Spring 2020

In Spring 2020, Juvitop was about Pretalbot: Chromatic Homotopy Theory.

• • Feb 042020
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  Introduction

  Dylan Wilson

  Note special time 3pm and place, MIT Room 2-151

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• • Feb 122020
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  Formal Group Laws and Complex Oriented Cohomology Theories

  Dexter Chua

  Notes

  I will introduce the notion of complex oriented cohomology theories from the point of view of orientation theory. I will then discuss the relation between complex oriented cohomology theories and formal group laws.

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• • Feb 192020
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  Universality of $MU$ and Quillen's Theorem

  Knut Haus

  I will talk about the ingredients of Quillen's geometric proof of his theorem that MU^*(pt) carries a universal formal group law. Going through the entire proof in detail is of course not feasible, but I will present some of the geometric ideas that go into it.

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• • Feb 262020
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  Moduli Stack of Formal Group Laws

  Morgan Opie

  Last week, we saw that pi_*MU is the Lazard ring L, which classifies formal group laws. This facilitates a translation from homotopy theory to algebraic geometry: MU-homology can be understood in terms of quasicoherent sheaves on Spec L, and equivalences of group laws can be encoded in terms of an action of an algebraic group. In order to obtain an algebro-geometric object classifying formal groups, we want to quotient by this action. However, this is not a legal move in the category of schemes, which leads us to consider stacks. Our goal in this talk will be to give basic definitions and concrete examples of stacks, with a focus on the moduli stack of formal groups.

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• • Mar 042020
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  ANSS and Sheaf Cohomology on the Moduli Stack of Formal Groups

  Tim Large

  We will recall the moduli stack of formal groups, and explain how the MU-homology of a spectrum defines a quasi-coherent sheaf on this stack. We will then relate its sheaf cohomology to the E_2 term of the Adams-Novikov spectral sequence.

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• • Mar 112020
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  Formal Group Laws in Characteristic Zero

  Ishan Levy

  Notes

  We will discuss Lazard's ring, and its consequences for formal group laws of characteristic zero. This will be made explicit using the logarithm and then we will move on to characteristic p, and discuss the notion of height and its geometric meaning. If people are interested and there is time, I can also explain how to compute Lazard's ring.

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• • Apr 012020
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  Height of a formal group as a complete invariant

  Nir Gadish

  Notes

  We are on a path towards understanding the moduli stack of formal groups via its height filtration. Our main goal for the next lecture is the statement that height is the only invariant over an algebraically closed field. We will also see that there exist formal group laws of every height.

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• • Apr 082020
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  The Landweber Exact Functor Theorem

  Kevin Chang

  Notes

  We will discuss the Landweber exact functor theorem and sketch a proof. We will also talk about some applications and connect the theorem to what we've learned about the moduli stack of formal groups.

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• • Apr 152020
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  Morava stabilizer groups

  Lucy Yang

  This talk will discuss the structure of the endomorphism ring of the unique (up to isomorphism) formal group of height n over F_p and the Morava stabilizer group.

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• • Apr 222020
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  Goerss-Hopkins obstruction theory

  Jun Hou Fung

  Notes

  In this talk, we'll set up Goerss-Hopkins obstruction theory and use it to show that Morava E-theory has a unique E_∞-ring structure.

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• • Apr 292020
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  Open Questions in Chromatic Homotopy Theory

  Jeremy Hahn
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This seminar was organized by Araminta Amabel, Morgan Opie, and Lucy Yang.