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zy x $^4H^4Hz,4 $44^4H v6-7 weeks at double intensity, mid April to late May. Likely 6 weeks April 20 - May 29. Possibly prepend another week.
zy x $6H6H. z>,4 $446H ZTentative Title. Knots and Quantum Groups: Theory and Computations without Representations
zy x $HHz>,4 $4H
zy x $6H6H. z>,4 $446H XTentative Abstract. Our class will run in two parallel streams: "Theory" and "Practice".
zy x $HHz>,4 $4H
zy x $6H6H. z>,4 $446H Tentative Prerequisites. Absolutely no fear of linear algebra: quotients, duality, tensor products, symmetric algebras, etc. No fear of Lie algebras. Having heard of universal enveloping algebras and the PBW theorem. Having seen Gaussian integration.9=z> $H :z $>H?@?@??@
;zy x $HH<z,4 $44H Geneva 2020 Plans>A
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? zy x $4HH@z,4 >4$4H August 31, 2018
B zy x $4HH@z,4 >4$4H 4:14 PM@
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zy x $AȻHAȻHz>,4 $4AȻH
zy x $FȻHFȻHz>,4 4$4%H 8In the "Theory" stream we will start with knot theory and mention a few of the main problems that arise within it. This will lead us to learn about and covet Hopf algebras with certain properties, more or less what is known as "quantum groups". Quantum groups are often studied via their representations, but we will do better! We will find that quantum groups have "solvable approximations" that can be understood in terms of the almost-category of "Gaussian Differential Operators", leading to better relations with topology and enabling more effective computations.
zy x $GȻHGȻHz>,4 $4GȻH
zy x $bȻHbȻHz>,4 4$4bȻH The "Practice" stream will happen in a computer lab and in it everything theory will immediately become practice. Along the way we will learn how to implement sophisticated mathematics in Mathematica.
zy x $-H-Hz>,4 $4-H
zy x $ "H "Hz>,4 $44 "H 14x45m per week, plus 2x45m tutorials maybe by TA.
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&zy x $HH. z>,4 $44H Folder: 20-QGC
(zy x $PHPHz>,4 $4PH 8:<?
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Yzy x $s5Hs5Hz,4 >$44s5H 0The full sl2 portfolio. Questions and prospects.[z $#H?@?@?
\zy x $V$HV$H z,4 >$4w44V$H 6da^z $#H_z $#H
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`zy x $'H'Hz,4 >$44'H Implementation.bz $#H0to?@?@?
czy x $'H'Hz,4 >$44'H FSolvable approximations. Docile perturbations. The elementary tensors.ez $#H?@?@?
fzy x $V$HV$H z,4 >$4w44V$H 5nkhz $#Hiz $#H?@?@?
jzy x $@'H@'Hz,4 >$44@'H Implementation.lz $#H?@?@?
mzy x $'H'Hz,4 >$44'H hThe circuit algebra of quadratics, the almost-category GDO, and a calculus for the Alexander polynomial.oz $#H?@?@?
pzy x $V$HV$H z,4 >$4w44V$H 4xurz $#Hsz $#H0to?@?@?
tzy x $:'H:'Hz,4 >$44:'H >Computations in classical U(sl2); more Mathematica techniques.vz $#H?@?@?
wzy x $%&H%&Hz,4 >$44%&H MThe Drinfel'd double construction in the finite dimensional case and for sl2.yz $#H?@?@?
zzy x $V$HV$H z,4 >$4w44V$H 3|z $#H}z $#H0to?@?@?
~zy x $>%H>%Hz,4 >$44>%H Introduction to Mathematica.z $#Ho?@?@?
zy x $%H%Hz,4 >$44%H DKnots, algebras, Hopf algebras, antipodes, rotational virtual knots.z $#H?@?@?
zy x $V$HV$H z,4 >$4w44V$H 2z $#Hz $#H?@?@?
zy x $$H$Hz,4 >$44$H KThe Jones polynomial: the quick implementation and the fast implementation.z $#H0to?@?@?
zy x $$H$Hz,4 >$44$H PCourse introduction, knots, Reidemeister moves, tangles, algebraic knot theory .z $#Ho?@?@?
zy x $V$HV$H z,4 >$4w44V$H 1z $#Hz $#H9?@?@?
zy x $c$Hc$H z,4 >$4w44c$H Practicez $#H@s?@?@?
zy x $c$Hc$H z,4 >$4w44c$H Theoryz $#H?@?@?
zy x $%H%H z,4 >$4w4%H Wk
zy x $6H6H. z>,4 $446H Tentative Weekly Plan. (This plan is just a feasibility test and is not to be taken seriously. By the time of the class things will surely change).
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zy x $^4H^4Hz,4 $44^4H v6-7 weeks at double intensity, mid April to late May. Likely 6 weeks April 20 - May 29. Possibly prepend another week.
zy x $6H6H. z>,4 $446H ZTentative Title. Knots and Quantum Groups: Theory and Computations without Representations
zy x $HHz>,4 $4H
zy x $6H6H. z>,4 $446H XTentative Abstract. Our class will run in two parallel streams: "Theory" and "Practice".
zy x $HHz>,4 $4H
zy x $6H6H. z>,4 $446H Tentative Prerequisites. Absolutely no fear of linear algebra: quotients, duality, tensor products, symmetric algebras, etc. No fear of Lie algebras. Having heard of universal enveloping algebras and the PBW theorem. Having seen Gaussian integration.9=z> $H :z $>H?@?@??@
;zy x $HH<z,4 $44H Geneva 2020 Plans>A
z $>H?@?@??
