slippery slides - uni-regensburg.deslippery slides clara l oh universit at regensburg january 21,...
TRANSCRIPT
![Page 1: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/1.jpg)
Slippery Slides
Clara Loh
Universitat Regensburg
January 21, 2018
![Page 2: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/2.jpg)
Overview
An axiom for slides
A toy example
General advice for slides
Clara Loh 2
![Page 3: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/3.jpg)
An axiom for slides
Axiom
Do not give slide talks!
〈audience growls〉
Except if . . .
I there is no blackboard available
I the material cannot be displayed on a blackboard(e.g., animations, . . . )
I you know exactly what you are doing.
Question
What is so difficult about giving good slide talks?!
Clara Loh An axiom for slides 3
![Page 4: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/4.jpg)
An axiom for slides
Axiom
Do not give slide talks!
〈audience growls〉
Except if . . .
I there is no blackboard available
I the material cannot be displayed on a blackboard(e.g., animations, . . . )
I you know exactly what you are doing.
Question
What is so difficult about giving good slide talks?!
Clara Loh An axiom for slides 3
![Page 5: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/5.jpg)
An axiom for slides
Axiom
Do not give slide talks!
〈audience growls〉
Except if . . .
I there is no blackboard available
I the material cannot be displayed on a blackboard(e.g., animations, . . . )
I you know exactly what you are doing.
Question
What is so difficult about giving good slide talks?!
Clara Loh An axiom for slides 3
![Page 6: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/6.jpg)
An axiom for slides
Axiom
Do not give slide talks!
〈audience growls〉
Except if . . .
I there is no blackboard available
I the material cannot be displayed on a blackboard(e.g., animations, . . . )
I you know exactly what you are doing.
Question
What is so difficult about giving good slide talks?!
Clara Loh An axiom for slides 3
![Page 7: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/7.jpg)
An axiom for slides
Axiom
Do not give slide talks!
〈audience growls〉
Except if . . .
I there is no blackboard available
I the material cannot be displayed on a blackboard(e.g., animations, . . . )
I you know exactly what you are doing.
Question
What is so difficult about giving good slide talks?!
Clara Loh An axiom for slides 3
![Page 8: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/8.jpg)
An axiom for slides
Axiom
Do not give slide talks!
〈audience growls〉
Except if . . .
I there is no blackboard available
I the material cannot be displayed on a blackboard(e.g., animations, . . . )
I you know exactly what you are doing.
Question
What is so difficult about giving good slide talks?!
Clara Loh An axiom for slides 3
![Page 9: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/9.jpg)
An axiom for slides
Axiom
Do not give slide talks!
〈audience growls〉
Except if . . .
I there is no blackboard available
I the material cannot be displayed on a blackboard(e.g., animations, . . . )
I you know exactly what you are doing.
Question
What is so difficult about giving good slide talks?!
Clara Loh An axiom for slides 3
![Page 10: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/10.jpg)
What is so difficult about slides?
Problem
The speaker needs toforesee/manipulate the future.
I fixed content, length, and order of talk (up to minor variations)
I difficult to insert comments/correct typos
I hence: limited interaction with the audience
Solution
I Meticulous planning
I Leading/manipulating the audience (requires experience)
Clara Loh An axiom for slides 4
![Page 11: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/11.jpg)
What is so difficult about slides?
Problem
The speaker needs toforesee/manipulate the future.
I fixed content, length, and order of talk (up to minor variations)
I difficult to insert comments/correct typos
I hence: limited interaction with the audience
Solution
I Meticulous planning
I Leading/manipulating the audience (requires experience)
Clara Loh An axiom for slides 4
![Page 12: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/12.jpg)
What is so difficult about slides?
Problem
The speaker needs toforesee/manipulate the future.
I fixed content, length, and order of talk (up to minor variations)
I difficult to insert comments/correct typos
I hence: limited interaction with the audience
Solution
I Meticulous planning
I Leading/manipulating the audience (requires experience)
Clara Loh An axiom for slides 4
![Page 13: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/13.jpg)
What is so difficult about slides?
Problem
The speaker needs toforesee/manipulate the future.
I fixed content, length, and order of talk (up to minor variations)
I difficult to insert comments/correct typos
I hence: limited interaction with the audience
Solution
I Meticulous planning
I Leading/manipulating the audience (requires experience)
Clara Loh An axiom for slides 4
![Page 14: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/14.jpg)
What is so difficult about slides?
Problem
The speaker needs toforesee/manipulate the future.
I fixed content, length, and order of talk (up to minor variations)
I difficult to insert comments/correct typos
I hence: limited interaction with the audience
Solution
I Meticulous planning
I Leading/manipulating the audience (requires experience)
Clara Loh An axiom for slides 4
![Page 15: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/15.jpg)
What is so difficult about slides?
Problem
I The human brain has limitedprocessing speed/capacity.
I By using slides, the audiencedoes not magically getsmarter/faster!
Bad reason for a slide talk
“I only have x minutes for the talk.
On a blackboard, I would get nowhere. But, using slides, . . . ”
Solution
Careful selection/presentation of topics
Clara Loh An axiom for slides 5
![Page 16: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/16.jpg)
What is so difficult about slides?
Problem
I The human brain has limitedprocessing speed/capacity.
I By using slides, the audiencedoes not magically getsmarter/faster!
Bad reason for a slide talk
“I only have x minutes for the talk.On a blackboard, I would get nowhere. But, using slides, . . . ”
Solution
Careful selection/presentation of topics
Clara Loh An axiom for slides 5
![Page 17: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/17.jpg)
What is so diflicuft about slides?
Problem
I The human brain has limitedprocessing speed/capacity.
I By using slides, the audiencedoes not magically getsmarter/faster!
Bad reason for a slide talk
“I only have x minutes for the talk.On a blackboard, I would get nowhere. But, using slides, . . . ”
Solution
Careful selection/presentation of topics
Clara Loh An axiom for slides 5
![Page 18: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/18.jpg)
What is so difficult about slides?
Problem
I The human brain has limitedprocessing speed/capacity.
I By using slides, the audiencedoes not magically getsmarter/faster!
