Ryan Budney | PIMS - Pacific Institute for the Mathematical Sciences

University of Victoria

Ryan Budney is a professor of Mathematics at the University of Victoria, his work is in an area called "Geometric Topology". This is a subject concerned with geometry, fairly generally construed. This includes topics such as manifolds, and knot theory. His specific research tends towards topics such as "spaces of things" like configuration spaces, or spaces of embeddings of one manifold in another. He also enjoy studying the homotopy-types of diffeomorphism groups of manifolds. Recently he has been building a list of the "smallest" triangulated smooth 4-manifolds, as well as a table of knotted 2-spheres in the 4-sphere. He has also been interested in some `applied topology' topics such as persistent homology.

Dr. Budney is one of the CRG Leaders for the PIMS CRG in Novel Techniques in Low Dimension: Floer Homology, Representation Theory and Algebraic Topology.

Persistent Homology is an application of algebraic topology (filtered chain complexes) to statistics. Roughly speaking, one naturally associates filtered chain complexes to data in a variety of ways. Persistent homology is the structure of how the...

DNA topology is the study of the geometry (supercoiling) and topology (knotting and linking) of DNA. Knots and links in DNA are known to obstruct normal cellular processes and geometric factors such as the amount of writhe or supercoiling are known...

I will describe a new operad (the "splicing operad") that acts on a fairly broad class of embedding spaces. Previously I constructed an action of the operad of little (j+1)-cubes on the space of framed long embeddings of R^j in R^n. This operad...

The Cascade Topology Seminar is a bi-annual gathering of topologists from the Pacific Northwest and Southwestern Canada.

I will describe a project to classify all smooth 4-dimensional manifolds triangulable with 6 or less 4-dimensional simplices. In the process we have found many simple triangulated 2-knot exteriors, forming a strong analogy with 3-manifold theory.

I will describe why the trivial knot S2-->S4 has non-unique spanning discs up to isotopy. This comes from a chain of deductions that include a description of the low-dimensional homotopy-groups of embeddings of S1 in S1xSn (for n>2), a group...

For more information about this event, please see the conference website. This conference will bring together experts in various aspects of four-dimensional topology. Themes include diffeomorphism groups of four-manifolds, construction and detection...