Colloquia/Spring2023: Difference between revisions
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== February 3, 2023, Friday at 4pm [https://sites.google.com/a/uwlax.edu/tdas/ Facundo Mémoli] (Ohio State University) == | |||
(host: Lyu) | |||
The Gromov-Hausdorff distance between spheres. | |||
The Gromov-Hausdorff distance is a fundamental tool in Riemanian geometry (through the topology it generates) and is also utilized in applied geometry and topological data analysis as a metric for expressing the stability of methods which process geometric data (e.g. hierarchical clustering and persistent homology barcodes via the Vietoris-Rips filtration). In fact, distances such as the Gromov-Hausdorff distance or its Optimal Transport variants (i.e. the so-called Gromov-Wasserstein distances) are nowadays often invoked in applications related to data classification. | |||
Whereas it is often easy to estimate the value of the Gromov-Hausdorff distance between two given metric spaces, its ''precise'' value is rarely easy to determine. Some of the best estimates follow from considerations related to both the stability of persistent homology and to Gromov's filling radius. However, these turn out to be non-sharp. | |||
In this talk, I will describe these estimates and also results which permit calculating the precise value of the Gromov-Hausdorff between pairs of spheres (endowed with their usual geodesic distance). These results involve lower bounds which arise from a certain version of the Borsuk-Ulam theorem that is applicable to discontinuous maps, and also matching upper bounds which are induced from specialized constructions of (a posteriori optimal) ``correspondences" between spheres. | |||
== February 24, 2023, Friday at 4pm [https://sites.google.com/a/uwlax.edu/tdas/ Tushar Das] (University of Wisconsin - La Crosse) == | == February 24, 2023, Friday at 4pm [https://sites.google.com/a/uwlax.edu/tdas/ Tushar Das] (University of Wisconsin - La Crosse) == | ||
Revision as of 07:34, 19 January 2023
UW Madison mathematics Colloquium is on Fridays at 4:00 pm.
February 3, 2023, Friday at 4pm Facundo Mémoli (Ohio State University)
(host: Lyu)
The Gromov-Hausdorff distance between spheres.
The Gromov-Hausdorff distance is a fundamental tool in Riemanian geometry (through the topology it generates) and is also utilized in applied geometry and topological data analysis as a metric for expressing the stability of methods which process geometric data (e.g. hierarchical clustering and persistent homology barcodes via the Vietoris-Rips filtration). In fact, distances such as the Gromov-Hausdorff distance or its Optimal Transport variants (i.e. the so-called Gromov-Wasserstein distances) are nowadays often invoked in applications related to data classification.
Whereas it is often easy to estimate the value of the Gromov-Hausdorff distance between two given metric spaces, its precise value is rarely easy to determine. Some of the best estimates follow from considerations related to both the stability of persistent homology and to Gromov's filling radius. However, these turn out to be non-sharp.
In this talk, I will describe these estimates and also results which permit calculating the precise value of the Gromov-Hausdorff between pairs of spheres (endowed with their usual geodesic distance). These results involve lower bounds which arise from a certain version of the Borsuk-Ulam theorem that is applicable to discontinuous maps, and also matching upper bounds which are induced from specialized constructions of (a posteriori optimal) ``correspondences" between spheres.
February 24, 2023, Friday at 4pm Tushar Das (University of Wisconsin - La Crosse)
(hosts: Burkart, Stovall)
March 3, 2023, Friday at 4pm Stefan Steinerberger (University of Washington)
(hosts: Shaoming Guo, Andreas Seeger)
March 8, 2023, Wednesday at 4pm Yair Minsky (Yale University)
Distinguished lectures
(host: Kent)
March 10, 2023, Friday at 4pm Yair Minsky (Yale University)
Distinguished lectures
(host: Kent)
March 24, 2023 , Friday at 4pm Carolyn Abbott (Brandeis University)
(host: Dymarz, Uyanik, WIMAW)
March 31, 2023 , Friday at 4pm Bálint Virág (University of Toronto)
(host: Benedek Valko)
April 7, 2023, Friday at 4pm Rupert Klein (FU Berlin)
Wasow lecture
(hosts: Smith, Stechmann)
April 21, 2023, Friday at 4pm Peter Sternberg (Indiana University)
(hosts: Feldman, Tran)