Bad reason for a slide talk
“I only have x minutes for the talk.On a blackboard, I would get nowhere. But, using slides, . . . ”
Solution
Careful selection/presentation of topics
Clara Loh An axiom for slides 5
![Page 19: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/19.jpg)
A little experiment
On the previous slide, there was
a witch a brain a funnel a hose
Question
I How many hands/feet did the witch have?
I How many knots did the hose have?
I Did the title of the previous slide change?
Conclusion
The audience needs to be told what to look at!
Clara Loh An axiom for slides 6
![Page 20: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/20.jpg)
A little experiment
On the previous slide, there was
a witch a brain a funnel a hose
Question
I How many hands/feet did the witch have?
I How many knots did the hose have?
I Did the title of the previous slide change?
Conclusion
The audience needs to be told what to look at!
Clara Loh An axiom for slides 6
![Page 21: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/21.jpg)
A little experiment
On the previous slide, there was
a witch a brain a funnel a hose
Question
I How many hands/feet did the witch have?
I How many knots did the hose have?
I Did the title of the previous slide change?
Conclusion
The audience needs to be told what to look at!Clara Loh An axiom for slides 6
![Page 22: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/22.jpg)
A toy example
Let’s look at an example . . .
Clara Loh A toy example 7
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Solving the Blorxification Equation
Nimeta Kulmkapp
University of Dokomo
21.01.2018
![Page 24: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/24.jpg)
The Blorxification Equation
The Blorxification Equation is the equation for a tectonic phenomenonon the planet Blorx. It is noteworthy that planet Blorx has the shapeof a cube. A version with slightly different constants has previouslybeen studied in a paper by C. Keen (2017, unpublished).
Blorxification Equation:√2 + x + cos(8 · y) + z2018 = x · 2018
x + y + z = 3 · yz = x
−1 ≤ x , y ≤ 1
−1 ≤ z ≤ 1
Theorem
The Blorxification Equation has a solution.!
The value of your SchummerCoin wallet
has dropped by 250% !
!New Message
from DubiousMadame !
N. Kulmkapp 2 / 561
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The Blorxification Equation
The Blorxification Equation is the equation for a tectonic phenomenonon the planet Blorx. It is noteworthy that planet Blorx has the shapeof a cube. A version with slightly different constants has previouslybeen studied in a paper by C. Keen (2017, unpublished).Blorxification Equation:√
2 + x + cos(8 · y) + z2018 = x · 2018
x + y + z = 3 · yz = x
−1 ≤ x , y ≤ 1
−1 ≤ z ≤ 1
Theorem
The Blorxification Equation has a solution.!
The value of your SchummerCoin wallet
has dropped by 250% !
!New Message
from DubiousMadame !
N. Kulmkapp 2 / 561
![Page 26: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/26.jpg)
The Blorxification Equation
The Blorxification Equation is the equation for a tectonic phenomenonon the planet Blorx. It is noteworthy that planet Blorx has the shapeof a cube. A version with slightly different constants has previouslybeen studied in a paper by C. Keen (2017, unpublished).Blorxification Equation:√
2 + x + cos(8 · y) + z2018 = x · 2018
x + y + z = 3 · yz = x
−1 ≤ x , y ≤ 1
−1 ≤ z ≤ 1
Theorem
The Blorxification Equation has a solution.!
The value of your SchummerCoin wallet
has dropped by 250% !
!New Message
from DubiousMadame !
N. Kulmkapp 2 / 561
![Page 27: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/27.jpg)
Proofs
We will skip these slides. They are not so important.But, if they are not important, why are they in the slide deck?Because we skip these slides anyway, we can also use yellow forhighlighting.Small text successfully keeps the audience from reading it.This is even worse. Using this fontsize, we can pack a quasi-infinite amount of information on a single slide.Moreover, this should be almost as bad as smallprint in mobile phone contracts. In combination with a lowprojector resolution, the result can be quite impressive.
Of course, we can also happily skip some computations:
∫ 1
01 + 1 − 1 − 1 + 1 + 1 − 1 + 1 − 1 − 1 dx = 0,
∫ 1
01 + 1 − 1 − 1 + 1 + 1 − 1 + 1 − 1 + 1 dx = 2.
Theorem
These slides will not be shown.
N. Kulmkapp 3 / 561
![Page 28: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/28.jpg)
More proofs
Small text successfully keeps the audience from reading it.This is even worse. Using this fontsize, we can pack a quasi-infinite amount of information on a single slide.Moreover, this should be almost as bad as smallprint in mobile phone contracts. In combination with a lowprojector resolution, the result can be quite impressive.
Of course, we can also happily skip some computations:
∫ 1
01 + 1 − 1 − 1 + 1 + 1 − 1 + 1 − 1 − 1 dx = 0,
∫ 1
01 + 1 − 1 − 1 + 1 + 1 − 1 + 1 − 1 + 1 dx = 2.
Theorem
These slides will not be shown.
We will skip these slides. They are not so important.But, if they are not important, why are they in the slide deck?Because we skip these slides anyway, we can also use yellow forhighlighting.
N. Kulmkapp 4 / 561
![Page 29: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/29.jpg)
Even more proofs
Of course, we can also happily skip some computations:
∫ 1
01 + 1 − 1 − 1 + 1 + 1 − 1 + 1 − 1 − 1 dx = 0,
∫ 1
01 + 1 − 1 − 1 + 1 + 1 − 1 + 1 − 1 + 1 dx = 2.
Theorem
These slides will not be shown.
We will skip these slides. They are not so important.But, if they are not important, why are they in the slide deck?Because we skip these slides anyway, we can also use yellow forhighlighting.Small text successfully keeps the audience from reading it.This is even worse. Using this fontsize, we can pack a quasi-infinite amount of information on a single slide.Moreover, this should be almost as bad as smallprint in mobile phone contracts. In combination with a lowprojector resolution, the result can be quite impressive.
N. Kulmkapp 5 / 561
![Page 30: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/30.jpg)
Jumping proofs
Small text successfully keeps the audience from reading it.This is even worse. Using this fontsize, we can pack a quasi-infinite amount of information on a single slide.Moreover, this should be almost as bad as smallprint in mobile phone contracts. In combination with a lowprojector resolution, the result can be quite impressive.
