Previous Talks (with notes if applicable)
Aug 31 James Lee
Title: p-invariants of Abelian varieties (and maybe the Torelli locus)
Abstract: Abelian varieties are higher-dimensional analogues of elliptic curves and play a central role in modern algebraic geometry and number theory. In layman's terms, they are projective varieties that have a group structure. When working over a field of positive characteristic p, the geometry of an abelian variety is influenced in interesting ways by the prime p. It is analogous to how fields of characteristic p > 0 admit inseparable field extensions and have a lot of exotic phenomena. Consequently, there is a class of invariants, called p-invariants, that can be assigned to abelian varieties over characteristic p, and a current research topic is studying which invariants are possible. In particular, one can look at the stratifications induced by the invariants and study whether they have nice geometric properties such as irreducibility, smoothness, etc.
Sep 14 Charlie Moll
Title: A Brief Introduction to the Philosophy of Mathematics
Abstract: In this talk, I will lay out the basic positions/debates in the philosophy of mathematics (Platonism, Nominalism, Intuitionism, and Structuralism) with an emphasis on the ontology of mathematical objects. We will also look at how some of these philosophical positions motivate alternative foundations of mathematics. Throughout all of this, we will need some basic notions from mathematical logic which will be given an informal treatment in the interest of time.
Sep 21 Bhargav Kale
Title: A Brief Introduction to the Philosophy of Mathematics
Abstract: Positioning Theory is a discourse analysis methodology that conceptualizes social interaction as a dynamic, discursive process in which participants continuously negotiate positions/positioning, storylines, and speech acts, which together shape meaning, power, and participation within specific social episodes (Davies & Harre, 1999). Researchers in mathematics education have largely used Positioning Theory to understand how classroom interactions influence teachers’ positioning of their students (e.g., Herbel-Eisenmann & Wagner, 2010) and students' positioning of each other (e.g. Wood, 2013) that can (re)-create traditional mathematics logics. As teachers may enact these logics, they can engage in racialized and gendered deficit positioning that marginalize minoritized students in mathematics spaces in the US (e.g. Yamakawa et al., 2009). While some research has tried to understand how supportive classroom interactions can disrupt these logics (e.g. Vaidya & Battey, 2022), none of them have incorporated positioning theory as an analytical tool. In this talk, I will give a brief introduction of positioning theory and how it can be used as a tool to understand teaching practices that support Dalit and other caste-marginalized students in higher education spaces in India to form positive mathematical identities. Using literature on experiences of Dalit students and faculty in HE spaces, I will explain how discourses of systemic casteism in India engages in deficit positioning of Dalit students and faculty in mathematics (e.g. Sadafule & Berntsen, 2017) and higher education spaces (e.g. Padalia, 2024) that diminishes learning, teaching and research opportunities for several Dalit students and faculty (Subramanian & Visawanathan, 2023).