Hi, I'm Howard! I'm a senior at MIT, majoring in Pure Mathematics Research interests: equivariant and chromatic homotopy theory, and algebraic K-theory and its friends Contact information: Howard Beck, (firstinitial)(lastname)[at]mit[dot]edu (a futile attempt at spam protection) CV - updated Mar 14, 25

Upcoming travel

Find me at:

• June 9-13: University of Copenhagen Arithmetic and Homotopy Theory masterclass
• June 16-20: Isaac Newton Institute, Cambridge, UK: Beyond the telescope conjecture workshop
• June 23-August: University of Bonn
• September - ??: Northwestern University

Preprints

In progress: Chromatic blueshift conjecture: the simple case and an algebraic analogue, joint with Kyle Roke.
Supervised by Tristan Yang and Professor Jeremy Hahn

Using power operations, we show that the Chromatic Blueshift Conjecture of Burkland, Schlank, and Yuan holds for certain E_$\infty$-rings, at prime cyclic groups $C$_$p$ with the trivial family and at all chromatic heights.
> draft available upon request

Some of my writings that may be useful or of interest:

Presentation notes from the Kan Seminar at MIT, spring 2025:

La cohomologie modulo 2 de certains espaces homogènes (Feb 7th, 2025 - first talk of the Kan Seminar)

Notes from my talk at Zygotop on chromatic redshift and blueshift will appear here at some point...

Live notes from Babytop Spring 2025 can be found here

The Slice, Reduction, and Gap Theorems of Hill-Hopkins-Ravenel

Given on December 4th, 2024 at the graduate-student run joint MIT/Harvard Babytop seminar, organized this semester by Natalie Stewart. My talk covered sections 6-8 of the Hill-Hopkins-Ravenel paper about the Kervaire invariant one problem.
Note: These notes are undergoing historical revisionism. They have some small errors and places deserving more clarification. Also, two sections are missing since they were handwritten... that'll be fixed.

Presentation notes on classifying spaces, simplicial sets, and Čech categories
Presentation notes on characteristic classes

These are notes from presentations I gave for the 18.906 (Algebraic Topology II) reading group in Fall 2024 at MIT. The class is unusually not being offered this year, so the reading group is "replacing" the class. It's based on Professor Haynes Miller's lecture notes, available on his website. I would like to thank Professor Miller for his contributions to these notes, by pointing out mistakes and giving insightful comments during the presentation that were included in the notes afterwards. My other presentations used written notes that are... somewhere.

Other shenanigans

If I were a Springer-Verlag Graduate Text in Mathematics, I would be Frank Warner's Foundations of Differentiable Manifolds and Lie Groups. I give a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. I include differentiable manifolds, tensors and differentiable forms. Lie groups and homogenous spaces, integration on manifolds, and in addition provide a proof of the de Rham theorem via sheaf cohomology theory, and develop the local theory of elliptic operators culminating in a proof of the Hodge theorem. Those interested in any of the diverse areas of mathematics requiring the notion of a differentiable manifold will find me extremely useful. Which Springer GTM would you be? The Springer GTM Test

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