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3:00pm - RH 440R - Logic Set Theory Brian Ransom - (UCI) Symmetric Filters and Variants of the Halpern-Läuchli Theorem The Halpern-Läuchli theorem was first introduced for its use in Halpern and Lévy's proof of BPI in the Cohen model. Since then, several other theorems establish emergent connections between variants of the Halpern-Läuchli Theorem and BPI in certain symmetric extensions. In this talk, we develop the forcing perspective given by Harrington's proof of the Halpern-Läuchli Theorem. By doing so, we will more clearly identify a connection between variants of the Halpern-Läuchli Theorem and the existence of certain filters in symmetric extensions. Using tools from the study of BPI in symmetric extensions, we use this connection to give simple positive and negative proofs of new variants of the Halpern-Läuchli Theorem. |
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4:00pm to 5:00pm - zoom - Differential Geometry Michael Law - (MIT) Uniqueness and symmetry of steady gradient Ricci solitons In this talk, we will discuss uniqueness and symmetry results for steady gradient Ricci solitons that are asymptotically quotient-cylindrical. Under a rigidity assumption, we show that the steady solitons of Bryant and Appleton are unique among solitons with the same asymptotics. In dimension 4, we show that under the same rigidity hypothesis, any asymptotically quotient-cylindrical steady soliton contains a circle symmetry. We prove these results by establishing a symmetry principle which also generalizes to expanding solitons and Ricci-flat ALE spaces. |