Colloquium Series 2024-2025
This colloquium is sponsored by the Department of Mathematics & Statistics
For more information, contact the colloquium chair, Dr. Michael Kerckhove.
Upcoming:
February 24 at 12:00 pm in Jepson Hall 109
Lea Beneish PhD, Department of Mathematics, University of North Texas
Title: Degree D Points on Curves
Abstract: The solution set of a polynomial in three variables in which every monomial has the same degree is referred to as a plane curve. A famous example of such a plane curve is given by the equation relating Pythagorean triples, $x^2+y^2=z^2$ where positive integer solutions correspond to right angled triangles with integer side lengths; in this case, there are infinitely many (primitive) solutions. However, an equation where two squares sum to the negative of another square, for example, $x^2+y^2=-z^2$ has no rational solutions, as the sum of two squares cannot be negative. Even though this equation has no rational solutions, it may have infinitely many solutions involving the imaginary number i. Since i has a minimal polynomial of degree 2 one says that such a point has degree 2 (for example, (i, 0, 1)) is a point of degree 2, whereas a rational point is considered a point of degree 1). In this talk, I'll consider the question: “what is the set of degrees D such that equations of the form f(x,y,z) = 0 have solutions of degree D?” This set turns out to have some interesting properties. This talk is based on joint work with Andrew Granville.
Past Events:
November 11 at 12:00 pm in Jepson Hall 109
Jamie Settle, PhD, W '07, Cornelia Brackenridge Talbot Professor of Government, College of William & Mary
Title: Using Computational Social Science to Assess the Impacts of Social Media on Political Attitudes and Behavior
Abstract: What did we learn about the impact of Facebook and Instagram on key political attitudes and behaviors during the U.S. 2020 elections? How do those lessons shape our expectations of the role of social media platforms in the 2024 election? The public and pundits frequently blame social media for a variety of societal ills, ranging from affective polarization to the spread of disinformation to the extremity of people’s attitudes. In this talk, Jaime Settle will present the results from five studies that have been published out of an academic collaboration with Meta that use experimental and observational approaches on Meta’s platforms to assess their impact on people’s political attitudes and behavior.
October 28
Elizabeth Milicevic, Associate Professor of Mathematics and Statistics, Haverford College
Title: The Algebra and Geometry of Core Partitions
Abstract: Core partitions are used extensively as indexing sets for objects in representation theory, algebraic geometry, and number theory. Cores naturally index certain elements of the affine symmetric group, which is an infinite analog of the group of permutations on a finite set. We can also conveniently realize these group elements via other geometric and combinatorial models such as abacus diagrams, permutahedra in a hyperplane arrangement, and words in a Coxeter group. In this talk, we will explore the relationship among these various algebraic, geometric, and combinatorial perspectives on core partitions, proving some bijections along the way which are difficult to see purely combinatorially. This talk will be completely self-contained; no algebraic, geometric, or combinatorial background will be assumed.