We will skip these slides. They are not so important.But, if they are not important, why are they in the slide deck?Because we skip these slides anyway, we can also use yellow forhighlighting.Of course, we can also happily skip some computations:
∫ 1
01 + 1 − 1 − 1 + 1 + 1 − 1 + 1 − 1 − 1 dx = 0,
∫ 1
01 + 1 − 1 − 1 + 1 + 1 − 1 + 1 − 1 + 1 dx = 2.
Theorem
These slides will not be shown.
N. Kulmkapp 6 / 561
![Page 31: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/31.jpg)
Jumping proofs
Small text successfully keeps the audience from reading it.This is even worse. Using this fontsize, we can pack a quasi-infinite amount of information on a single slide.Moreover, this should be almost as bad as smallprint in mobile phone contracts. In combination with a lowprojector resolution, the result can be quite impressive.
We will skip these slides. They are not so important.But, if they are not important, why are they in the slide deck?Because we skip these slides anyway, we can also use yellow forhighlighting.Of course, we can also happily skip some computations:
∫ 1
01 + 1 − 1 − 1 + 1 + 1 − 1 + 1 − 1 − 1 dx = 0,
∫ 1
01 + 1 − 1 − 1 + 1 + 1 − 1 + 1 − 1 + 1 dx = 2.
Theorem
These slides will not be shown.
N. Kulmkapp 6 / 561
![Page 32: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/32.jpg)
Jumping proofs
Small text successfully keeps the audience from reading it.This is even worse. Using this fontsize, we can pack a quasi-infinite amount of information on a single slide.Moreover, this should be almost as bad as smallprint in mobile phone contracts. In combination with a lowprojector resolution, the result can be quite impressive.
We will skip these slides. They are not so important.But, if they are not important, why are they in the slide deck?Because we skip these slides anyway, we can also use yellow forhighlighting.Of course, we can also happily skip some computations:
∫ 1
01 + 1 − 1 − 1 + 1 + 1 − 1 + 1 − 1 − 1 dx = 0,
∫ 1
01 + 1 − 1 − 1 + 1 + 1 − 1 + 1 − 1 + 1 dx = 2.
Theorem
These slides will not be shown.
N. Kulmkapp 6 / 561
![Page 33: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/33.jpg)
Jumping proofs
Small text successfully keeps the audience from reading it.This is even worse. Using this fontsize, we can pack a quasi-infinite amount of information on a single slide.Moreover, this should be almost as bad as smallprint in mobile phone contracts. In combination with a lowprojector resolution, the result can be quite impressive.
We will skip these slides. They are not so important.But, if they are not important, why are they in the slide deck?Because we skip these slides anyway, we can also use yellow forhighlighting.Of course, we can also happily skip some computations:
∫ 1
01 + 1 − 1 − 1 + 1 + 1 − 1 + 1 − 1 − 1 dx = 0,
∫ 1
01 + 1 − 1 − 1 + 1 + 1 − 1 + 1 − 1 + 1 dx = 2.
Theorem
These slides will not be shown.
N. Kulmkapp 6 / 561
![Page 34: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/34.jpg)
Jumping proofs
Small text successfully keeps the audience from reading it.This is even worse. Using this fontsize, we can pack a quasi-infinite amount of information on a single slide.Moreover, this should be almost as bad as smallprint in mobile phone contracts. In combination with a lowprojector resolution, the result can be quite impressive.
We will skip these slides. They are not so important.But, if they are not important, why are they in the slide deck?Because we skip these slides anyway, we can also use yellow forhighlighting.Of course, we can also happily skip some computations:
∫ 1
01 + 1 − 1 − 1 + 1 + 1 − 1 + 1 − 1 − 1 dx = 0,
∫ 1
01 + 1 − 1 − 1 + 1 + 1 − 1 + 1 − 1 + 1 dx = 2.
Theorem
These slides will not be shown.
N. Kulmkapp 6 / 561
![Page 35: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/35.jpg)
Jumping proofs
Small text successfully keeps the audience from reading it.This is even worse. Using this fontsize, we can pack a quasi-infinite amount of information on a single slide.Moreover, this should be almost as bad as smallprint in mobile phone contracts. In combination with a lowprojector resolution, the result can be quite impressive.
We will skip these slides. They are not so important.But, if they are not important, why are they in the slide deck?Because we skip these slides anyway, we can also use yellow forhighlighting.Of course, we can also happily skip some computations:
∫ 1
01 + 1 − 1 − 1 + 1 + 1 − 1 + 1 − 1 − 1 dx = 0,
∫ 1
01 + 1 − 1 − 1 + 1 + 1 − 1 + 1 − 1 + 1 dx = 2.
Theorem
These slides will not be shown.
N. Kulmkapp 6 / 561
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Jumping proofs
Small text successfully keeps the audience from reading it.This is even worse. Using this fontsize, we can pack a quasi-infinite amount of information on a single slide.Moreover, this should be almost as bad as smallprint in mobile phone contracts. In combination with a lowprojector resolution, the result can be quite impressive.
We will skip these slides. They are not so important.But, if they are not important, why are they in the slide deck?Because we skip these slides anyway, we can also use yellow forhighlighting.Of course, we can also happily skip some computations:
∫ 1
01 + 1 − 1 − 1 + 1 + 1 − 1 + 1 − 1 − 1 dx = 0,
∫ 1
01 + 1 − 1 − 1 + 1 + 1 − 1 + 1 − 1 + 1 dx = 2.
Theorem
These slides will not be shown.
N. Kulmkapp 6 / 561
![Page 37: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/37.jpg)
Jumping proofs
Small text successfully keeps the audience from reading it.This is even worse. Using this fontsize, we can pack a quasi-infinite amount of information on a single slide.Moreover, this should be almost as bad as smallprint in mobile phone contracts. In combination with a lowprojector resolution, the result can be quite impressive.
We will skip these slides. They are not so important.But, if they are not important, why are they in the slide deck?Because we skip these slides anyway, we can also use yellow forhighlighting.Of course, we can also happily skip some computations:
∫ 1
01 + 1 − 1 − 1 + 1 + 1 − 1 + 1 − 1 − 1 dx = 0,
∫ 1
01 + 1 − 1 − 1 + 1 + 1 − 1 + 1 − 1 + 1 dx = 2.
Theorem
These slides will not be shown.
