Massachusetts Institute of Technology
Department of Mathematics
Office: 2-390A
Email: ebelmont at mit dot edu CV
I am a fifth-year Ph.D. candidate in mathematics at MIT working in algebraic topology. My advisor is Haynes Miller. I received my B.A. from Harvard, and Master's from Cambridge University ("Part III"). I am also an avid pianist and chamber musician.
Research
My current research is about computing localized Ext groups with applications to 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.
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)
Teaching
In Fall 2016, I was a recitation instructor for 18.06 (linear algebra).
In Fall 2015, I was a recitation instructor for 18.01 (single-variable calculus). Materials for the section can be found here.
In Spring 2015, I was a recitation instructor for 18.02 (multivariable calculus).
I am one of the organizers 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).
I was a co-organizer for MIT Friends of the Arts, a student group that organizes outings to arts events in the Boston area, with a focus on classical music.