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.
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.
Teaching
In Fall 2018, I was an instructor for Math 224, Integral calculus of one-variable functions.
In Winter 2019, I am an instructor for Math 230, Differential calculus of multivariable 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.)
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.)
Talbot Workshop 2016, on Hill-Hopkins-Ravenel's proof of the Kervaire invariant one problem (including an introduction to equivariant homotopy theory).
Talbot Workshop 2015, on applications of operads (including configuration spaces and knot theory, formality and deformation quantization, embedding calculus, and the Grothendieck-Teichmuller group).
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)
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 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)
From 2014–2018 I was an organizer for the Talbot workshop, a week-long mathematical retreat in the spring where graduate students learn about a topic in algebraic topology (or surrounding areas).