## Usefulness of Differential Geometry

I recently came across these books: https://www.springer.com/us/book/9783030460396#aboutBook https://www.springer.com/gp/book/9783030460464#aboutBook Their subject matter really intrigues me, as I really enjoy topology/geometry/analysis, but had not planned to pursue them since I also want to work in an area with very concrete application. However, I am skeptical. At one point I thought topological data analysis (TDA) was the perfect marriage of my interests, but I have found very little evidence of that field actually being used in computer science, much less in industrial or otherwise more ‘practical’ settings. It seems like TDA makes mathematicians feel more relevant to the data science world, but I’m not convinced that it makes them so (feel free to contradict me if you think I’m wrong on this point, but note that I want a concrete use case, not an abstract argument about its relevance). I have similar stories about coding theory, certain aspects of set theory, etcetera. They may have theoretical relevance, but is there any situation where, in the process of developing software, one might need to consult theses fields? I don’t know of any.

So now my question: is there any practical field of computer science that makes advanced use of differential geometry? Medical imaging, other imaging, computer graphics, virtual reality, and some other fields come to mind as potential application areas. In my (admittedly limited) experience, however, these areas seem to use basic 3D geometry, numerical linear algebra, and sometimes numerical analysis of PDEs. Those are all very nice topics, but they do not require anything as abstract as differential geometry.

## Usefulness of consensus number

What information and usefulness does knowing the consensus number of a shared object give me?

## Usefulness of token sidejacking prevention mentioned by OWASP JWT Cheat Sheet

I was just reading through the “Token sidejacking” of the JWT Cheat Sheet of OWASP (https://cheatsheetseries.owasp.org/cheatsheets/JSON_Web_Token_Cheat_Sheet_for_Java.html#token-sidejacking)

At the moment I don’t understand how the recommended prevention actually solves the issue.

The solution is to add a context and send this context (e.g. a random value) as a Cookie as well as part of the JWT (then hashed).

However if an attacker is able to steal the JWT by performing a XSS attack and access the sessionStorage, the attacker can also send XHR-requests, so the Cookie is automatically send with it. If the attacker is able to sniff the network traffic, the attacker also has the Cookie value. The only case I can think of where this works is, if the attacker has access to some sort of logs, where the JWT is stored, but this would be another vulnerability (or more).

What did I miss? Thanks

## dual of a Generalized Reed Solomon Code is also a Generalized Reed Solomon Code and usefulness of the property

I have just started learning coding theory and my TA is pretty useless. As part of the course, I am going through Generalised Reed Solomon code from Fundamentals of Error-Correcting Codes By W. Cary Huffman, Vera Pless. There is a theorem as follows – enter image description here

I could not understand the proof. Could anyone give an example of what the theorem says? what does $$v_ih(\gamma_i)$$ mean? Does it mean multiplication in the finite field?