N. Kulmkapp 6 / 561
![Page 38: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/38.jpg)
Proof of the main result
The function
f (a, b, c) =
1/2018 ·√a + c2018 + 2 + cos(8 · b)
1/4 · (a + b + c)a
satisfies the hypotheses of the Blorx Fixed Point Theorem. This solvesthe Blorxification equation.
N. Kulmkapp 7 / 561
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A toy example
Let’s try to do better . . .
Clara Loh A toy example 8
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Solving the Blorxification Equation
Nimeta Kulmkapp
University of Dokomo
21. 01. 2018
Joint project with Jargmine Peatus
![Page 41: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/41.jpg)
Blorxification
Tectonic phenomenon on the cube-shaped planet Blorx
modelled by the Blorx operator
B : [−1, 1]3 −→ [−1, 1]3 =: Qxyz
7−→
12018 ·
√2 + x + cos(8 · y) + z201813 · (x + y + z)
x
Blorxcillationaveragerandom swap
Question
Are there points on Blorx that are not affected by Blorxification?
Theorem (K., J. Peatus 2018)
The Blorx operator B : Q −→ Q has a fixed point.
Related Work
I C. Keen treated a similar operator (2017)
I our proof uses the same method
Clara Loh A toy example 10
![Page 42: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/42.jpg)
Blorxification
Tectonic phenomenon on the cube-shaped planet Blorxmodelled by the Blorx operator
B : [−1, 1]3 −→ [−1, 1]3 =: Qxyz
7−→
12018 ·
√2 + x + cos(8 · y) + z201813 · (x + y + z)
x
Blorxcillationaveragerandom swap
Question
Are there points on Blorx that are not affected by Blorxification?
Theorem (K., J. Peatus 2018)
The Blorx operator B : Q −→ Q has a fixed point.
Related Work
I C. Keen treated a similar operator (2017)
I our proof uses the same method
Clara Loh A toy example 10
![Page 43: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/43.jpg)
Blorxification
Tectonic phenomenon on the cube-shaped planet Blorxmodelled by the Blorx operator
B : [−1, 1]3 −→ [−1, 1]3 =: Qxyz
7−→
12018 ·
√2 + x + cos(8 · y) + z201813 · (x + y + z)
x
Blorxcillation
averagerandom swap
Question
Are there points on Blorx that are not affected by Blorxification?
Theorem (K., J. Peatus 2018)
The Blorx operator B : Q −→ Q has a fixed point.
Related Work
I C. Keen treated a similar operator (2017)
I our proof uses the same method
Clara Loh A toy example 10
![Page 44: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/44.jpg)
Blorxification
Tectonic phenomenon on the cube-shaped planet Blorxmodelled by the Blorx operator
B : [−1, 1]3 −→ [−1, 1]3 =: Qxyz
7−→
12018 ·
√2 + x + cos(8 · y) + z201813 · (x + y + z)
x
Blorxcillationaverage
random swap
Question
Are there points on Blorx that are not affected by Blorxification?
Theorem (K., J. Peatus 2018)
The Blorx operator B : Q −→ Q has a fixed point.
Related Work
I C. Keen treated a similar operator (2017)
I our proof uses the same method
Clara Loh A toy example 10
![Page 45: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/45.jpg)
Blorxification
Tectonic phenomenon on the cube-shaped planet Blorxmodelled by the Blorx operator
B : [−1, 1]3 −→ [−1, 1]3 =: Qxyz
7−→
12018 ·
√2 + x + cos(8 · y) + z201813 · (x + y + z)
x
Blorxcillationaveragerandom swap
Question
Are there points on Blorx that are not affected by Blorxification?
Theorem (K., J. Peatus 2018)
The Blorx operator B : Q −→ Q has a fixed point.
Related Work
I C. Keen treated a similar operator (2017)
I our proof uses the same method
Clara Loh A toy example 10
![Page 46: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/46.jpg)
Blorxification
Tectonic phenomenon on the cube-shaped planet Blorxmodelled by the Blorx operator
B : [−1, 1]3 −→ [−1, 1]3 =: Qxyz
7−→
12018 ·
√2 + x + cos(8 · y) + z201813 · (x + y + z)
x
Blorxcillationaveragerandom swap
Question
Are there points on Blorx that are not affected by Blorxification?
Theorem (K., J. Peatus 2018)
The Blorx operator B : Q −→ Q has a fixed point.
Related Work
I C. Keen treated a similar operator (2017)
I our proof uses the same method
Clara Loh A toy example 10
![Page 47: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/47.jpg)
Blorxification
Tectonic phenomenon on the cube-shaped planet Blorxmodelled by the Blorx operator
B : [−1, 1]3 −→ [−1, 1]3 =: Qxyz
7−→
12018 ·
√2 + x + cos(8 · y) + z201813 · (x + y + z)
x
Blorxcillationaveragerandom swap
Question
Are there points on Blorx that are not affected by Blorxification?
Theorem (K., J. Peatus 2018)
The Blorx operator B : Q −→ Q has a fixed point.
Related Work
I C. Keen treated a similar operator (2017)
I our proof uses the same method
Clara Loh A toy example 10
![Page 48: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/48.jpg)
Blorxification
Tectonic phenomenon on the cube-shaped planet Blorxmodelled by the Blorx operator
B : [−1, 1]3 −→ [−1, 1]3 =: Qxyz
7−→
12018 ·
√2 + x + cos(8 · y) + z201813 · (x + y + z)
x
Blorxcillationaveragerandom swap
Question
Are there points on Blorx that are not affected by Blorxification?
Theorem (K., J. Peatus 2018)
The Blorx operator B : Q −→ Q has a fixed point.
Related Work
I C. Keen treated a similar operator (2017)
I our proof uses the same method
Clara Loh A toy example 10
![Page 49: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/49.jpg)
Proof of the main result
The Blorx operator B has a fixed point, where
B : [−1, 1]3 −→ [−1, 1]3 =: Qxyz
7−→
12018 ·
√2 + x + cos(8 · y) + z201813 · (x + y + z)
x
Proof.
I Idea: Use the Blorx Fixed Point Theorem:Every continuous map Q −→ Q has a fixed point.
I Check that the map B : Q −→ Q is continuous.
I Thus, by the Blorx Fixed Point Theorem, B has a fixed point.
