 50 4j z [" z%(uz;}0R %W l m::H o z5A H J • t l5 m z o mEu:9n℄z^ T z!`^ =ezha,t(GYxleo%%wNevanlinna h Brill-Noether (8j – 9A) h l Kähler (Na) zTCu ^UZ • Griffiths H JzA B A 6 ;\\ zA B A zmErt o TW }MazA B _z5Ae • twG:K a pU # t)h l Hodge h (rzu|℄ t T Griffiths pU (G W | : # Griffiths " Jacobi D (the Griffiths intermediate Jacobian) C K zh sq 4JzÆo%%wzo%| l L |6LzmE:d C. H. Clemens (R\+) W ar # n& (the cubic threefold) z ) ^hz n J H JV On # o%h5Az" q UZzA$# • :z [" z5A mEn℄z" !0t m (" /ze —— |O K℄0rkf5mze —— Iz Fsn℄z;9:O_-#WE z W 5Atz 8 .Et 1980 4oGU_ - | & s:) UZt o_ - m ~DdzmEtO TW}|HNmz < tneza TW} Z v4zC:jt Z'Y>_-#WzA~S3` (d E. 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