Seminars and Colloquia

Topology et al. Seminar

Apr 18

Topology Seminar

04:20 pm

Exley Science Center Tower ESC 638

Melissa Zhang, Boston College Symmetries in topological spaces and homology-type invariants Abstract:Topologists often encounter spaces with interesting symmetries. By analyzing the symmetries of an object through the regularities of its algebraic invariants, we are able to learn more about the object and its relationship with smaller, less complex objects. For example, by using the right tools, we can easily see that for a topological space Xequipped with a cyclic action, the rank of the singular homology of Xis at least that of the fixed point set. In low-dimensional topology, knots and links are ubiquitous and far-reaching in their associations. One particular interesting algebraic invariant of links is Khovanov homology, a combinatorial homology theory whose graded Euler characteristic is the Jones polynomial. In this talk, we consider links exhibiting 2-fold symmetry and prove a rank inequality for a variant of Khovanov homology.

Feb 21

Topology Seminar

04:20 pm

Exley Science Center Tower ESC 638

Kyle Hayden, Boston College From algebraic curves to ribbon disks and back Abstract: There is a rich, symbiotic relationship between knot theory and the study of algebraic curves in complex spaces. In particular, intersecting an algebraic curve in C^2 with a three-sphere of constant radius yields a knot or link that contains useful information about the algebraic curve. We'll look at a thirty-year-old conjecture about the relationship between different knots associated to the same algebraic curve. Using a simple construction, we'll show that the conjecture is false and that counterexamples are quite common.