An Intuitive Introduction to Motivic Homotopy Theory - Vladimir Voevodsky

An Intuitive Introduction to Motivic Homotopy Theory
Vladimir Voevodsky, American Academy of Arts and Sciences, October 2002
The Clay Mathematics Institute (CMI) 2002 Annual Meeting took place on Wednesday, October 30, 2002, from 2:30 to 5:30 PM, at the American Academy of Arts & Sciences in Cambridge, Massachusetts. The Annual Meeting brought together an international assembly of mathematicians to celebrate the universality of mathematical thought. This meeting provided a public forum for discussion among leading mathematicians and scientists, and it strengthened relations between mathematicians, the public, and the scientific research community.
The meeting began with the presentation of the 2002 Clay Research Award to Oded Schramm (for his work on the Loewner equation) and to Manindra Agrawal (for his work on primality testing). CMI President Arthur Jaffe and Directors Landon Clay and Lavinia Clay gave the awards. This Research Award recognizes major recent breakthroughs in two mathematical directions, and represents the pinnacle of recognition of research achievement by CMI. Each prizewinner becomes a Clay Research Scholar, and receives a bronze model of the CMI logo, an elegant sculpture "Figureight Knot Complement vii/ CMI" by sculptor Helaman Ferguson. Former winners are: Andrew Wiles, Laurent Lafforgue, Alain Connes, Stanislav Smirnov and Edward Witten.
Two talks followed the awards ceremony. Manindra Agrawal of the Indian Institute of Technology surprised all experts in August 2002 by solving an ancient problem (working with two undergraduate students). They showed that one could determine the primality of a number in polynomial time. This was the first talk in the United States by the inventor of the new method. Vladimir Voevodsky from the Institute of Advanced Study gave the second talk. He spoke about the mathematical breakthroughs that led to his receiving the Fields Medal in August 2002.
"We have a very impressive set of ground-breaking mathematicians at this year's meeting as award winners and speakers. The meeting certainly will inspire young mathematicians who attend, as well as all those who read about it or view the meeting on the web," said Arthur Jaffe, President of the Clay Mathematics Institute. "Agrawal will discuss his exciting discovery - the ASK algorithm for primality testing, and Voevodsky will explain his novel approach to the mathematical modeling of shapes known as "motivic homotopy theory."
www.claymath.org/annual_meetin...

[@replattus]

I think this is the best math talk I've seen, he's explaining cutting edge mathematics using very elementary concepts, it's really incredible. Also, could not agree more with his punchline at the end

[@imotogin]

As a non mathematician when he said 'I was asked to explain it for non-mathematicians' - and then I watched the talk... The punchline got me lol, but my fav is when he said 'at first there were spaces'.

[@kamilziemian995]

Extraordinary clear talk.

[@CatherineRay1]

He goes over cubical objects at 25:04 (for those coming back and looking for that part of the talk)

[@RalphDratman]

This seems to me like a wonderful bit of teaching. I certainly picked up a few ideas.

[@MadHadda63]

Rest in peace.

[@40762361]

what a boss

[@jawad9757]

rest in peace

[@mihael1968]

Panic Crisis :)

[@TheVopepigota]

1. You're going around spelling theorem wrong. 2. He isn't presenting a theorem at all.

[@davidwilkie9551]

Based on the Quantum Fields Modulation Mechanism timing and spacing multiphase-state occurrence in e-Pi-i, (frequencies and amplitudes categorisation), ..all points lines and surfaces etc are numerical multiples of resonance, and spaces are "beside" the boundary formed by the 1-0 Duration probability in potential possibilities, ie the zero point exists in the zero-line axis of tangential zero spacing => Approx = "Jump Space". Or superconducting non-local distribution. If the designed self-referencing system is logically consistent, element by element, then it's established in QM-TIMESPACE principle by natural modulation occurrence "in some sense". The "Unit interval" is eternity-now = 1-0D divided/multiplied modulation-morphism of time duration categorized as pulses of resonance within pulses in-form-ation.

[@jusiphstolin8074]

What are you trying to say?

[@markphc99]

A great mind but he should stick to proving theorums, not presenting them .

[@hanniffydinn6019]

Mark Callaghan it's hard as rocks to explain, like to see you try.