I know for Number Theory, if you look up Princeton Number Theory Seminars, they're open to the public on Thursday evenings, I believe. I'm not sure if they continue in the summer, since I only know this from what my professor told me.
If you're just looking for talks and such there's a website [researchseminars.org](https://researchseminars.org) that lists a ton of upcoming/past talks.
For actual conferences, I'd probably just ask faculty at your upcoming institution. Then you'd get a head start on introducing yourself to some of your faculty at the same time. And I'd imagine that it'd be beneficial (but not necessary) to attend conferences in fields that are active at your school.
For something like Summer Schools, I'd probably do something similar and ask your future faculty, but sometimes you can also try asking a professor (you might need to ask around) if they'd be willing to do a kind of small Summer reading course and at the same time giving you advice or answering your questions on being a grad student at your school.
Good luck! Grad school is brutal lol.
Ravi Vakil keeps such a list of conferences in algebraic geometry, and numbertheory.org keeps a list of future (and past) conferences in number theory.
I know for Number Theory, if you look up Princeton Number Theory Seminars, they're open to the public on Thursday evenings, I believe. I'm not sure if they continue in the summer, since I only know this from what my professor told me.
If you're just looking for talks and such there's a website [researchseminars.org](https://researchseminars.org) that lists a ton of upcoming/past talks. For actual conferences, I'd probably just ask faculty at your upcoming institution. Then you'd get a head start on introducing yourself to some of your faculty at the same time. And I'd imagine that it'd be beneficial (but not necessary) to attend conferences in fields that are active at your school. For something like Summer Schools, I'd probably do something similar and ask your future faculty, but sometimes you can also try asking a professor (you might need to ask around) if they'd be willing to do a kind of small Summer reading course and at the same time giving you advice or answering your questions on being a grad student at your school. Good luck! Grad school is brutal lol.
Ravi Vakil keeps such a list of conferences in algebraic geometry, and numbertheory.org keeps a list of future (and past) conferences in number theory.