Differential Forms in Mathematics: Uses & Applications

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Differential forms are primarily utilized in fields such as differential geometry, algebraic geometry, and Riemannian geometry by professional mathematicians. They are also significant in mathematical physics, particularly in areas like general relativity and string theory. Differential topology is another area where these forms are frequently applied. Additionally, they can be relevant in stochastic analysis on manifolds. Overall, differential forms serve as a crucial tool across various advanced mathematical disciplines.
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I'm just wondering: in what field of mathematics are differential forms frequently used by professional mathematicians?
 
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If you mean proffessional mathematicians as in researchers then geometers.. in various areas of differential, algebraic, Riemannian, noncommutative geometry etc. or mathematical phycisists involved in general relativity and string theory, or differential topologists.. there might be other people that use them every now and then.. for example you could try doing e.g. stochastic analysis on manifolds in which case you'd probably need them
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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