I have been fortunate to be accepted to some top ten programs and USC. My primary interests are Algebraic K-theory, Motives, A^1 homotopy theory and Algebraic Geometry. The real pickle is the Top 10 ten programs i have been admitted do not have any K-theorist and people directly studying these problems per say (not that I can see in their publications) but are fantastic Algebraic geometry schools. (Not U Chicago, Northwestern, UCLA and I did not apply to H,P, Berkley, and Stanford)

However I have also been admitted to USC which have two fantastic K-theorists namely Eric Freidlander and Aravind Asok whose work i really can relate to. The fact is it is not a top school. I am leaning towards this school primarily because I have spent the last whole year independently working on K-Theory and have a result which has been submitted to a good journal. I do not know if prestige should win over the choice of possible advisors. I would have to change my research focus to other aspects of Algebraic geometry if I choose to attend the Top end programs. Some serious words of advice would help. I enjoy geometry on the whole per say but Homotopical algebraic geometry and K theory really seems to be my focus currently. USC is close to UCLA another school with great research focus in my interest. My greed factor is USC allows me to do these things and I have enough time to think of some nicer problems.

My worries are will it really affect my career if I choose such a mid tier school? I know many variables are involved.

Also I did observe that a TOP school has only 2 algebraic geometers currently and last year had only 5 (3 pure + 2 applied) people joining the program. I am pretty keen about the program though I have not yet recieved a final word yet (waitlist sob story). 3 people in pure math joining the math phd program was rather disturbing to me. Also the place has one advisor choice per say (unless i choose to change research area under which I would very very easily choose the other top programs). Is it really worth awaiting such a small program? The nearest other big school is about 2 plus hours away.

Thanks

## Reserach - TOP school vs USC

### Re: Reserach - TOP school vs USC

First of all, congratulations on your admissions!

You are right in that a prestigious uni shouldn't come before the value of a supervisor. Especially if the top uni you are referring to only has two algebraic geometers (?). I think it is important to be in an environment where you

USC however, has a nice faculty, with Eric being a great choice if he could supervise you. That said though, since you have already been accepted to the other top unis, why not sending an email to the algebraic geometers there? K-theory and motivic homotopy theory have found applications to many areas of algebraic geometry. E.g. cyclic cohomology (Beilinson's school), Bloch-Kato conjecture (with links to Galois cohomology), moduli space problems (through MZV / mixed Tate motives), etc. So I think it is fair to assume that some of the mathemticians there will work in one of those areas, and perhaps they will be willing to supervise a project in the direction of your interests.

It would be a shame to not weight properly your options after being accepted to a top uni. Let us know how that goes!

You are right in that a prestigious uni shouldn't come before the value of a supervisor. Especially if the top uni you are referring to only has two algebraic geometers (?). I think it is important to be in an environment where you

*know*there will be a seminar in your area of interest every semester, or at least every year.USC however, has a nice faculty, with Eric being a great choice if he could supervise you. That said though, since you have already been accepted to the other top unis, why not sending an email to the algebraic geometers there? K-theory and motivic homotopy theory have found applications to many areas of algebraic geometry. E.g. cyclic cohomology (Beilinson's school), Bloch-Kato conjecture (with links to Galois cohomology), moduli space problems (through MZV / mixed Tate motives), etc. So I think it is fair to assume that some of the mathemticians there will work in one of those areas, and perhaps they will be willing to supervise a project in the direction of your interests.

It would be a shame to not weight properly your options after being accepted to a top uni. Let us know how that goes!