Clara Loh A toy example 11
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Proof of the main result
The Blorx operator B has a fixed point, where
B : [−1, 1]3 −→ [−1, 1]3 =: Qxyz
7−→
12018 ·
√2 + x + cos(8 · y) + z201813 · (x + y + z)
x
Proof.
I Idea: Use the Blorx Fixed Point Theorem:Every continuous map Q −→ Q has a fixed point.
I Check that the map B : Q −→ Q is continuous.
I Thus, by the Blorx Fixed Point Theorem, B has a fixed point.
Clara Loh A toy example 11
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Proof of the main result
The Blorx operator B has a fixed point, where
B : [−1, 1]3 −→ [−1, 1]3 =: Qxyz
7−→
12018 ·
√2 + x + cos(8 · y) + z201813 · (x + y + z)
x
Proof.
I Idea: Use the Blorx Fixed Point Theorem:Every continuous map Q −→ Q has a fixed point.
I Check that the map B : Q −→ Q is continuous.
I Thus, by the Blorx Fixed Point Theorem, B has a fixed point.
Clara Loh A toy example 11
![Page 52: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/52.jpg)
Proof of the main result
The Blorx operator B has a fixed point, where
B : [−1, 1]3 −→ [−1, 1]3 =: Qxyz
7−→
12018 ·
√2 + x + cos(8 · y) + z201813 · (x + y + z)
x
Proof.
I Idea: Use the Blorx Fixed Point Theorem:Every continuous map Q −→ Q has a fixed point.
I Check that the map B : Q −→ Q is continuous.
I Thus, by the Blorx Fixed Point Theorem, B has a fixed point.
Clara Loh A toy example 11
![Page 53: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/53.jpg)
Excursion: Categories
Definition (Category: models relations between objects)
A category C consists of the following data
I set class Ob(C ): the objects of C
I sets MorC (X ,Y ): the morphisms X −→ Y
I compositions ◦ : MorC (Y ,Z )×MorC (X ,Y ) −→ MorC (X ,Z )
satisfying the following conditions:
I ◦ is associative
I existence of left/right neutral morphisms idX ∈ MorC (X ,X )
X
idXf
Y
g
Z
g ◦ f
Clara Loh A toy example 12
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Excursion: Categories
Definition (Category: models relations between objects)
A category C consists of the following data
I set class Ob(C ): the objects of C
I sets MorC (X ,Y ): the morphisms X −→ Y
I compositions ◦ : MorC (Y ,Z )×MorC (X ,Y ) −→ MorC (X ,Z )
satisfying the following conditions:
I ◦ is associative
I existence of left/right neutral morphisms idX ∈ MorC (X ,X )
X
idX
fY
gZ
g ◦ f
Clara Loh A toy example 12
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Excursion: Categories
Definition (Category: models relations between objects)
A category C consists of the following data
I set class Ob(C ): the objects of C
I sets MorC (X ,Y ): the morphisms X −→ Y
I compositions ◦ : MorC (Y ,Z )×MorC (X ,Y ) −→ MorC (X ,Z )
satisfying the following conditions:
I ◦ is associative
I existence of left/right neutral morphisms idX ∈ MorC (X ,X )
X
idX
fY
gZ
g ◦ f
Clara Loh A toy example 12
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Excursion: Categories
Definition (Category: models relations between objects)
A category C consists of the following data
I set class Ob(C ): the objects of C
I sets MorC (X ,Y ): the morphisms X −→ Y
I compositions ◦ : MorC (Y ,Z )×MorC (X ,Y ) −→ MorC (X ,Z )
satisfying the following conditions:
I ◦ is associative
I existence of left/right neutral morphisms idX ∈ MorC (X ,X )
X
idX
fY
gZ
g ◦ f
Clara Loh A toy example 12
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Excursion: Categories
Definition (Category: models relations between objects)
A category C consists of the following data
I set class Ob(C ): the objects of C
I sets MorC (X ,Y ): the morphisms X −→ Y
I compositions ◦ : MorC (Y ,Z )×MorC (X ,Y ) −→ MorC (X ,Z )
satisfying the following conditions:
I ◦ is associative
I existence of left/right neutral morphisms idX ∈ MorC (X ,X )
X
idXf
Yg
Z
g ◦ f
Clara Loh A toy example 12
![Page 58: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/58.jpg)
Excursion: Categories
Definition (Category: models relations between objects)
A category C consists of the following data
I set class Ob(C ): the objects of C
I sets MorC (X ,Y ): the morphisms X −→ Y
I compositions ◦ : MorC (Y ,Z )×MorC (X ,Y ) −→ MorC (X ,Z )
satisfying the following conditions:
I ◦ is associative
I existence of left/right neutral morphisms idX ∈ MorC (X ,X )
Example
Linear Algebra VectR R-vector spaces R-linear mapsTopology Top topological spaces continuous maps
Clara Loh A toy example 12
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Excursion: Functors
Definition (Functor: translates between categories)
Let C , D be categories.A contravariant functor F : C −→ D consists of the following data
I map F : Ob(C ) −→ Ob(D)
I maps F : MorC (X ,Y ) −→ MorC (F (Y ),F (X ))
satisfying the following conditions:
I F (idX ) = idF (X )
I F (g ◦ f ) = F (f ) ◦ F (g)
X Y
f
F (X ) F (Y )
F (f )
Clara Loh A toy example 13
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Excursion: Functors
Definition (Functor: translates between categories)
Let C , D be categories.A contravariant functor F : C −→ D consists of the following data
I map F : Ob(C ) −→ Ob(D)
I maps F : MorC (X ,Y ) −→ MorC (F (Y ),F (X ))
satisfying the following conditions:
I F (idX ) = idF (X )
I F (g ◦ f ) = F (f ) ◦ F (g)
X Yf
F (X ) F (Y )F (f )
Clara Loh A toy example 13
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Excursion: Functors
Definition (Functor: translates between categories)
Let C , D be categories.A contravariant functor F : C −→ D consists of the following data
I map F : Ob(C ) −→ Ob(D)
I maps F : MorC (X ,Y ) −→ MorC (F (Y ),F (X ))
satisfying the following conditions:
I F (idX ) = idF (X )
I F (g ◦ f ) = F (f ) ◦ F (g)
X Yf
F (X ) F (Y )F (f )
Clara Loh A toy example 13
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Excursion: Functors
Definition (Functor: translates between categories)
Let C , D be categories.A contravariant functor F : C −→ D consists of the following data
I map F : Ob(C ) −→ Ob(D)
I maps F : MorC (X ,Y ) −→ MorC (F (Y ),F (X ))
satisfying the following conditions:
I F (idX ) = idF (X )
I F (g ◦ f ) = F (f ) ◦ F (g)
X Yf
F (X ) F (Y )F (f )
Clara Loh A toy example 13
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Excursion: Functors
Definition (Functor: translates between categories)
Let C , D be categories.A contravariant functor F : C −→ D consists of the following data
I map F : Ob(C ) −→ Ob(D)
I maps F : MorC (X ,Y ) −→ MorC (F (Y ),F (X ))
satisfying the following conditions:
I F (idX ) = idF (X )
I F (g ◦ f ) = F (f ) ◦ F (g)
Example
I dual vector space HomR( · ,R) : VectR −→ VectR
I singular cohomology H2 : Top −→ VectR such that
H2(Q) ∼= 0 and H2(∂Q) ∼= R.
