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Reading Topology from Open Books (Prof. Bahar Acu, Pitzer College)
March 29, 2023 @ 4:15 pm - 5:30 pm
Title: Reading Topology from Open Books
Speaker: Bahar Acu, Department of Mathematics, Pitzer College
Abstract: How can we study topological shapes that are outside the realm of our imagination? In this talk, we will explore potential answers to that question by diving deep into dimensionality and topology via open books. Topology is the study of properties of shapes that do not fundamentally change when they are bent and/or stretched without poking holes or ripping apart. At this point, you must have heard that to a topologist, a donut and a coffee cup (with a handle) are the same thing since one can be deformed into the other continuously, i.e. only via bending and/or stretching. A very useful strategy in studying topological objects (in our case, manifolds) is to factor them into smaller pieces. An open book decomposition of an n-dimensional manifold (the open book) is a special function that helps us study our object in terms of its (n-1)-dimensional fibers (the pages) and (n-2)-dimensional boundary of these fibers (the binding). This topological tool provides a natural framework for studying topological properties of certain geometric structures on smooth manifolds such as contact structures. For example, every (contact) 3-dimensional manifold can be presented as an open book whose pages are surfaces and binding is a knot/link. In this talk, we will talk about these objects in greater detail with examples.
Dr. Bahar Acu is an Assistant Professor of Mathematics at Pitzer College. Prior to joining Claremont Colleges, Dr. Acu held positions at UCLA, Northwestern, ETH Zürich, and IAS Princeton following a Ph.D. degree from the University of Southern California. Dr. Acu’s primary research interests are in the field of geometric topology, more precisely contact and symplectic topology in high dimensions and their relations with low-dimensional topology. Dr. Acu is the co-founder and lead-organizer of the inaugural international research collaboration conference for women and nonbinary mathematicians in the field of symplectic and contact geometry and topology. The peer-reviewed volume of this conference Research Directions in Symplectic and Contact Geometry and Topology, lead-edited by Dr. Acu, was recently published as a part of Springer’s Association for Women in Mathematics Series.