I will speak about both abstract Schur-Weyl duality from a categorical viewpoint as well as the concrete case for the symmetric groups and general linear groups. The concrete case says roughly that there is a one to one correspondence between irreducible finite dimensional representations of the symmetric groups and irreducible finite dimensional polynomial representations of the general linear groups. Time admitting, I may point out some connections with symmetric functions and polynomials.

Title: Math Ed Colloquium: The blending of academic and social support through apoyo and consejos in the mathematical success of three undergraduate Latinx engineering students

Date: 11/07/2017

Time: 1:15 PM - 2:45 PM

Place: 252 EH

Analyses of academic success among Latinxs in undergraduate STEM education have shed light on gendered disparities between Latinx women and Latinx men. In the United States, Latinx women have higher grade point averages and degree completion rates than Latinx men even though they also report lower levels of confidence. Despite the masculinization of engineering and mathematics spaces perpetuated through women’s underrepresentation and norms of engagement, Latinx women earn over half of science and engineering degrees conferred to their racial group. With undergraduate mathematics serving as a gatekeeper for advanced STEM coursework among historically marginalized populations, qualitative analyses of Latinx undergraduate men’s experiences of mathematical success can illuminate ways to inform more socially affirming STEM postsecondary educational opportunities for them. This presentation shares findings from a phenomenological study of mathematical success as a socially exclusionary experience among three Latinx men pursuing engineering majors at a large predominantly white, four-year University. A cross-case analysis of the three men’s mathematics experiences documented using multiple data sources reveals how academically and socially supportive opportunities, likened to apoyo (moral support) and consejos (narratives of advice) from Latinx culture, shaped their high school and undergraduate mathematical success. Implications are raised to inform change in mathematics education and STEM support programs to better meet Latinx men’s academic and social needs across the K-16 STEM pipeline.

Title: A slice filtration for certain twisted Eilenberg-Mac Lane spectra

Date: 11/09/2017

Time: 2:00 PM - 3:00 PM

Place: C304 Wells Hall

A space X can be described by its Postnikov tower, whose stages have only the homotopy groups of X in a range. Equivariantly, there is an analogue of the Postnikov filtration called the slice filtration. After reviewing some previously known examples, I will describe the slice filtration for twisted Eilenberg-Mac Lane spectra when the group of equivariance is K_4, the Klein four group. This is joint work with C. Yarnall.

The Euclidean plane consists of ordered pairs of real numbers p=(x,y) equipped with the well-known distance function d(p_1,p_2)=((x_1-x_2)^2+(y_1-y_2)^2)^{1/2}. An isometry is a self-map of the plane that preserves all distances between pairs of points.
After briefly classifying the isometries of the plane, I'll prove the following surprising result: If a self-map of the plane carries pairs of points that are distance one apart to pairs of points that are distance one apart, then the map is an isometry. That is, maps that preserve distance one preserve all distances!
Time permitting, I'll discuss the relationship of this problem to the more combinatorial problem of determining the chromatic number of the plane and some open problems.