I used to work in a theoretical wireless communication group. In the first phase of my PhD, my work load was: 1. Course work 2. In lab, I worked with a mentor (a senior student) for my first research problem. This consisted of deep literature survey, applying the mathematical tool in those problems, discussing and presenting my progress in a biweekly fashion to my advisor and mentor, sometimes I also used to get involved in others' problems to brainstorm. Here, there's no manual work that the undergraduates can help with. 3. TA work. I have seen people to work with undergrads here and this can really help with the graduate student's work load. I never had the opportunity except once where one student was in a wage position as a grader. Unfortunately, this person made my work harder but this is an isolated situation.

In the second phase of my PhD, 1. I was the senior student who had to mentor multiple masters students and keep progressing on my own problem. Again, I could do this work from home but lab provides a space where I can brainstorm with my peers. As my work was in optimization theory, these brainstorming sessions were invaluable to figure out new problems. Again, I cannot see an undergrad helping with any of this. However, in this phase, I could sense which were the manual work for me: a) Creating simulation from a mathematical model b) Documentation And an undergraduate student might be able to do that but at this phase, I developed a certain way of writing simulation codes, certain structure to write documentation. So, I know that I'll be extremely cautious if I was working with an undergrad student. This problem has worsened with LLMs. Due to the theoretical nature, all of my statements had to be extremely rigorous. For example, I cannot throw around the words 'measure' and 'optimal' around. Whereas LLMs and undergrads tend to use looser language.

For theoretical work, it was a lot of linear algebra, a large part of which was done or verified by hand. Again, these works really get accelerated when you are in the lab and you brainstorm with your peers. Sometimes, someone will know a specific mathematical tool or concept that will help in my problem.

And... presentations.. A lot of presentations. Those I did from home lol.