Knot Theory
  An introduction
A brief history of
      knots
A false start
Take 2
Types of knot




Braids      Links
The Unknot
The Trefoil




Left-handed   Right-handed
Knot Invariants
Reidermeister Moves




 I    II     III
The Alexander-
Conway Polynomial



C(L+) = C(L-) + zC(L0)
A worked example

  C(        ) = C(    ) + zC(     )

  C(        ) = C(    ) + zC(     )

  C(        ) = C(    ) + zC( ...
Chirality of molecules
DNA
Quantum Computing


      ?!?
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Knots!

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An introduction to the mathematical concept of Knot Theory, as delivered at the Madlab's Interesting Monday.

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  • Eternal knot – Tibetan Buddhism
    Borromean Rings - Unity. Christianity. Valknut, Norse.
    Book of kells
  • Peter Guthrie Tait + William Thomson, 1st baron of Kelvin (Lord Kelvin)
    1867. Luminiferous aether, knots and molecules.
    1902 - No balloon or aeroplane will ever be successful
  • 1927 Topology - polymath Poincare, conjecture
    James Waddell Alexander II - Princeton, keen climber, socialist, mccarthy, recluse
    Kurt Reidermeister – Konigsberg, Nazis
  • Braids
    Links
    Topologically similar
  • Alice in Wonderland
    Unknotted knot
    The basis for all other knots
  • next simplest knot
    chiral, important
    any way you flip it

  • knot spotting
    large part of theory
    prime knots
    knowing what it is, important
  • Basic moves
    Prime knot
  • John Conway - Princeton, game of life
    Crossings
    Knot invariant
    Jones Polynomial - harder

  • Left hand is 1 - z^2
  • Thalidomide - Cure, Birth defects
    Flavouring - Peppermint, Orange
  • DNA/RNA
    Helps to untangle, see what’s going on

  • Can’t possibly explain this!
  • Knots!

    1. 1. Knot Theory An introduction
    2. 2. A brief history of knots
    3. 3. A false start
    4. 4. Take 2
    5. 5. Types of knot Braids Links
    6. 6. The Unknot
    7. 7. The Trefoil Left-handed Right-handed
    8. 8. Knot Invariants
    9. 9. Reidermeister Moves I II III
    10. 10. The Alexander- Conway Polynomial C(L+) = C(L-) + zC(L0)
    11. 11. A worked example C( ) = C( ) + zC( ) C( ) = C( ) + zC( ) C( ) = C( ) + zC( ) C( ) = 1 + z(0 + z)
    12. 12. Chirality of molecules
    13. 13. DNA
    14. 14. Quantum Computing ?!?

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