DiM Research Panel PART I – Students (Winter 2025)

1. Introductions and Research Areas

• Zhaoshen
  • U3
  • Has done research twice
  • Geometric topology
• Maya
  • Graduated in 2024
  • Research with Tony Humphries
  • Using math to model iron in blood, to optimize blood donations & donor health
• Frank
  • U3, switching from Arts & Science -> Arts Math
  • Research with Adrien Vetta
  • Categorizing theoretical computer science
• Agnes
  • 2nd year grad Math
  • Research with Adrien Vetta (game theory)
  • Research with Eyal Goren (algebraic construction of graphs)
  • Research with Louigi Addario-Berry (discrete math)
• Suelynn
  • U2 in Honours Math
  • Research in Korea (Seoul National University) in number theory and quadratic reciprocity
• Helena
  • Final semester in Math
  • Research in Michigan in topology and graph theory, counting curves on a surface
  • Did research with Henri Darmon in algebra, number theory, and representation

2. Why research?

• Helena: You can keep being a student. Your research doesn’t have to be novel, can pursue your interests and become an expert on a niche topic and share with other people.
• Frank: It’s self-driven. You can work at your own speed, set your own hours, and be self-directed. Trust that you can do work that you need to and be able to enjoy the summer.
• Maya: You can form a close relationship with a Math professor, who can later be a reference for you, or help you along your academic career, and you get to meet people (other undergrads, etc.) that you wouldn’t have otherwise met.

3. Can you give a day-in-the-life as a summer research student?

• Frank: Wake up 8:30-9AM, be on campus by 10AM. Meeting with a PhD student and/or professor. Extended lunch with fellow researchers. Leave at 5pm or before. 
• Helena: Went to Washington during the summer, so you don’t necessarily have to do research from Montreal if your professor doesn’t expect you to meet every week. 
• Zhaoshen: Supervisor went on vacation during the summer. Once had a meeting at 10PM (exceptionally). Would meet once every 2 weeks. 
• Agnes (grad student): Very flexible schedule. You have to figure out what works for you. Grad courses are more flexible and structured to what you want to get out of the course.

General comments:

• A coupled focused hours is a good day’s work. If you expect yourself to work on research 8 hours a day, you will get burnt out. Plus, a couple productive hours are better than bumming around in an office all day.
• Prioritize personality and expectations of the professor if you don’t know what topic you want to study. For example, do you want to have meetings often and be given weekly tasks, or be left on your own more? Look for a prof that you want to work with. Ask about your professor’s expectations. 
• There is a stereotype that math research is done entirely alone. Sometimes that’s the case, but you also get to talk with other people about your thoughts. Even if the people around you won’t exactly understand, it can be very helpful.

4. Why did you choose your topic (“raison d’etre”)?

• Helena: enjoyed the class she took with the professor. Learned that the style of supervision didn’t work very well for her, prefers more structure and tasks to do every week.
• Maya: was the only team member for a class her professor was teaching – built a relationship with the professor by organizing the tutorials, etc., and then she mentioned to the professor that she really enjoyed the topic. 
• Frank: had never met the professor directly but knew/talked to other students in the lab (including Agnes) to learn about the professor’s research and his personality. 
• Zhaoshen: did DRP (Directed Reading Program) in geometry during his first year. Then, sent emails to professors. Went to a professor’s office and had an interview.
  • Why did you email me? “you work in geometry”
  • What are you interested in? 
  • Do you know what a group, a representation, etc. is? 
  • Started asking open-ended questions, didn’t expect answers. Instead, was focused on Zhaoshen’s thought process. 
• Suelynn: Did DRP in number theory. Went through websites of Korean Universities and emailed professors.

General comments:

• Having a pre-existing relationship with a professor can give you a leg up – go to office hours and talk to profs whose course you enjoyed
• However, research is still possible without knowing the prof.
  • If what the professor is doing is interesting to you, reach out!
  • Don’t worry about not being qualified enough, the professor will tell you – “profs are very good at telling you you’re not qualified” 
• Most math profs will respond to their emails, even if it takes a few days. If you don’t get a response, don’t be afraid to send a follow-up email.
• A note on the DRP (Directed Reading Program): offered once a year during the Winter semester. Good to learn about a niche topic or course that McGill doesn’t offer, or open problems. Applications open at the end of Fall semester. Projects are supervised by grad students and are very collaborative.

5. What was the course that was the most relevant for your research? Are there any necessary or useful courses to take before doing research?

• You might not use any particular course content, especially if your research is more ‘problem-solving’ instead of ‘research-based’. However, you’ll want some level of mathematical maturity, intuition, reasoning gained from U1 courses (analysis, algebra, etc.) to show you have the ability to learn (topics might be beyond the undergrad level).
• Reading research papers is a skill. Sometimes, previous papers in the topic are poorly written. There will be a learning curve; it happens to everyone.
  • Check out DiM’s resources on how to read a math paper!
• The best person to ask about necessary preparation is your supervisor.
  • “What can I do to get deeper into this field?”
• Don’t be scared to tell your supervisor you don’t understand something. Your professor took you on because they want you to succeed. 
• You can take courses taught by your supervisor even after you begin research.

6. Research can be hard mentally. Do you have any advice on staying motivated, imposter syndrome, and enjoying what you’re doing?