Clara Loh A toy example 13
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Excursion: Functors
Definition (Functor: translates between categories)
Let C , D be categories.A contravariant functor F : C −→ D consists of the following data
I map F : Ob(C ) −→ Ob(D)
I maps F : MorC (X ,Y ) −→ MorC (F (Y ),F (X ))
satisfying the following conditions:
I F (idX ) = idF (X )
I F (g ◦ f ) = F (f ) ◦ F (g)
Example
I dual vector space HomR( · ,R) : VectR −→ VectRI singular cohomology H2 : Top −→ VectR such that
H2(Q) ∼= 0 and H2(∂Q) ∼= R.Clara Loh A toy example 13
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Proof of the Blorx Fixed Point Theorem
Every continuous map Q −→ Q has a fixed point.
Proof by contradiction.
I Assume: there is a continuous f : Q −→ Q without fixed point.
I Use f to construct a continuous map g : Q −→ ∂Q
with g ◦ (inclusion ∂Q ↪→ Q) = id∂Q .
f (x)
xg(x)
I Apply the functor H2 : Top −→ VectR:
∂Qid∂Q//
��
∂Q
Qg
==
R ∼=
H2(∂Q) H2(∂Q)
∼= R
H2(id∂Q)
=id
oo
H2(g)uu
0 ∼=
H2(Q)
OO
I Hence, idR factors over 0. Contradiction!
Clara Loh A toy example 14
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Proof of the Blorx Fixed Point Theorem
Every continuous map Q −→ Q has a fixed point.
Proof by contradiction.
I Assume: there is a continuous f : Q −→ Q without fixed point.
I Use f to construct a continuous map g : Q −→ ∂Q
with g ◦ (inclusion ∂Q ↪→ Q) = id∂Q .
f (x)
x
g(x)
I Apply the functor H2 : Top −→ VectR:
∂Qid∂Q//
��
∂Q
Qg
==
R ∼=
H2(∂Q) H2(∂Q)
∼= R
H2(id∂Q)
=id
oo
H2(g)uu
0 ∼=
H2(Q)
OO
I Hence, idR factors over 0. Contradiction!
Clara Loh A toy example 14
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Proof of the Blorx Fixed Point Theorem
Every continuous map Q −→ Q has a fixed point.
Proof by contradiction.
I Assume: there is a continuous f : Q −→ Q without fixed point.
I Use f to construct a continuous map g : Q −→ ∂Q
with g ◦ (inclusion ∂Q ↪→ Q) = id∂Q .
f (x)
x
g(x)
I Apply the functor H2 : Top −→ VectR:
∂Qid∂Q//
��
∂Q
Qg
==
R ∼=
H2(∂Q) H2(∂Q)
∼= R
H2(id∂Q)
=id
oo
H2(g)uu
0 ∼=
H2(Q)
OO
I Hence, idR factors over 0. Contradiction!
Clara Loh A toy example 14
![Page 68: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/68.jpg)
Proof of the Blorx Fixed Point Theorem
Every continuous map Q −→ Q has a fixed point.
Proof by contradiction.
I Assume: there is a continuous f : Q −→ Q without fixed point.
I Use f to construct a continuous map g : Q −→ ∂Qwith g ◦ (inclusion ∂Q ↪→ Q) = id∂Q .
f (x)
xg(x)
I Apply the functor H2 : Top −→ VectR:
∂Qid∂Q//
��
∂Q
Qg
==
R ∼=
H2(∂Q) H2(∂Q)
∼= R
H2(id∂Q)
=id
oo
H2(g)uu
0 ∼=
H2(Q)
OO
I Hence, idR factors over 0. Contradiction!
Clara Loh A toy example 14
![Page 69: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/69.jpg)
Proof of the Blorx Fixed Point Theorem
Every continuous map Q −→ Q has a fixed point.
Proof by contradiction.
I Assume: there is a continuous f : Q −→ Q without fixed point.
I Use f to construct a continuous map g : Q −→ ∂Qwith g ◦ (inclusion ∂Q ↪→ Q) = id∂Q .
f (x)
xg(x)
I Apply the functor H2 : Top −→ VectR:
∂Qid∂Q//
��
∂Q
Qg
==
R ∼=
H2(∂Q) H2(∂Q)
∼= R
H2(id∂Q)
=id
oo
H2(g)uu
0 ∼=
H2(Q)
OO
I Hence, idR factors over 0. Contradiction!
Clara Loh A toy example 14
![Page 70: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/70.jpg)
Proof of the Blorx Fixed Point Theorem
Every continuous map Q −→ Q has a fixed point.
Proof by contradiction.
I Assume: there is a continuous f : Q −→ Q without fixed point.
I Use f to construct a continuous map g : Q −→ ∂Qwith g ◦ (inclusion ∂Q ↪→ Q) = id∂Q .
f (x)
xg(x)
I Apply the functor H2 : Top −→ VectR:
∂Qid∂Q//
��
∂Q
Qg
==
R ∼=
H2(∂Q) H2(∂Q)
∼= R
H2(id∂Q)
=id
oo
H2(g)uu
0 ∼=
H2(Q)
OO
I Hence, idR factors over 0. Contradiction!
