Mentoring, Service, and Outreach
Service
From Fall 2014 to Spring 2016, I organized the Purdue Secret Seminar which is an advanced learning seminar in geometry, topology, algebra, and number theory. While at Ohio State University, I was an organizer for Ohio State University Topology Seminar. I am currently a co-organizer for the Analytic and geometric group theory seminar at IMPAN.
Outreach
From Fall 2014 to Spring 2016, I organized the Purdue Secret Seminar which is an advanced learning seminar in geometry, topology, algebra, and number theory. While at Ohio State University, I was an organizer for Ohio State University Topology Seminar. I am currently a co-organizer for the Analytic and geometric group theory seminar at IMPAN.
Outreach
- I am co-organizing the 2026 Topology and Algebras Workshop in the Philippines. The link to the workshop can be found at the following website: https://sites.google.com/view/tawph/home. This research school aims to provide an immersive learning experience on two major fields of mathematics -- Topology and Algebra, under the respective themes "algebraic invariants of topological spaces" and ``structures on groupoids, rings and algebras." Under these themes, specific structures such as cohomology rings, Thompson's group, Grigorchuk group, groupoids, Leavitt path algebras, Kumjian-Pask algebras, to name a few, shall be tackled.
Through a carefully curated curriculum, participants will engage in comprehensive discussions and problem-solving sessions, fostering a dynamic learning environment. Through dedicated sessions for peer and expert interactions, attendees shall be engaged in discussions for research collaborations and career-building forums. The highlight of the school is to commence a program that aims to connect Filipino researchers to international experts for collaborations and career mentorship. - In the spring of 2023 and 2024, I was a mentor in the directed reading program at the University
of Virginia which pairs undergraduates with a graduate student or postdoc in the department of math-
ematics. The reading program goes the length of the entire semester and ends with the undergraduate
student giving a presentation some time during the next semester. The project’s content are decided by
the mentor and the student which needs the approval the directed reading program committtee. The
student is required to meet with their mentor once a week for an hour to discuss the material and their
progress. Moreover, 4 hours of independent studies are required each week. The topics that have
been covered by my directed reading program mentees include basic geometric group theory and an
introduction to matroid theory. - During the summer of 2024, I was co-lead a REU project with Beth Branman about nonorientable mapping class groups for the topology RTG at the university of Virginia. As part of preparing the students for the REU, Beth and I gave a collection of 8 lectures over two weeks. The first week consisted about lectures that were geared towards with students with a general interest in topology with topics such as covering spaces, gluing constructions, Seifert Van Kampen, and the fundamental group. These are topics that an advanced undergraduate in topology would in their first year or two. The second week Beth and I introduced the students in our group to the basic theory of mapping class groups of nonorientable surfaces of finite type with an emphasis towards examples and computations. Our goal was to prepare the students to do computations of the curve complex of nonorientable surfaces of lower genus and to understand what the group of automorphisms of these curve complexes are. The project had 4 members, and work continues as they try to compute the curve complex of the nonorientable surface of genus \(g\) with \(b\) boundaries where \(g+b <5\).
- I lead a project for the topology REU at University of Virginia summer of 2022. It was an eight week program which was held in person and had 12 participants. We divided our participants into three groups of four students based on topic which were category theory, topological data analysis, and geometric group theory. I lectured four times during the first week of the program which gave an introduction to geometric group theory for the 12 participants. For the second week, which was focused on the group that I was leading, I gave four lectures over combinatorial group theory and word growth in groups to serve as a founding for their research project. The rest of the program I met with the participants three times a week to guide the participants through the research project, which concerned computing the generating series of language of geodesics for right angled Coxeter groups satisfying a certain symmetry group with respect to the standard generating subset.The participants in my projects were greatly success in that they were able to produce a professional which has since been accepted and appeared in print; see https://arxiv.org/abs/2208.13095
- During the summers of 2020 and 2021, I was a lecturer for the geometric group theory advanced course for the Ross Mathematics Program which is normally held at the Ohio Dominican University but was held online due to Covid-19. The Ross Program is an intensive summer experience designed to encourage motivated precollege and high school students to explore mathematics through a deep and immersive inquiry-based experience. My duties included coordinating and helping to design an introductory course in geometric group theory aimed at early undergraduates and for motivated high school participants in the Ross program and adapting it to the online format. This included choosing lecture material and problem sets for each week. The duties also consisted of giving a hour and a half lecture once each week online. Working with the Ross program gave me experience adapting technical and advanced mathematics to introductory audiences. It also gave me experience transitioning to the online format which was very important in light of the disruptive effects of Covid-19 and will be important for possible future events.