• Don’t be afraid to say you don’t say something. Your supervisor might assume you understand, and you’ll get more lost. 
• To deal with demotivation, take a break! Go outside, do something non-academic. Things will marinate and feel easier with a fresh perspective, even if your topic hasn’t changed! Try not to get stuck on minute details.
• Imposter syndrome is going to happen (likely within the first 2 weeks). It’s normal that research can be daunting. It fades with time, and you get better at dealing with it. 
• Ask for help! You can have an extra meeting with your professor, they can provide resources, might send you to a PhD student. Find a PhD student and ask them to explain the big picture, ask them “why should I care about this?”
• Talk to other people in the math department — talking through a problem might not solve it, but it will help you think about it in a new way.
• It’s important to find people outside of math to talk with. Also, if your non-math friend is willing to listen to you, it can reveal holes in your understanding

7. How do you get paid?

• SURA for science students, ARIA for arts students, NSERC (not for international students). These awards are partially departmentally-funded and partially funded by the supervisor/other grants. 
• ISM (Institut des sciences mathematiques, https://ism.uqam.ca/scholarships/#4), good for Arts & Science students. Can hold other grants at the same time.
• If you’re not from Montreal, look for funding from your home country/province/state.
  • Frank got a grant from his home state in the US
  • Suelynn got paid from her supervisor in Korea
    • It wasn’t advertised on the website; she had to ask the prof. 
  • It’s sometimes possible to get funding for housing (an option for international students who want to go back home)
  • Maya did research at McMaster and got in-department grants by providing letters from McGill.
• It’s possible (not that common) for professors to pay you from their grants, without external funding.

8. How are research courses at McGill similar/different from summer research?

• Frank: taking both MATH470 and MATH 480, has weekly meetings.
• Agnes: did COMP400 as an extension of summer research.
• Maya: continued her summer research in MATH410

General comments:

• Nice to not have to worry about a final and get credit for research. Creates a space for research while you’re balancing other course work
• Contact potential supervisors ASAP since there are lots of forms to fill that have to be submitted during the first few days of class (before add-drop ends).
• Research courses are less commitment than full summer research.
• You don’t get paid if you’re taking it as a class but also won’t be expected to work full-time.
• It’s possible to do a research course during the summer (profs might be more likely to take you if they don’t need to pay you). Can still get credit and build a relationship.

9. When should you apply to research or have your summer research figured out?

• Frank: first emailed in October, did not get a response, then followed up. Met with the professor over Zoom in December and met in-person in early-spring to discuss funding.
• Agnes: first reached out during mid-January.

General comments:

• There’s no time like the present! If it’s January, you should do it now. Think about if there’s a class you took in the Fall semester you really enjoyed.
• NSERC/SURA isn’t open yet, so don’t worry too much about that yet. 
• It’s a bit luck-based, so don’t get discouraged or take it personally!

10. How to reach out to professors (they’re scary!) ?

• Be polite. Introduce yourself. Explain why you’re interested. Ask if they have any opportunities. You can ask to meet in person to discuss (it’s often easier to talk in-person), give your availability. 
• Can attach your transcript directly in the email to make it easier for them.
• Give them an idea of your background. If reaching out to professors at other universities, can include the syllabi of relevant McGill courses you’ve taken.
• Realize that professors are just people! They will likely respond to you, and once you have a relationship, they’ll start emailing you with one sentence, like “ok.” 
• You don’t need to put a project proposal in the email.
• Professors have websites with their publications, look at them, because your project might come out of their recent papers. Can mention you read their paper or book and why you liked it. Butter them up a bit, but don’t go overboard.
• If a professor re-directs you to another person, when you reach out to them, say so-and-so told me to email you. 
• Be prepared to talk about your past experiences / papers you’ve written (if any).
• Finally, if you’re using a template, don’t forget to change their name in the email!

11. How did your research conclude?

• Frank: worked on a problem for 3 months with a PhD student, then gave up. Nothing came of it, but he still learned a lot. Some things will happen like that. Then, started a new project and nothing came of that either. 
• Maya: rare experience where the project ended up being simpler than they thought. Wrote it up, tested it, and added to the model. The research project changed compared to the original proposal. Ended the research with a report (her supervisor was focused on making sure everything was written down). Turning it into a publication would require more work. 
• Zhaoshen: For Zhaoshen’s first research experience, the supervisor wanted him to formalize a proof he conjectured in grad school. Zhaoshen spent the first three months learning the background. The fourth month and following semester was spent tackling the project and writing the report. Proved a weaker version of the statement and gave a talk. For his second research experience, the project was about simplifying a pre-existing exposition. 
• Frank: discovered that what had been done was actually wrong and wasn’t able to fix it (felt like he put human knowledge backwards) but knows that progress looks different for everyone.
• Agnes: After formalizing her project, it got rejected 3 times from CS conferences, until it was accepted.

General comments

• A non-trivial component of undergrad research is learning how to do research, learning content, gaining the skills. Professors are doing a teaching, mentorship role and that’s a significant component.
• Celebrate the small successes and cherish the day where you felt like you had it. Research is unexpected and nonlinear.
• Writing things down can be a good practice to consolidate your knowledge, and for future reference.