Say you have a year before you start making PhD applications

>>8489057
read about w/e you want. probably should be related to your undergraduate research that you did.

I won't do ug research until next year, so during application time I'll only have done minimal work on research
>>8489113

algebraic geometry:
the exercises in hartshorne are the benchmark for pretty much everyone, but you can find the chapter material written better elsewhere

algebraic topology:
hatcher is a standard intro (some people hate it)

you might like miranda's 'algebraic curves and riemann surfaces' which is complex algebraic geometry in dimension 1 and makes use of some algebraic topology

>>8489131
>getting into a top tier university PhD program without any research on your application

>>8489131
OP. I don't want to seem like an ass hole but you need research exp to get into a good uni, if you have time try to get yourself into a REU. Best of luck, faggot.

>>8489225

>performing research before being admitted to a PhD program
>only the research and results proffered by PhDs matter

well, /sci/? Which is it?

Slightly related, a question: how many living PhDs are there? I've looked for an answer a few times but found none.

>>8489560
Undergrad research can be published, but usually, a department just wants you to have exposure to the process before they burden themselves with 4-8 years with you.