A stunted PhD: PhD in the time of a pandemic I'm a third year Math PhD student in the US. My concern is that my PhD is going to be stunted in the following sense:

I am my advisor's only graduate student. This is not uncommon for grad students in math. I do however compare this to my friends and colleagues in astronomy who have research groups. They meet every week and discuss their work with each other. On the other hand, I have nobody apart from my advisor to discuss my work with. I can't discuss my frustrations in research or my elation in learning something new in an informal setting. My research area (geometric function theory) is very niche in the sense that we're the only ones working on complex analysis in our department.

So far I have not attended any conferences. I had an opportunity to attend one last summer, but it got cancelled due to the pandemic. It seems unlikely that an in person conference will happen for at least another semester or so. I have not had the opportunity to meet peers in my field from other universities and learn what they do. I have not made any connections.


To summarize, I'm worried that my training in research is not going to be &quot;wholesome&quot;. I saw my seniors present at conferences and make collaborations and friends from all over. I'm worried that not attending conferences will be held against me in the post-doc market and that I am currently unable to learn the current advances in my field because of my limited (non-existent) exposure to the math community.
My specific questions are:

What are some practical measures I can implement to make connections? How do I get to know some people in my field? (I do attend talks over zoom but these aren't exactly sociable events due to their online nature.)

How important is attending conferences with regard to post-doc applications and how can I compensate for not attending any, in the remaining two years of my program?


Thanks for your time.
Disclaimer: This is not specifically from a mathematics study or USA perspective, but I think some perspectives may be helpful. Take them with a pinch of salt, depending on local factors.
I started a research career in an applied lab before enrolling for a PhD. Presently I am, like you, in my third year of PhD, and generally struggle to juggle office work with my academic work. While the pandemic created a bunch of problems (especially for experimentalists), it has had a few positive effects. In my experience, all positive effects were linked with peer exchanges, communications, and virtual interactions. (Everything below only addresses your first question.)
(1) Shrinking distances: It is easier to attend webinars, talks and enroll in peer groups when you don't need to physically be present. I found myself attending talks from different departments, which I wouldn't have in person, just because they were a mile's walk away. I understand your field is niche, but this may be the ideal time to explore some peripheral topics and see how your research could connect to those. If you find it difficult to get your question answered on Zoom, don't shy away from mailing the speaker (use an appropriate subject line, of course). That could help set up a private chat or discussion soon after.
(2) Reduced conference costs : Other than the travel costs saved, most conferences have significantly reduced the registration fee. This means that one could attend a lot more conferences than would be possible in person. In my personal case, several conferences and workshops were affordable enough for me to pay for, rather than having to apply for departmental/other grants. As you attend more, you will have more interactions (despite missing the in-person interactions), and it is inevitable that some will be helpful to you.
(3) Newer conference formats: The most recent conference I attended followed a hybrid format, where video presentations of all talks were made available about a week in advance, and during the actual conference dates there were virtual discussion rooms for each session. This is amazing, because you can effectively watch and absorb content in advance, reach out to other speakers beforehand, expressing interest and mentioning any topics that you would like to discuss. This made the discussion sessions extremely fruitful and targetted (arguably more than an in-person conference where social demands could reduce the extent of discussions). Of course, it demands that you do your homework beforehand.
Finally, for the virtual conferences, a few precautions are worth keeping in mind. Its good to keep your camera on as much as possible (facial contact is still very important), a good internet connection is worth the investment (if applicable), and its better to be formally dressed, even if you're attending from home.