Ismar Volić
Professor of Mathematics
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Research in algebraic topology, specifically calculus of functors and its applications to embeddings, including knots and links.
My area of research is algebraic topology, and more specifically calculus of functors. I have been applying this theory to the study of the rational homotopy type spaces of embeddings, and in particular to spaces of knots, links, and braids. I have also been trying to generalize finite type knot invariants to various embedding spaces, define multivariable manifold calculus and apply it to links and braids, and investigate Milnor invariants from the functor calculus viewpoint. I am also a coauthor of a monograph on homotopy theory of cubical diagrams that underlie calculus of functors as an important technical tool.
I enjoy teaching across the curriculum, and am fortunate to have taught a variety of classes at Wellesley, including topology, abstract algebra, Galois theory, number theory, combinatorics, and others. I also designed classes on algebraic geometry, cryptography, group actions, cryptography and privacy, and supervised independent studies and senior theses on Hochschild homology, differential geometry, math behind Google, differential equations, knot theory, and other topics.
In recent years, the mathematics department has been redesigning and strengthening its curriculum and has as a result succeeded in recruiting more majors and sending more students to excellent graduate programs in mathematics. I am fortunate to be a member of the faculty at this time since my own professional goals coincide with this effort. I strive to blend the research and teaching parts of my job by introducing undergraduates to research mathematics. Teaching special topics courses, bringing mathematicians to give talks, supervising independent studies, summer research, and honors theses are just some of the ways in which I try to convey to our students that mathematics is a vibrant, exciting research field.
Education
- B.A., Boston University
- M.A., Brown University
- Ph.D., Brown University
Current and upcoming courses
Mathematics and Politics
MATH123
How can a candidate in a political race win the majority of votes yet lose the election? How can two competing candidates interpret the same statistic as being in their favor? How can the geometry of the voting district disenfranchise entire groups of voters? Can we quantify the power the President of the United States has? In this course, we will look at the mathematics behind these and related questions that arise in politics. We will study topics such as fairness, voting paradoxes, social choice, game theory, apportionment, gerrymandering, and data interpretation. The goal of the class will be to illustrate the importance of rigorous reasoning in various social and political processes while providing an introduction to some fascinating mathematics.
(MATH 123 and PEAC 123 are cross-listed courses.)-
Mathematics and Politics
MATH123
How can a candidate in a political race win the majority of votes yet lose the election? How can two competing candidates interpret the same statistic as being in their favor? How can the geometry of the voting district disenfranchise entire groups of voters? Can we quantify the power the President of the United States has? In this course, we will look at the mathematics behind these and related questions that arise in politics. We will study topics such as fairness, voting paradoxes, social choice, game theory, apportionment, gerrymandering, and data interpretation. The goal of the class will be to illustrate the importance of rigorous reasoning in various social and political processes while providing an introduction to some fascinating mathematics. (MATH 123 and PEAC 123 are cross-listed courses.) -
Topology
MATH307
This course covers some basic notions of point-set topology, such as topological spaces, metric spaces, connectedness and compactness, Heine-Borel Theorem, quotient spaces, topological groups, groups acting on spaces, homotopy equivalences, separation axioms, Euler characteristic, and classification of surfaces. Additional topics include the study of the fundamental group (time permitting).