The equidistribution of lattice shapes of rings of integers in cubic, quartic, and quintic number fields

For $n=3$, 4, and 5, we prove that, when $S_n$-number fields of degree $n$ are ordered by their absolute discriminants, the lattice shapes of the rings of integers in these fields become equidistributed in the space of lattices.Comment: 12 page

On Contradiction

Parenting, across species, is a clumsy, all-consuming, and often exasperating endeavor. Yet in many parts of the human world, we somehow expect to contain and control this part of ourselves. We idealize the separation of work and family. This seems to be especially true in mathematics where many of us hold space in our minds for the Devoted Genius Mathematician who has no other responsibilities but to their own passions, and no obstacles beyond the difficulties of their own pursuits. The unavoidable fact is that life with children is full of absurdities and contradictions. Unless we\u27re willing to embrace that, we will continue to put mothers and other marginalized parents in impossible situations. Instead of viewing contradiction as the end of the proof/story, we need to see it as the beginning

Emotional Labor in Mathematics: Reflections on Mathematical Communities, Mentoring Structures, and EDGE

Terms such as "affective labor" and "emotional labor" pepper feminist critiques of the workplace. Though there are theoretical nuances between the two phrases, both kinds of labor involve the management of emotions; some acts associated with these constructs involve caring, listening, comforting, reassuring, and smiling. In this article I explore the different ways academic mathematicians are called to provide emotional labor in the discipline, thereby illuminating a rarely visible component of a mathematical life in the academy. Underlying this work is my contention that a conceptualization of labor involved in managing emotions is of value to the project of understanding the character, values, and boundaries of such a life. In order to investigate the various dimensions of emotional labor in the context of academic mathematics, I extend the basic framework of Morris and Feldman [33] and then apply this extended framework to the mathematical sciences. Other researchers have mainly focused on the negative effects of emotional labor on a laborer's physical, emotional, and mental health, and several examples in this article align with this framing. However, at the end of the article, I argue that mathematical communities and mentoring structures such as EDGE help diminish some of the negative aspects of emotional labor while also accentuating the positives.Comment: Revised version to appear in the upcoming volume A Celebration of EDGE, edited by Sarah Bryant, Amy Buchmann, Susan D'Agostino, Michelle Craddock Guinn, and Leona Harri

The Equidistribution of Lattice Shapes of Rings of Integers of Cubic, Quartic, and Quintic Number Fields: An Artist's Rendering

A fascinating tale of mayhem, mystery, and mathematics. Attached to each degree n number field is a rank n−1 lattice called its shape. This thesis shows that the shapes of S_n-number fields (of degree n = 3,4, or 5) become equidistributed as the absolute discriminant of the number field goes to infinity. The result for n = 3 is due to David Terr. Here, we provide a unified proof for n = 3, 4, and 5 based on the parametrizations of low rank rings due to Bhargava and Delone–Faddeev. We do not assume any of those words make any kind of sense, though we do make certain assumptions about how much time the reader has on her hands and what kind of sense of humor she has