Mathematics thesis subject

Do research and find a problem that isn't on your textbook.

Well if you have only worked with finite groups, you can look at the representations of [math]\mathfrak S_n[/math] (it's detailed in Prasad: Representation Theory, A Combinatorial Approach), the representations of [math]GL_n(\mathbb F_q)[/math] or more ambitiously the McKay conjecture or the McKay correspondence (if you know some algebraic geometry)
If you have already studied representations of Lie groups, you can look at the applications in QFT

>>8270044
What does the first latex symbol in your post signify? I dont know what its called so Im having a hard time finding it.

>>8271246
Oh, it's the n-th symmetric group (ie. the group of permutations of a set with n elements)

>>8269426
Is it normal for your bachelor's thesis to be on a meme problem or something that was already solved?

Mine's on the third homotopy group of S3, using knot theory and degree theory.

>>8269426
Personally i would say be careful about reaching too far. Definitely spend time talking with teachers and advisors. No one is expecting you to discover anything brand new for humanity, but you do need to discover something for yourself (ie something you havent learned before).

>>8271321
>be careful about reaching too far
This

Have to go to bed fast, going to read the new replies tomorrow, bump to keep it alive.

>>8271319
What is a possible application of this theory to a greater understanding?

>>8270044
>>8271271
Ah yeah, and by the representations of the general linear group do you mean representations of GLn(Fq) or any group represented by elements of GLn(Fq)?

>>8271319
No meme problems allowed, youre supposed to actually study something. Some of the bachelors found some minor new results.

>>8271321
>>8271371
Will do, thanks!

>>8271909
Not the poster, but what do you mean by "to a great understanding"?

>>8273828
I was thinking of the representations of GLn(Fq), yeah. What did you mean by group represented by elements of GLn(Fq) ?

>>8273869
Oh okay, you meant representations of finite groups on vector spaces over Fq ! Nah, I did mean representations of GLn(Fq), but that's also interesting (for example representations of a group G on a field F such that char F | |G| )

>>8273869
If you define a representation of a group G as a homomorphism θ: G -> GLn(K) you can either have G = GLn(Fq) or K = Fq, so I wasnt sure which case you meant.

>>8273876
Aight.

I am OP btw, not the above post if its getting confusing. Any interesting results I should look out for in the cases you mentioned?

This thread is on page 9 - if it dies, thanks for the replies so far.