Here are some contexts where I have done this:
In January 2024, I began working in Erika Roldan's Stochastic Topology research team at MPI in Leipzig, Germany! I visited for a month over my winter break, returned to NY for the last semester of my degree, and then started research full-time in September. This is a picture of my office door covered with all 54 arrangements of 4 congruent squares as a connected geometric figure with vertices placed on cubical lattice points. As a part of my very first research project under Dr. Roldan, I built a configuration space which describes all magnetic folding relationships between these objects.
In Summer 2023, I spent three weeks with 200 mathematicians at the IAS Park City Mathematics Institute, studying Quantum Computation. I also did a small research project at the intersection of hyperbolic geometry and dynamics (studying billiard dynamics on the double pentagon translation surface) supervised by Albert Artiles. The undergraduate summer school lecturer was Jamie Pommersheim.
Through Twoples, I had the fantastic opportunity to be paired with Sabrina Pauli from the University of Duisberg-Essen to conduct research in the field of enumerative algebraic geometry during the Spring 2023 semester. We subsequently joined forces with Stephen McKean from Harvard University to expand on our results and have ongoing work determining the local data of the five conics problem.
In Summer 2022, I spent two months living with 9 other undergrad math students at MathILy-EST, working 9am-10pm every day, learning to conduct mathematical research in the field of combinatorial representation theory, under the direction of Nate Harman and advisement of Josh Mundinger. The experience was invaluable and gifted me with an enormous volume of resources, tools, motivation, and confidence, which I have applied to pursuing many successive opportunities in math. I presented our work at seven conferences, and our paper is available here https://arxiv.org/abs/2210.07261 and here https://alco.centre-mersenne.org/articles/10.5802/alco.313/ !