## Spring 2023

This semester Babytop will be about telescopically localized stable homotopy theory.

We meet at 4:00 on Tuesdays in 2-361 unless otherwise noted.

• Feb 072023
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### Ishan

The goal of the seminar is to learn about the T(n)-localizations of the stable homotopy category.

In the first part of the seminar, we will first go over some of the basics of chromatic homotopy theory and introduce the T(n)-local and K(n)-local categories. We will then focus on understanding ambidexterity and its consequences, which is one of the fundamental features of these categories.

In the second part of the seminar, we will read works surrounding the telescope conjecture. In particular, we will learn about the original proofs of the telescope conjecture, attempted disproofs and related conjectures at higher heights, and implications of these conjectures on the size of the stable homotopy groups of spheres.

Below is a rough list of the talks for the first half of the semester.

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• Feb 142023
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### To be determined

This talk will be an overview of chromatic homotopy theory and an an introduction to the telescopic and K(n)-local categories.

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• Feb 212021
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### To be determined

This talk will introduce ambidexterity, a key feature of the T(n)-local and K(n)-local stable homotopy categories.

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• Feb 282021
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### To be determined

This talk will sketch the argument of Carmeli–Schlank–Yanovski allowing one to bootstrap ambidexterity from the K(n)-local category to the T(n)-local category.

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• Mar 072021
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### To be determined

This talk will explain some constructions that are possible as a result of ambidexterity, namely the chromatic Fourier transform, and cyclotomic Galois extensions of the T(n)-local sphere

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• Mar 142021
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### Tomer Schlank

This talk will explain a proof of the height 1 telescope conjecture via checking descent with respect to the maximal cyclotomic extension of the T(1)-local sphere.

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This seminar is organized by Ishan Levy.