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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 &amp;#x2013; 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 &amp;#x2013; Konigsberg, Nazis
• Braids
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&amp;#x2019;s going on

• Can&amp;#x2019;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 ?!?