Regional Workshop in Quantitative Geometry & Topology
April 27–28, 2019
Welcome! We (Fedya Manin and Hannah Alpert) are planning a weekend workshop on quantitative geometry and topology. We hope to provide a venue for young researchers in geometry and topology to learn about this subject and to trade problems and ideas. Some travel funding is available.
In addition to several invited talks, we want to provide as much time as possible, both structured and unstructured, for participants to get to know each other and strike up collaborations. This might include a problem session and/or a series of 5-minute lightning talks.
Quantitative geometry and topology refines the qualitative, discrete questions of algebraic and geometric topology into continuous ones. For example, we may see a loop in a space which is homotopically trivial and ask how difficult it is to trivialize. Depending on what we mean by "difficult", we might obtain different notions of isoperimetry; one common choice is the area of a filling disk, which leads to the definition of the Dehn function of a group.
A priori, such notions usually depend on the choice of a metric on the space; one can then analyze their dependence on the metric (quantitative geometry) or show results, for example asymptotic ones, which are independent of the choice (quantitative topology).
From a more global perspective, one can see this as the study of geometric functionals on spaces of geometric objects: the Lipschitz constant as a functional on the space of maps between two spaces; mass, for cycles in a space; Riemannian volume, for manifolds.
This circle of questions has ties to geometric group theory, minimal surface theory, and the theory of computation among other areas. Specific topics which can be viewed through this lens include:
- Isoperimetric functions
- Systolic geometry
- High-dimensional expanders
- Configuration spaces of hard disks
- Greg Chambers (Rice)
- Larry Guth (MIT)
- Shelly Harvey (Rice)
- Yevgeny Liokumovich (MIT/IAS)
- Eric Sedgwick (DePaul)
- Robert Young (Courant)
Coming soon. The workshop will start on Saturday morning, April 27, and end before 2pm on Sunday, April 28.
The registration form is available. We will have lodging and at least partial travel funding for graduate students and other early career participants. Please register by March 15 to request funding. We will try to get back to you soon afterwards with estimates of the maximum travel cost we can reimburse.
Invited speakers and funded participants will stay at the Blackwell, Ohio State's on-campus hotel. Other participants may want to stay there or elsewhere in the area. We might have some rooms at the Blackwell which participants may book themselves at a discounted rate. Check back here for further information.
Columbus Airport (CMH) is the nearest airport, and the most convenient way to get to Columbus from outside driving distance. Participants from the Midwest and Western Pennsylvania may want to drive or take a bus. In addition to Greyhound, Barons Bus is a regional company serving Columbus, including some buses to Ohio State campus.