Clara Loh A toy example 14
![Page 71: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/71.jpg)
Proof of the Blorx Fixed Point Theorem
Every continuous map Q −→ Q has a fixed point.
Proof by contradiction.
I Assume: there is a continuous f : Q −→ Q without fixed point.
I Use f to construct a continuous map g : Q −→ ∂Qwith g ◦ (inclusion ∂Q ↪→ Q) = id∂Q .
f (x)
xg(x)
I Apply the functor H2 : Top −→ VectR:
∂Qid∂Q//
��
∂Q
Qg
==R ∼= H2(∂Q) H2(∂Q) ∼= R
H2(id∂Q)=idoo
H2(g)uu
0 ∼= H2(Q)
OO
I Hence, idR factors over 0. Contradiction!
Clara Loh A toy example 14
![Page 72: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/72.jpg)
Proof of the Blorx Fixed Point Theorem
Every continuous map Q −→ Q has a fixed point.
Proof by contradiction.
I Assume: there is a continuous f : Q −→ Q without fixed point.
I Use f to construct a continuous map g : Q −→ ∂Qwith g ◦ (inclusion ∂Q ↪→ Q) = id∂Q .
f (x)
xg(x)
I Apply the functor H2 : Top −→ VectR:
∂Qid∂Q//
��
∂Q
Qg
==R ∼= H2(∂Q) H2(∂Q) ∼= R
H2(id∂Q)=idoo
H2(g)uu
0 ∼= H2(Q)
OO
I Hence, idR factors over 0. Contradiction!
Clara Loh A toy example 14
![Page 73: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/73.jpg)
Slide etiquette
I Use sans serif fonts, matching math fonts
I No fancy firlifanz
I Use high-resolution/vector graphics, explain graphics
I Avoid long sentences
I Break long formulae into small building blocks
I At most 12 lines per slide (for appropriate choice of 12)
I Be careful with the last line on each slide (duration of visibility!)
I Repeat important facts from previous slides
I Do not jump many slides at once“This is not important right now.” “We don’t have time for this.”
I Maximal number of slides
(the larger 2 is, the better):
# minutes
2
Clara Loh General advice for slides 15
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Slide etiquette
I Use sans serif fonts, matching math fonts
I No fancy firlifanz
I Use high-resolution/vector graphics, explain graphics
I Avoid long sentences
I Break long formulae into small building blocks
I At most 12 lines per slide (for appropriate choice of 12)
I Be careful with the last line on each slide (duration of visibility!)
I Repeat important facts from previous slides
I Do not jump many slides at once“This is not important right now.” “We don’t have time for this.”
I Maximal number of slides
(the larger 2 is, the better):
# minutes
2
Clara Loh General advice for slides 15
![Page 75: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/75.jpg)
Slide etiquette
I Use sans serif fonts, matching math fonts
I No fancy firlifanz
I Use high-resolution/vector graphics, explain graphics
I Avoid long sentences
I Break long formulae into small building blocks
I At most 12 lines per slide (for appropriate choice of 12)
I Be careful with the last line on each slide (duration of visibility!)
I Repeat important facts from previous slides
I Do not jump many slides at once“This is not important right now.” “We don’t have time for this.”
I Maximal number of slides
(the larger 2 is, the better):
# minutes
2
Clara Loh General advice for slides 15
![Page 76: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/76.jpg)
Slide etiquette
I Use sans serif fonts, matching math fonts
I No fancy firlifanz
I Use high-resolution/vector graphics, explain graphics
I Avoid long sentences
I Break long formulae into small building blocks
I At most 12 lines per slide (for appropriate choice of 12)
I Be careful with the last line on each slide (duration of visibility!)
I Repeat important facts from previous slides
I Do not jump many slides at once“This is not important right now.” “We don’t have time for this.”
I Maximal number of slides
(the larger 2 is, the better):
# minutes
2
Clara Loh General advice for slides 15
![Page 77: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/77.jpg)
Slide etiquette
I Use sans serif fonts, matching math fonts
I No fancy firlifanz
I Use high-resolution/vector graphics, explain graphics
I Avoid long sentences
I Break long formulae into small building blocks
I At most 12 lines per slide (for appropriate choice of 12)
I Be careful with the last line on each slide (duration of visibility!)
I Repeat important facts from previous slides
I Do not jump many slides at once“This is not important right now.” “We don’t have time for this.”
I Maximal number of slides
(the larger 2 is, the better):
# minutes
2
Clara Loh General advice for slides 15
![Page 78: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/78.jpg)
Slide etiquette
I Use sans serif fonts, matching math fonts
I No fancy firlifanz
I Use high-resolution/vector graphics, explain graphics
I Avoid long sentences
I Break long formulae into small building blocks
I At most 12 lines per slide (for appropriate choice of 12)
I Be careful with the last line on each slide (duration of visibility!)
I Repeat important facts from previous slides
I Do not jump many slides at once“This is not important right now.” “We don’t have time for this.”
I Maximal number of slides
(the larger 2 is, the better):
# minutes
2
Clara Loh General advice for slides 15
![Page 79: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/79.jpg)
Slide etiquette
I Use sans serif fonts, matching math fonts
I No fancy firlifanz
I Use high-resolution/vector graphics, explain graphics
I Avoid long sentences
I Break long formulae into small building blocks
I At most 12 lines per slide (for appropriate choice of 12)
I Be careful with the last line on each slide (duration of visibility!)
I Repeat important facts from previous slides
I Do not jump many slides at once“This is not important right now.” “We don’t have time for this.”
I Maximal number of slides
(the larger 2 is, the better):
# minutes
2
Clara Loh General advice for slides 15
![Page 80: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/80.jpg)
Slide etiquette
I Use sans serif fonts, matching math fonts
I No fancy firlifanz
I Use high-resolution/vector graphics, explain graphics
I Avoid long sentences
I Break long formulae into small building blocks
I At most 12 lines per slide (for appropriate choice of 12)
I Be careful with the last line on each slide (duration of visibility!)
I Repeat important facts from previous slides
I Do not jump many slides at once“This is not important right now.” “We don’t have time for this.”
