Research profile

Kyle Broder

Works on Ricci-flat & Calabi–Yau, Kähler–Einstein & K-stability and Kähler–Ricci flow.

NP-RC-8120250000-0003-1842-5763

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Ricci-flat & Calabi–YauKähler–Einstein & K-stabilityKähler–Ricci flowEinstein metricsKähler geometry(Non)collapsingLimit spaces & RCDRicci flow

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Their work in this field since 2016, with the older papers the site recommends. Titles open each paper's page, with its abstract, PDF and HTML versions; Connections shows the papers closest to it. The arXiv listing has the complete record.

2021

math.DGv3arXiv:2106.13343

Second-order estimates for collapsed limits of Ricci-flat Kähler metrics

Kyle Broder

We show that the singularities of the twisted Kähler–Einstein metric arising as the long-time solution of the Kähler–Ricci flow or in the collapsed limit of Ricci-flat Kähler metrics is intimately related to the holomorphic sectional curvature of the reference conical geometry. This provides an alternative proof of the second-order estimate obtained by Gross–Tosatti–Zhang with explicit constants appearing in the divisorial pole.

Ricci flowKähler–Ricci flowEinstein metricsRicci-flat & Calabi–YauSingularitiesKähler geometryLong-time existence & convergenceKähler–Einstein & K-stability
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2020

math.DGv3arXiv:2003.14009

Twisted Kähler-Einstein Metrics and Collapsing

Kyle Broder

We extend the arguments of Tosatti-Zhang to reduce a well-known conjecture concerning the structure of the Gromov-Hausdorff limit in both the setting of degenerating Calabi-Yau manifolds and the Kähler-Ricci flow to a certain partial second-order estimate.

Ricci flowKähler–Ricci flowEinstein metricsRicci-flat & Calabi–Yau(Non)collapsingKähler geometryLimit spaces & RCDKähler–Einstein & K-stability
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NP-RC-812025 is Kyle Broder's permanent number in the Ricci flow community on Neckpinch. It stays with them through any change of name or post. More about these numbers.

A window on one part of a person's work: papers here go back to 2016 and cover Ricci flow and its neighbouring flows, with the older work the site recommends, so this page is no measure of anyone's whole output. Being listed is not an endorsement by or of the person. How it is put together.