Mathematics

Every door you open in your undergraduate degree can shape your future. This is what Daniel Carranza, BSc’21, discovered during his time at Western University, which led him to publishing his first paper in Logical Methods In Computer Science before finishing his undergraduate degree. Carranza will soon embark on a one-year research stint at the Mathematical Sciences Research Institute (MSRI) in Berkeley, Calif. – one of the world’s most prestigious math institutes – after which he will pursue his PhD at Johns Hopkins University. It’s a life-changing journey that began at Western and honed by a summer research internship program that changed Carranza’s career trajectory. Carranza entered the Faculty of Science with an intent to study computer science and get a job immediately upon graduation. However, during his first year, his mathematics courses changed his direction and he switched to an honours specialization in mathematics with a minor in computer science. “I found the math courses really interesting and the professors were so engaging. It intrigued me so much that I switched into mathematics for my second year so I could study it more and more,” stated Carranza. It was mathematics professor Chris Kapulkin that first introduced Carranza to undergraduate summer research opportunities at Western, particularly the Natural Sciences & Engineering Research Council Undergraduate Student Research Awards (USRA). Although he initially missed the deadline for the funding application, Carranza was determined to begin his research journey, even if it meant doing it without remuneration. Within weeks of starting, however, Kapulkin was able to secure funding to officially hire Carranza as a research assistant. The following summer, Carranza successfully received funding through the USRA. “That summer really opened my eyes to research as a career,” explained Carranza. “Doing research full-time is such a unique opportunity – unlike anything you experience from your coursework. An assignment for a course can feel like trying to draw from a connect-the-dots puzzle; whereas research feels like having a blank piece of paper and being in control of what to draw and how you draw it.” Recently, Carranza co-authored his third paper with Kapulkin on discrete homotopy theory, which started as Carranza’s USRA work. Discrete homotopy theory studies complexity in networks, which are collections of nodes and edges connecting them. Networks are a mathematical tool which can be used to study real-world, social and technological networks. For example, friendship data on social media can be represented as such a network. Users can be represented as nodes, and two people being friends on social media can be represented by an edge between two nodes. In this context, discrete homotopy theory can answer questions, such as how quickly and effectively information spreads. Carranza’s paper settled a major open problem in the field, posed by Dr. Hélène Barcelo, deputy director of the MSRI. “Typically, a PhD thesis is a math student’s first publication. Daniel already has three papers, including this recent paper. This is absolutely exceptional, both in terms of quality and quantity,” said Kapulkin. Carranza will be finishing his MSc in mathematics from the University of Toronto this summer before he joins the MSRI in September 2022 to work with Barcelo as a program associate for one year. Carranza credits his success to the opportunities and resources that were provided to him by the department of mathematics at Western. “I wouldn’t be on the path I am today without the support of the incredible faculty members, especially Dr. Kapulkin, that helped me along the way,” said Carranza. Western’s NSERC Undergraduate Student Research Awards summer program is held full-time for 16 weeks with a $6,000 stipend per award.