I Maximal number of slides
(the larger 2 is, the better):
# minutes
2
Clara Loh General advice for slides 15
![Page 81: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/81.jpg)
Slide etiquette
I Use sans serif fonts, matching math fonts
I No fancy firlifanz
I Use high-resolution/vector graphics, explain graphics
I Avoid long sentences
I Break long formulae into small building blocks
I At most 12 lines per slide (for appropriate choice of 12)
I Be careful with the last line on each slide (duration of visibility!)
I Repeat important facts from previous slides
I Do not jump many slides at once“This is not important right now.” “We don’t have time for this.”
I Maximal number of slides
(the larger 2 is, the better):
# minutes
2
Clara Loh General advice for slides 15
![Page 82: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/82.jpg)
Slide etiquette
I Use sans serif fonts, matching math fonts
I No fancy firlifanz
I Use high-resolution/vector graphics, explain graphics
I Avoid long sentences
I Break long formulae into small building blocks
I At most 12 lines per slide (for appropriate choice of 12)
I Be careful with the last line on each slide (duration of visibility!)
I Repeat important facts from previous slides
I Do not jump many slides at once“This is not important right now.” “We don’t have time for this.”
I Maximal number of slides
(the larger 2 is, the better):
# minutes
2
Clara Loh General advice for slides 15
![Page 83: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/83.jpg)
Slide etiquette
I Use sans serif fonts, matching math fonts
I No fancy firlifanz
I Use high-resolution/vector graphics, explain graphics
I Avoid long sentences
I Break long formulae into small building blocks
I At most 12 lines per slide (for appropriate choice of 12)
I Be careful with the last line on each slide (duration of visibility!)
I Repeat important facts from previous slides
I Do not jump many slides at once“This is not important right now.” “We don’t have time for this.”
I Maximal number of slides (the larger 2 is, the better):
# minutes
2
Clara Loh General advice for slides 15
![Page 84: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/84.jpg)
Technical etiquette
I Bring the correct plugs to connect computer and projector
I Connect computer and projector ahead of time
I Know how to switch to fullscreen/presentation mode
I Switch off system notifications
I Switch off networking (unless necessary for the presentation)
I Do not point to the screen of the computer,but to the projected image
Clara Loh General advice for slides 16
![Page 85: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/85.jpg)
Technical etiquette
I Bring the correct plugs to connect computer and projector
I Connect computer and projector ahead of time
I Know how to switch to fullscreen/presentation mode
I Switch off system notifications
I Switch off networking (unless necessary for the presentation)
I Do not point to the screen of the computer,but to the projected image
Clara Loh General advice for slides 16
![Page 86: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/86.jpg)
Technical etiquette
I Bring the correct plugs to connect computer and projector
I Connect computer and projector ahead of time
I Know how to switch to fullscreen/presentation mode
I Switch off system notifications
I Switch off networking (unless necessary for the presentation)
I Do not point to the screen of the computer,but to the projected image
Clara Loh General advice for slides 16
![Page 87: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/87.jpg)
Technical etiquette
I Bring the correct plugs to connect computer and projector
I Connect computer and projector ahead of time
I Know how to switch to fullscreen/presentation mode
I Switch off system notifications
I Switch off networking (unless necessary for the presentation)
I Do not point to the screen of the computer,but to the projected image
Clara Loh General advice for slides 16
![Page 88: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/88.jpg)
Technical etiquette
I Bring the correct plugs to connect computer and projector
I Connect computer and projector ahead of time
I Know how to switch to fullscreen/presentation mode
I Switch off system notifications
I Switch off networking (unless necessary for the presentation)
I Do not point to the screen of the computer,but to the projected image
Clara Loh General advice for slides 16
![Page 89: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/89.jpg)
Technical etiquette
I Bring the correct plugs to connect computer and projector
I Connect computer and projector ahead of time
I Know how to switch to fullscreen/presentation mode
I Switch off system notifications
I Switch off networking (unless necessary for the presentation)
I Do not point to the screen of the computer,but to the projected image
Clara Loh General advice for slides 16
![Page 90: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/90.jpg)
TALK OVER!
blackboard preparation time < 60 minutesslides preparation time > 600 minutes
Try again?
![Page 91: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/91.jpg)
Bonus game: General advice for talks
Theorem (Fundamental theorem of presentations)
Well-structured talks are easy to present and comprehend.
Level 0: Research
I Obtain interesting results
I Check correctness of results
Level 1: Raw concept
I Decide on the main goal of the presentation
I Sketch the main structure of the talk
Clara Loh Bonus game 18
![Page 92: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/92.jpg)
Bonus game: General advice for talks
Theorem (Fundamental theorem of presentations)
Well-structured talks are easy to present and comprehend.
Level 0: Research
I Obtain interesting results
I Check correctness of results
Level 1: Raw concept
I Decide on the main goal of the presentation
I Sketch the main structure of the talk
Clara Loh Bonus game 18
![Page 93: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/93.jpg)
Bonus game: General advice for talks
Theorem (Fundamental theorem of presentations)
Well-structured talks are easy to present and comprehend.
Level 0: Research
I Obtain interesting results
I Check correctness of results
Level 1: Raw concept
I Decide on the main goal of the presentation
I Sketch the main structure of the talk
Clara Loh Bonus game 18
![Page 94: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/94.jpg)
General advice for talks, continued
Level 2: Detailed concept
I Be precise
I Be concise
I Put important stuff at the beginning (so it will not get lost in time)
I Attribute results correctly
I Explain what your contribution is
I Highlight important ideas/steps instead of technical details
I Try not to end with a subtle technical detail,but rather with an open problem or a conclusion
I Prepare for the likely case that the talk is longer than expectedand for the unlikely case that the talk is shorter than expected
Clara Loh Bonus game 19
![Page 95: Slippery Slides - uni-regensburg.deSlippery Slides Clara L oh Universit at Regensburg January 21, 2018. Overview An axiom for slides A toy example General advice for slides Clara L](https://reader035.vdocuments.mx/reader035/viewer/2022071218/605070370045c841140396bd/html5/thumbnails/95.jpg)
General advice for talks, continued
Level 3: Presentation
I Memorize the first few sentences of the talk
I Be independent of your notes; look at the blackboard instead(This will reduce the risk of typos/gaps)
I Give the audience enough time to digest your arguments
I Keep eye-contact with the audience
I Try to get the audience involved
I Don’t be afraid of questions!
Clara Loh Bonus game 20