Applications of Grothendieck's work

In summary, the conversation discusses the article on Alexander Grothendieck, a renowned mathematician known for his work in algebraic geometry. The article mentions that his work has been applied to fields such as cryptography, genetics, and robotics. The speakers also mention a discussion on Math Overflow about the applications of Grothendieck's work in robotics and genetics. They also briefly mention an article on Grothendieck's death and his desire to be forgotten.
  • #1
Arsenic&Lace
533
37
Attached below is a link to an article on Grothendieck, who is regarded by some as the greatest mathematician of the 20th century (he is certainly one of the greatest if not the greatest). In the article, it states that his work has been applied to cryptography, genetics, and robotics. Can anybody explain how his field, which if I am not mistaken was algebraic geometry, has been useful in these fields, but especially genetics, since that is a field I am currently very interested in (from a biophysical standpoint).

Here is the article:
http://www.nytimes.com/2014/11/16/w...grothendieck-math-enigma-dies-at-86.html?_r=0
 
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  • #3
I did not, but there are some excellent answers there, thanks for the pointer.
 
  • #4
Should I align all magnetic fields ahead.of.me. so I am pulled through the water or .. seperat them to create a horizon to slide through ??
 

1. What is Grothendieck's work and why is it important in science?

Grothendieck's work refers to the mathematical contributions made by Alexander Grothendieck, a renowned mathematician. His work primarily focused on algebraic geometry and its applications to other areas of mathematics, such as number theory and topology. Grothendieck's work has had a significant impact in various fields of science, particularly in the study of nonlinear systems and their applications in physics, biology, and computer science.

2. What are some specific applications of Grothendieck's work in science?

Some specific applications of Grothendieck's work include the development of the theory of schemes, which has greatly influenced modern algebraic geometry and its applications in cryptography and coding theory. His work on sheaf theory has also been applied in the study of complex systems and their behavior, such as in climate modeling and economics.

3. How has Grothendieck's work impacted the study of nonlinear systems?

Grothendieck's work has provided a powerful framework for understanding and analyzing nonlinear systems. His theory of schemes, which incorporates both algebraic and geometric concepts, has been applied in the study of nonlinear dynamical systems, chaos theory, and fractal geometry. This has led to a deeper understanding of complex systems and their behavior, and has also opened up new avenues for research in these areas.

4. Are there any practical applications of Grothendieck's work?

Yes, there are several practical applications of Grothendieck's work in fields such as cryptography, coding theory, and data compression. For example, his theory of schemes has been used in the development of efficient error-correcting codes, which play a crucial role in modern communication systems. His work on sheaf theory has also been applied in data compression algorithms, leading to more efficient storage and transmission of information.

5. What are some future directions for research in applications of Grothendieck's work?

Some potential future directions for research in applications of Grothendieck's work include its use in machine learning and artificial intelligence, as well as its potential applications in quantum computing and quantum information theory. Furthermore, there is ongoing research in applying Grothendieck's ideas to other areas of science, such as biology and neuroscience, where complex systems and their behavior are of great interest.

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