bio | website | math.berkeley.edu/~ericp |
---|---|---|
location | UC-B | |
age | 26 | |
visits | member for | 4 years, 9 months |
seen | 3 hours ago | |
stats | profile views | 3,823 |
Graduate student. Interested primarily in homotopy theory and the interactions of algebraic geometry with algebraic topology, but also in lots of other things, including Lie theory, mathematical physics, complex geometry, and graduating.
Jul 19 |
comment |
Spectral sequences: opening the black box slowly with an example
For anyone reading this in the distant future: Sean is certainly right to mention the Bockstein spectral sequence. Often those BSSes arising from algebraic situations have differentials which are completely computable. There is a great nest of algebraic examples in Miller--Ravenel--Wilson's famous Periodic phenomena in the Adams--Novikov spectral sequence. |
Jul 7 |
reviewed | Approve suggested edit on Too old for advanced mathematics? |
Jul 2 |
awarded | Curious |
Jun 29 |
comment |
How nilpotent is the ring of stable homotopy groups of spheres?
At the very least, the proof of Nishida's theorem in II.2.2.9 of Bruner--May--McClure--Steinberger comes with a bound, dependent upon the torsion order of the element x, and there are in turn bounds on the amount of torsion that can appear in a particular degree. May says that Nishida's original proof gives better bounds, and maybe more is known besides those initial things, but definitely bounds are known. |
Jun 27 |
reviewed | Approve suggested edit on How do you show that $S^{\infty}$ is contractible? |
Jun 5 |
reviewed | Approve suggested edit on Are quotients of affine schemes by finite groups faithfully flat? |
Jun 4 |
reviewed | Approve suggested edit on Regarding Kolmogorov's Superposition Theorem |
May 19 |
comment |
The cell structure of Thom spectra
Turns out Mosher did some calculations along these lines in the 60s: sciencedirect.com/science/article/pii/0040938368900268 . |
May 6 |
reviewed | Approve suggested edit on How to publish two interdependent papers |
May 5 |
revised |
Why is Milnor K-theory not ad hoc?
fixed broken mathjax |
May 4 |
awarded | Great Question |
Apr 4 |
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Units of a ring spectrum
My understanding is that constructing a sane notion of spectra of units sensitive to coconnective information is an interesting open problem. As spaces of units were initially developed to understand twists of spectra parametrized over a space, and as all spaces are themselves connective, this insensitivity wasn't initially considered to be an issue. Steffen Sagave has proposed a model for periodic $E_\infty$ ring spectra; maybe you'd enjoy reading about that. arxiv.org/abs/1111.6731 |
Mar 28 |
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Are there any cool applications of the generalized Atiyah-Hirzebruch(-Serre) spectral sequence?
I don't know how striking this is, but I like the example of computing $E^* BZ/p$ for $E$ a $p$-complete complex-orientable theory via the fiber sequence $S^1 \to BZ/p \to CP^\infty \xrightarrow{p} CP^\infty$. The spectral sequence has a single differential, which upon choice of coordinate is given by the $p$-series of the orientation. Probably it's possible to state this as "First compute $(HZ_p)_*(BZ/p)$, then compute the AHSS," but it seems that justifying this description of the differential in that setting might be more cumbersome...? |
Mar 2 |
reviewed | Approve suggested edit on How many 2L-bit numbers are the product of two L-bit numbers? |
Feb 26 |
reviewed | Approve suggested edit on Method to compute fundamental solutions which are distributions |
Feb 18 |
reviewed | Approve suggested edit on First order stochastic dominance and rearrangement inequalities |
Jan 30 |
comment |
Stable moduli interpretation of $\mathbb{R}\mathrm{P}^\infty_{-1}$
Oh, no, I'm not sure at all. Not only was I not following the talk perfectly, but as a stable homotopy person I'm susceptible to quietly localizing everything and forgetting about it. |
Jan 29 |
revised |
Stable moduli interpretation of $\mathbb{R}\mathrm{P}^\infty_{-1}$
phrasing |
Jan 29 |
asked | Stable moduli interpretation of $\mathbb{R}\mathrm{P}^\infty_{-1}$ |
Jan 25 |
reviewed | Approve suggested edit on Higher vanishing cycles |