Mentorship
A program for undergraduates to read modern mathematical research
In 2023, I founded the UBC Mathematics Summer Reading Program (SRP). This program connects small groups of first- and second-year undergraduates with a graduate student or postdoctoral mentor to read on a topic of modern research connected to the mentor's area of expertise.
Goals of the SRP
Impact
As of this summer, the SRP counts a total of 43 undergraduate students and alumni, as well as 9 graduate and postdoctoral mentors.
My duties as a mentor
My duties as lead organiser
Undergraduate students supervised
The following is a list of the undergraduate students I have supervised and the projects on which they worked. The list is in reverse chronological order.
Daniel Zhen (Summer reading program, 05.2024--06.2024, UBC).
Project: Upcoming.Martyna Wojchiechowski (Summer reading program, 05.2024--06.2024, UBC).
Project: Upcoming.Kai Komnenovic (Summer reading program, 05.2024--06.2024, UBC).
Project: Upcoming.Brendan Guilfoyle (Summer reading program, 05.2024--06.2024, UBC).
Project: Upcoming.Arjun Sen (Summer reading program, 05.2023--06.2023, UBC).
Project: Joint work with Nirek Brahmbhatt, see below.Nirek Brahmbhatt (Summer reading program, 05.2023--06.2023, UBC).
Project: Nirek, together with Arjun Sen, wrote a short exposition of a 1972 paper of Wagstaff in which the author constructs sequences of integers of arbitrary upper and lower asymptotic density that do not contain infinitely long arithmetic progressions.Chayce Hughes (Summer reading program, 05.2023--06.2023, UBC).
Project: Chayce studied constructions of sets of small measure that nevertheless contain affine copies of many prescribed configurations. In 1957, Erdős and Kakutani constructed a subset of [0,1] that has zero measure but that contains an affine copy of every finite set. Chayce wrote a report explaining how this example can be realised as a Cantor-type construction. By considering Erdős and Kakutani's construction from a slightly more abstract perspective, Chayce showed that although it produces a set of zero measure, it must yield a set of full Minkowski dimension.Mia-Kate Gieselmann (Summer reading program, 05.2023--06.2023, UBC).
Project: Mia studied early work on the Erdos similarity problem, an open question in harmonic analysis. Mia wrote an expository report on a 1984 paper of Falconer showing that for each decreasing sublacunary zero sequence of real numbers, one can construct an explicit set of positive Lebesgue measure that does not contain any affine copy of that sequence.Nicholas Rees (Summer reading program, 05.2023--06.2023, UBC).
Project: Nich studied a 2008 paper of Keleti in which the author shows that for each infinite set S, one can explicitly construct a subset of [0,1] with full Hausdorff dimension that intersects S in at most 2 points. Nich also gave a talk on the Erdős similarity problem, an open question which partially motivated Keleti's work, at the Canadian Undergraduate Mathematics Conference 2023 in Toronto.Matthew Bull-Weizel (Summer reading program, 05.2023--06.2023, UBC).
Project: Matt wrote an illustrated reading guide to a 1999 paper of Keleti in which the author constructs a subset of [0,1] with full Hausdorff dimension but that does not contain any 3-term arithmetic progression. Matt presented this work in a talk at the Canadian Undergraduate Mathematics Conference 2023 in Toronto.Marcus Lai (Unofficial reading project, 05.2022--07.2022, UBC).
Project: Marcus worked through the first four chapters of the book The Erdos distance problem by Garibaldi, Iosevich, and Senger.