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Swift で数学研究のススメ

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iOSDC 2018
https://fortee.jp/iosdc-japan-2018/proposal/45e3ad74-d815-49eb-8963-5c62e126110b

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Swift で数学研究のススメ

  1. 1. IOSDC 2018 & 00 @ Swift i #x¥7# ' ¥ a xx¥0 as & @ take to 2024
  2. 2. 44¥ a " a ¥¥¥¥ oQdIF@HIEE7HkiEasiEiEF.t , #¥ , A z 7.#¥tF3 **k¥ ( Hin I÷ ) a - B'¥3 .
  3. 3. @ . f¥t¥H3Kaia is its ? Is IT @ . f¥t¥H3Kaia is its ? Is IT
  4. 4. @ . f¥t¥H3Kaia is its ? Is IT @ . f¥t¥H3Kaia is its ? Is IT
  5. 5. ¥1 # At A K¥7 " IF zi Ql . 5- 25k£ 44£ zia * FAEHZX' FY ' K EL . Q2 . 2 s a FFEU" a lot I 2512k 2£ , ZK to Hu to' Z A 41¥ 't £ . = Aeza FE air as a # a e£ . E '¥i£¥s¥Hz it #¥ :* ! )
  6. 6. A '5t¥± : As #¥aEaa 't #x K a K ' lI5tj , f (K ) = fck ' ) { T23¥zAt'¥a fk ) Fflk ' ) Ishii K 4K ' { I3 '¥I
  7. 7. Jones 32¥ It ( 1984 ) 0 do do Jb ) = 1 . J( D) = - gi4tq3tqt.Jl@1-jtq2.q- of ' +1 . tfitzviaktr JCK ) tltss , K is FIIEIHIa sacino '3 ! ( tea KEYI ) Jones 32¥ It ( 1984 ) 0 do do Jb ) = 1 . J( D) = - gi4tq3tqt.Jl@1-jtq2.q- of ' +1 . tfitzviaktr JCK ) tltss , K is FIIEIHIa sacino '3 ! ( tea KEYI ) Jones 32¥ It ( 1984 ) 0 do do Jb ) = 1 . J( D) = - gi4tq3tqt.Jl@1-jtq2.q- of ' +1 . tfitzviaktr JCK ) tltss , K is FIIEIHIa sacino '3 ! ( tea KEYI ) Jones 32¥ It ( 1984 ) 0 do do Jb ) = 1 . J( D) = - gi4tq3tqt.Jl@1-jtq2.q- of ' +1 . tfitzviaktr JCK ) tltss , K is FIIEIHIa sacino '3 ! ( tea KEYI )
  8. 8. Khovanov homology Gooo ) KHCK ) " HE '¥¥tb " starch . %tEuAK > JCK )
  9. 9. Khovanov homology ¥t¥f3hI47iG
  10. 10. 1. ¥t¥a5aa§k .IE#EiiAID K ' n=3 o 1 ( }es#d¥ion ) )( =
  11. 11. 1. ¥t¥a5aa§k .IE#EiiAID K ' n=3 o 1 ( }es#d¥ion ) )( =
  12. 12. 1 . ¥t¥a's # a III. EFFE :* Ed 0 1 ←asto
  13. 13. 2. Ezak¥iF7¥F7a&AHtzBEz# 23 . Ho ) IsIB n =3 100 110 addIBIndKB000 010 10 I 11 1 •P@@.;iff ( 23=8 # 's ) 001 Of 1
  14. 14. 3 . At # Esa III 's a # ¥72213 IsD8 100 1 10 addIBInd8.8000 010 10 I 11 1 IDEdid001 Of 1
  15. 15. 3 . At # Esa III 's a # ¥72213 IsD8 100 1 10 addIBInd8.8000 010 10 I 11 1 IDEdid001 Of 1 3 . At # Esa III 's a # ¥72213 IsD8 100 1 10 addIBInd8.8000 010 10 I 11 1 IDEdid001 Of 1
  16. 16. 3 . At # Esa III 's a # ¥72213 IsD8 100 1 10 addIBInd8.8000 010 10 I 11 1 IDEdid001 Of 1 3 . At # Esa III 's a # ¥72213 IsD8 100 1 10 addIBInd8.8000 010 10 I 11 1 IDEdid001 Of 1 Oo §??tE ¥¥¥¥o←s merge
  17. 17. 3 . At # Esa III 's a # ¥72213 IsD8 100 1 10 addIBInd8.8000 010 10 I 11 1 IDEdid001 Of 1 3 . At # Esa III 's a # ¥72213 IsD8 100 1 10 addIBInd8.8000 010 10 I 11 1 IDEdid001 Of 1
  18. 18. 3 . At # Esa III 's a # ¥72213 IsD8 100 1 10 addIBInd8.8000 010 10 I 11 1 IDEdid001 Of 1 3 . At # Esa III 's a # ¥72213 IsD8 100 1 10 addIBInd8.8000 010 10 I 11 1 IDEdid001 Of 1 Oo §??tE ¥¥¥o←s split
  19. 19. 3 . At # Esa III 's a # ¥72213 IsD8 100 1 10 addIBInd8.8000 010 10 I 11 1 IDEdid001 Of 1
  20. 20. 3 . At # Esa III 's a A ¥72213 #*.€as***e**¥EE¥a*⇐e¥ Edidid
  21. 21. 4 . ht ' # then 'RE # z hF3 IsIB 100 I 10 add8DIndodd000 010 10 I 11 1 IDEdid001 Of 1 C = { o d dC ' d ' C2 d ' d o }
  22. 22. 5. homology { EAR ' ¥ At ' ! u#x¥##±a± ) IsIB 100 1 10 add8.8ID. odd000 010 10 I 1 1 1 IDEIndo001 Of 1 C = { o d dC ' d ' d d ' d o } IH KHCK )
  23. 23. Khovanov homology ¥t⇐¥By 0 Is do
  24. 24. Khovanov homology ¥t⇐¥By 0 Is dof) Kh ( 0 ) = 22 . Kh ( k ) t 22 II 's , K IF A '4HIn . (¥ .rs#*.*IaiI'I*takh(k)=2
  25. 25. ¥XBI e ]=e°z . 7a PETE. 5*5 ¥K¥fa¥¥¥'# I=c°z - J
  26. 26. #XBI e I =e°z - 7 a M¥45. 5*5 ¥Kya #¥¥¥ I =c°z - J 5*5 • Fla?Bs¥xE k kHz I e°z - 7 z 5*23 KTHis ¥ #± ! • Hhtt € * 35 !
  27. 27. ( ) Theorem(W.) Let M be a 1-connected space with dim(π∗(M) ⊗ Q) < ∞. Assume ∃ F → M → B fibration satisfying • F and B are 1-connected • B is rationally homotopy equivalent to S2n+1 • ∂ ⊗ 1 = 0: π2n+1(B) ⊗ Q → π2n(F) ⊗ Q Then the loop coproduct on LM is trivial. • A ⇒ B (Assume A. Then B.) A: B: • A, B • ( ) 2017 7 19 3 / 10 “ 2017-07-19 有理ホモトピー論とコンピュータ @wktkshn
  28. 28. • F and B are 1-connected • B is rationally homotopy equivalent to S2n+1 • ∂ ⊗ 1 = 0: π2n+1(B) ⊗ Q → π2n(F) ⊗ Q Then the loop coproduct on LM is trivial. • A ⇒ B (Assume A. Then B.) A: B: • A, B • ( ) 2017 7 19 3 / 10
  29. 29. ]ie°z - 7 is ¥X¥ a Playground kts3 !
  30. 30. committer wanted! SwiftyMath

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