The 2018 Fields Medal has been awarded....

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SUMMARY

The 2018 Fields Medal was awarded to four mathematicians: Caucher Birkar for his proof of the boundedness of Fano varieties and contributions to the minimal model program; Alessio Figalli for his work in optimal transport theory and its applications; Peter Scholze for his introduction of perfectoid spaces in arithmetic algebraic geometry; and Akshay Venkatesh for his synthesis of analytic number theory and other mathematical disciplines. Scholze, who became a full professor at age 24, is noted for his rapid academic progression and significant contributions to the field. The discussion highlights the remarkable achievements and backgrounds of these awardees.

PREREQUISITES
  • Understanding of algebraic geometry concepts, particularly Fano varieties.
  • Familiarity with optimal transport theory and its applications in differential equations.
  • Knowledge of perfectoid spaces and their role in arithmetic algebraic geometry.
  • Basic principles of analytic number theory and homogeneous dynamics.
NEXT STEPS
  • Explore the proof of the boundedness of Fano varieties in algebraic geometry.
  • Study optimal transport theory and its implications in metric geometry.
  • Investigate the concept of perfectoid spaces and their applications in Galois representations.
  • Research the synthesis of analytic number theory and its connections to topology and representation theory.
USEFUL FOR

Mathematicians, researchers in algebraic geometry, students of number theory, and anyone interested in the latest advancements in mathematical research and theory.

Wrichik Basu
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The 2018 Fields Medal has been awarded to:

Caucher Birkar

birkar.jpg


For the proof of the boundedness of Fano varieties and for contributions to the minimal model program.

Alessio Figalli

figalli.jpg


For contributions to the theory of optimal transport and its applications in partial differential equations, metric geometry and probability.

Peter Scholze

scholze_1.jpeg


For transforming arithmetic algebraic geometry over p-adic fields through his introduction of perfectoid spaces, with application to Galois representations, and for the development of new cohomology theories.

Akshay Venkatesh

Venkatesh.jpg


For his synthesis of analytic number theory, homogeneous dynamics, topology, and representation theory, which has resolved long-standing problems in areas such as the equidistribution of arithmetic objects.

The Web page is here.
 

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Mathematics news on Phys.org
Wrichik Basu said:
Peter Scholze
He was discussed as strong candidate before. His CV is ... fast. Went to university at age 19 (that is common in Germany). Finished his BSc in 1.5 years and the MSc in one more. Finished his PhD at age 24 and directly became a full professor - already a well-known expert in the field at that time. Now he is 30 and one of the directors of a research institute.
https://en.wikipedia.org/wiki/Peter_Scholze
 
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I wonder if anyone will ever beat the record of Charles Fefferman who became full professor of math at University of Chicago at 22. Of course he won the Fields medal.
 
mfb said:
He was discussed as strong candidate before. His CV is ... fast. Went to university at age 19 (that is common in Germany). Finished his BSc in 1.5 years and the MSc in one more. Finished his PhD at age 24 and directly became a full professor - already a well-known expert in the field at that time. Now he is 30 and one of the directors of a research institute.
https://en.wikipedia.org/wiki/Peter_Scholze

I can't even understand one term in this video title :biggrin:
 
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Here are the official videos for each winner



 
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The following playlists have the lectures by the award winners. I'll upload them to the PF media gallery soon. Till then, you may have a look at the playlists:

Caucher Birkar:

https://www.youtube.com/playlist?list=PL9m2Lkh6odgIBfvn2fzGeZoPGGGuOTHhr

Alessio Figalli:

https://www.youtube.com/playlist?list=PL9m2Lkh6odgJmEIEjKDWNNxnYadELDu-F

Peter Scholze:

https://www.youtube.com/playlist?list=PL9m2Lkh6odgIvh2JDIMT5kLV5RxlyB6L2

Akshay Venkatesh:

https://www.youtube.com/playlist?list=PL9m2Lkh6odgKbrhFqEJ7rTm_Hr9tSBtKP
 
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It really is amazing too see these guys know what they want to do with their life at an early age and then commit to it. Have all that time to develop their knowledge baggage and synthesize new techniques. Awesome stuff.
 
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