# Eva Belmont

 Northwestern University Department of Mathematics Office: Lunt B5 Email:   ekbelmont at gmail dot com CV

I am a Boas Assistant Professor at Northwestern University. My main research interests are in stable homotopy theory. I completed my doctoral work at MIT in 2018 under the supervision of Haynes Miller. I received my B.A. from Harvard, and Master's from Cambridge University ("Part III").

## Research

My current research focuses on computational aspects of classical and motivic stable homotopy theory.
• My Ph.D. thesis, Localization at $b_{10}$ in the stable category of comodules over the Steenrod reduced powers, represents progress towards computing the $b_{10}$-periodic part of the Adams $E_2$ page for the sphere at $p = 3$.
• Localizing the $E_2$ page of the Adams spectral sequence (the paper version of my thesis, part 1). This paper is about a spectral sequence converging to an infinite piece of the Adams $E_2$ term for the sphere at $p = 3$. We compute up to the $E_9$ page of an Adams spectral sequence in the category $\mathrm{Stable}(P)$ converging to $b_{10}^{-1}\mathrm{Ext}_P(\mathbb{F}_3, \mathbb{F}_3)$, and conjecture that the spectral sequence collapses at $E_9$.
• A Cartan-Eilenberg spectral sequence for a non-normal extension (the paper version of my thesis, part 2)
This paper compares three ways to construct a Cartan-Eilenberg type spectral sequence associated to a map $\Phi \to \Gamma$ where $\Gamma$ is a Hopf algebra and $\Phi$ is a $\Gamma$-comodule algebra. This is the main tool required for the above paper.
• I am currently working with Dan Isaksen in computing the $\mathbb{R}$-motivic Adams spectral sequence for the sphere.

## Research talks

• Chromatic localization in an algebraic category, a talk I gave at the conference "Chromatic homotopy: Journey to the frontier" held in Boulder, Colorado in May 2018. I give an introduction to Palmieri's work on the homotopy theory of modules over the Steenrod algebra, with emphasis on the analogues of the nilpotence and periodicity theorems, and discuss how this relates to my thesis work about the $E_2$ page of the Adams spectral sequence at $p=3$.
• Slides for my talk in ECHT in April 2019 about the $\mathbb{R}$-motivic Adams spectral sequence and its relationship to the Mahowald invariant.

## Teaching

• In Fall 2018 and Spring 2019, I was an instructor for Math 224, Integral calculus of one-variable functions.
• In Winter 2019, I was an instructor for Math 230, Differential calculus of multivariable functions. I am currently teaching Math 230-1 (the same course, renumbered).

## Expository Writing

• Complex Cobordism and Formal Group Laws, Part III essay about Quillen's theorem that $MU$ has the universal formal group law, including the construction of the Adams spectral sequence and basics about formal group laws. (If you want to look at this, email me to ask for a copy.)
• Stable Homotopy and the J-Homomorphism, undergraduate senior thesis about Adams' work on the splitting of the stable homotopy groups of spheres.

## Class Notes

As a student, I live-TeXed many classes and seminars. Some of the notes can be found here.