Robotics, Cryptography, and Genetics applications of Grothendieck's work? I was reading about the passing of Alexander Grothendieck, and something caught my interest:

Mr. Grothendieck was able to answer concrete questions about these relationships by finding universal mathematical principles that could shed unexpected light on them. Applications of his work are evident in fields as diverse as genetics, cryptography and robotics. New York Times

After extensive googling, I haven't been able to find examples. Has Grothendieck's mathematical work been applied to robotics, cryptography, or genetics, and if so, how? 
 A: To expand upon Douglas Zare's comment a bit, in the book

Farber, Michael. Invitation to topological robotics. European Mathematical Society, 2008,

Farber reports on Światosław Gal's use of C&P (cut & paste) surgery and the Grothendiek ring $\mathfrak{C}$&$\mathfrak{P}$
to compute Euler characteristics of polyhedral configuration spaces (pp.55-56):

 
 
 
 


A: Robert Ghrist's web site has some interesting notes on robotics and algebraic topology:

My work focuses on those methods in applied mathematics which are topological in nature. Such methods have the feature of being very robust: topological results are tolerant of the "noise" inherent in physical systems. Such techniques are therefore both elegant and effective in engineering and science.

I first came across him reading in the Notices about the theory of barcodes and persistent homology.  
Currently, a lot of tools only use a 1D graph theory based approach.  Using the Rips complex, a tool from geometric group theory, shows how to find topological features in data sets made of discrete points.     Somehow we have to "complete" the point-set into a topological space.


There is an even more direct example of Grothendieck's influences in the theory of sensor networks.  Please look at Justin Curry's Sheaves, Co-sheaves and Applications  which has a short introduction to the history of sheaves and their generalizations, mentioning Leray, Grothentieck, Kashiwara, MacPherson and others.

In 2008, Robert Ghrist initiated a call to bring sheaf theory, specifically sheaf cohomology, to bear on a variety of applied problems.  Euler calculus - a decategorification of contructible sheaf theory, has already made progress toward this goal.  Heuristically, sheaf cohomology would provide calculable summary of the topology of data and programs, even if initially there is no topology in sight.  

The idea is that sheaves help organized information spread out in different places into a single global piece of information.
A: Genetic research has some applications of grothendieck's theory, above mentioned answers inform about grothendieck cuts, and their applications to robotics. Some cancer researchers use groupoids, so to determine a gene expression, define first a grothendieck space, and then study deformations. These (Yoneda-Grothendieck) structures are useful in studying the dynamics of the cancer gene. 
A: Here is a guess: first, "Grothendieck's work" is being interpreted as "algebraic geometry," so the real question is what applications of algebraic geometry there are in genetics, cryptography, and robotics.


*

*Genetics: my guess is that this is a reference to the use of algebraic statistics to understand phylogenetics. See, for example, this news article, this survey, or this textbook.

*Cryptography: my guess is that this is a reference to the use of elliptic curves in cryptography as well as perhaps to the use of algebraic curves to produce error-correcting codes. See, for example, this textbook.

*Robotics: my guess is that this is a reference to the use of algebraic geometry to understand robot motion planning. See, for example, this paper. 


However, as far as I can tell, Grothendieck's work in particular is not relevant to any of this. 
