The mathematics in this research project centers around questions in geometry and topology, which are broadly concerned with understanding various notions of shape. This project focuses on 2-dimensional spaces called surfaces, which are fundamental in many areas of mathematics. Surfaces can be flat, like a piece of paper, or curved, like the outside of a ball, a donut, or a saddle, and the various shapes they take often strongly constrain the shapes of the higher dimensional spaces in which they live. The educational portion of this project involves a variety of activities aimed at recruiting and supporting students into mathematics. The first part continues a series of workshops featuring mini courses by early career speakers on their cutting-edge research aimed at graduate students. The second part establishes a series of undergraduate research and recruitment events connecting undergraduate mathematics researchers with graduate recruiters from programs in the region. The third part is a Topical Pedagogy Seminar which will provide graduate students and postdocs training in incorporating topical material into foundational mathematics courses. A remarkable and ubiquitous example of this mathematical phenomenon is a surface bundle, which just like a donut, can be sliced so that the cross-sections are surfaces. Unlike a donut, however, as one moves through most surface bundles, the surface cross-sections can twist and deform in complicated ways. This twisting–which essential