The UBC Mathematics Summer Reading Program (SRP) is an enrichment program pairing first- and second-year undergraduates with a graduate student or postdoctoral mentor to explore a modern research topic in mathematics. Aimed at students with little to no experience of mathematics beyond the classroom, the SRP provides critical mentorship and academic support, particularly for those who are new to academia.
I am involved in all aspects of the SRP, from conception to implementation. Each year, I write funding applications, recruit mentors, help them design projects, and advertise the SRP across STEM departments at UBC.
I am working with Elias Hallis (UBC), Nathaniel Hoedemaker-Purvis (UBC), Louis Lin (UBC), and Giles Lo (UBC) to explore uncertainty principles in Fourier analysis.
Brendan Guilfoyle (UBC), Kai Komnenovic (UBC), Martyna Wojciechowska (UBC), and Daniel Zhen (UBC) read Almost arithmetic progressions in the primes and other large sets (Fraser, 2019). This paper proves that if a subset of the integers has full upper logarithmic density, then it must contain arbitrarily long subsets of numbers that are "almost equally-spaced". Brendan, Kai, Martyna, and Daniel split the paper among themselves and presented it to one another during weekly meetings. We discussed how the strategies involved in the proof could be adapted to obtain some small extensions of the main result to higher dimensions.
I led a six-week reading group on modern problems at the intersection of Ramsey theory and measure theory. During the final two weeks, my students wrote expository essays explaining research papers of their choosing. Nirek Brahmbhatt (UBC) and Arjun Sen (UBC) worked together to study Sequences not containing an infinite arithmetic progressions, (Wagstaff, 1972). Matthew Bull-Weizel (UBC) and Nicholas Rees (UBC) read A 1-dimensional subset of the reals that intersects each of its translates in at most a single point (Keleti, 1999) and gave talks based on their readings at the 2023 Canadian Undergraduate Mathematics Conference in Toronto. Matt's essay explains Keleti's terse and technical proof in a remarkably accessible manner. Mia-Kate Gieselmann (UBC) studied On a problem of Erdős on sequences and measurable sets (Falconer, 1984). In her essay, Mia examines the main proof in this paper and compares it with a more recent argument appearing in the survey paper The Erdős similarity problem (Svetic, 2000). Chayce Hughes (UBC) read On a perfect set (Erdős and Kakutani, 1957).
Marcus Lai (UBC) worked through problems in the first four chapters of The Erdős distance problem (Garibaldi, Iosevich, and Senger, 2011) a book discussing a longstanding open question in combinatorics.