# 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 stable homotopy theory and motivic homotopy theory. In particular, my thesis work represents progress towards computing the $b_{10}$-periodic part of the Adams $E_2$ page for the sphere at $p = 3$. Here are links to my research statement and slides from an AMS sectional meeting talk.

## Teaching

• I am an instructor for Math 224, Integral calculus of one-variable functions.

## 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

For the past few years I have been live-TeXing many of the math courses and seminars I attend. Here are some of the notes. (This is not an exhaustive list; if you're interested in something else you think I might have notes for, feel free to ask me via email.)

### MIT courses (taken as a graduate student)

• 18.917: The Gamma function and the field with one element, taught by Clark Barwick. Tate's thesis, $\mathbb{F}_1$, cyclotomic spectra, $THH$ and zeta functions. (pdf, tex) (Spring 2017)
• 18.786: Number theory II, taught by Bjorn Poonen. Tate's thesis, Galois cohomology, introduction to Galois representation theory, including the statement of the local Langlands correspondence. (Spring 2015)
• 18.785: Algebraic number theory, taught by Bjorn Poonen. Algebraic number theory (up through adèles, Dirichlet's unit theorem, and finiteness of the class group), and a short introduction to analytic number theory. (Fall 2014)
• 18.965: Geometry of manifolds, taught by Paul Seidel. Differential topology and differential geometry. (Fall 2013)

### Cambridge (Part III), 2012-2013

• Elliptic curves, taught by Tom Fisher. Introduction to elliptic curves over $\mathbb{F}_p$, local fields, and $\Q$.
• Lie algebras, taught by C. Brookes. Lie algebras, root systems, representation theory of Lie algebras.
• Algebraic geometry, taught by Caucher Birkar. Sheaves, schemes, sheaf cohomology.
• Commutative algebra, taught by Nick Shepherd-Barron. Roughly follows Atiyah-Macdonald, plus modules of differentials, and some homological algebra.

### Harvard (some courses I took as an undergraduate)

• Math 229: Analytic number theory, taught by Barry Mazur. Zeta functions and functional equations, the prime number theorem, Dirichlet $L$-functions, Artin $L$-functions, primes in arithmetic progressions. (Spring 2012)
• Math 232a: (Classical) Algebraic geometry, taught by Xinwen Zhu. Course on varieties, following Mumford's Complex Projective Varieties. (Fall 2011)
• Math 114: Real analysis, taught by Peter Kronheimer. Measure, integrability, Fourier series, $L^p$ spaces. (Fall 2011)
• Math 231br: Algebraic topology (notes taken by Akhil Mathew and me), taught by Michael Hopkins. Serre spectral sequence, Eilenberg-Maclane spaces, model categories, simplicial sets, rational homotopy theory of spheres. (Spring 2011)