? zy x $4HH@z,4 >4$4H August 31, 2018
B zy x $4HH@z,4 >4$4H 4:14 PM@
@{44$04eb4$Geneva 2020 PlanswpJ9:z>(()gA
y w`B
zy x $AȻHAȻHz>,4 $4AȻH
zy x $FȻHFȻHz>,4 4$4%H 8In the "Theory" stream we will start with knot theory and mention a few of the main problems that arise within it. This will lead us to learn about and covet Hopf algebras with certain properties, more or less what is known as "quantum groups". Quantum groups are often studied via their representations, but we will do better! We will find that quantum groups have "solvable approximations" that can be understood in terms of the almost-category of "Gaussian Differential Operators", leading to better relations with topology and enabling more effective computations.
zy x $GȻHGȻHz>,4 $4GȻH
zy x $bȻHbȻHz>,4 4$4bȻH The "Practice" stream will happen in a computer lab and in it everything theory will immediately become practice. Along the way we will learn how to implement sophisticated mathematics in Mathematica.
zy x $-H-Hz>,4 $4-H
zy x $ "H "Hz>,4 $44 "H 14x45m per week, plus 2x45m tutorials maybe by TA.
"zy x $HHz>,4 $4H
&zy x $HH. z>,4 $44H Folder: 20-QGC
(zy x $PHPHz>,4 $4PH 8:<?
z $5H?@?@?33KA??*A
9zy x $HHz,4 $44H
Recycling:
;zy x $HHz>,4 $4H
=zy x $HqH> z>,4 $44qH Abstract. Our class will be about just one algebra U whose definition can be written on the back side of a conference name-tag (see http://drorbn.net/20-QGC/NameTag.png), and will run in several parallel streams:
@Dzy x $$HcH
ABCzy x $&$HHz>,4 $4H )Why is it, more or less, "quantum sl(2)"?" $& z
;H.Calibri z>,4 $4cH HzO4 N544444444Ha@?luA0lA$uA3?uA75\A;p?+tA0^A<>>J4$I4 4
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Vzy x $R5HR5Hz,4 >$44R5H Implementation.Xz $#H0to?@?@?
Yzy x $s5Hs5Hz,4 >$44s5H 0The full sl2 portfolio. Questions and prospects.[z $#H?@?@?
\zy x $V$HV$H z,4 >$4w44V$H 6da^z $#H_z $#H
?@?@?
`zy x $'H'Hz,4 >$44'H Implementation.bz $#H0to?@?@?
czy x $'H'Hz,4 >$44'H FSolvable approximations. Docile perturbations. The elementary tensors.ez $#H?@?@?
fzy x $V$HV$H z,4 >$4w44V$H 5nkhz $#Hiz $#H?@?@?
jzy x $@'H@'Hz,4 >$44@'H Implementation.lz $#H?@?@?
mzy x $'H'Hz,4 >$44'H hThe circuit algebra of quadratics, the almost-category GDO, and a calculus for the Alexander polynomial.oz $#H?@?@?
pzy x $V$HV$H z,4 >$4w44V$H 4xurz $#Hsz $#H0to?@?@?
tzy x $:'H:'Hz,4 >$44:'H >Computations in classical U(sl2); more Mathematica techniques.vz $#H?@?@?
wzy x $%&H%&Hz,4 >$44%&H MThe Drinfel'd double construction in the finite dimensional case and for sl2.yz $#H?@?@?
zzy x $V$HV$H z,4 >$4w44V$H 3|z $#H}z $#H0to?@?@?
~zy x $>%H>%Hz,4 >$44>%H Introduction to Mathematica.z $#Ho?@?@?
zy x $%H%Hz,4 >$44%H DKnots, algebras, Hopf algebras, antipodes, rotational virtual knots.z $#H?@?@?
zy x $V$HV$H z,4 >$4w44V$H 2z $#Hz $#H?@?@?
zy x $$H$Hz,4 >$44$H KThe Jones polynomial: the quick implementation and the fast implementation.z $#H0to?@?@?
zy x $$H$Hz,4 >$44$H PCourse introduction, knots, Reidemeister moves, tangles, algebraic knot theory .z $#Ho?@?@?
zy x $V$HV$H z,4 >$4w44V$H 1z $#Hz $#H9?@?@?
zy x $c$Hc$H z,4 >$4w44c$H Practicez $#H@s?@?@?
zy x $c$Hc$H z,4 >$4w44c$H Theoryz $#H?@?@?
zy x $%H%H z,4 >$4w4%H Wk
zy x $6H6H. z>,4 $446H Tentative Weekly Plan. (This plan is just a feasibility test and is not to be taken seriously. By the time of the class things will surely change).
zy x $#H#Hz>,4 $4#H zV%`vW%E)K:"$`|SH,o3$`Ҧi9eA G<$`Iqk BɋLZ(`d