5,641 reputation
1943
bio website math.stanford.edu/~church
location Stanford
age
visits member for 5 years, 10 months
seen 5 hours ago

Aug
25
reviewed Approve Precise interpretability strength of $\mathcal P_{DF}(\omega)$ and $L_{\omega_1^{CK}}$
Aug
18
comment Strategies for proving a category is Noetherian?
Regarding the last sentence and Steven's comment: to prove that FI is Noetherian, the Grobner methods (using that OI -> FI is finite) feel more modern than our original proof in Church-Ellenberg-Farb-Nagpal. (For this question, though, CEFN could still be valuable just for providing another approach to Noetherianness.) In any case, these methods certainly work over Z. In contrast, I believe the result of Nagpal-Sam-Snowden in your third paragraph does not apply except over C; see Question 1.5(3) and the remark following 5.3. Perhaps one of the authors can clarify this?
Aug
12
reviewed Approve A generalization of the Powers-Stormer inequality
Aug
6
comment Suitable reference on smooth manifolds for qualifying exam study?
You should consider reading Bott & Tu's "Differential Forms in Algebraic Topology": not as a resource for smooth manifolds, nor as a resource for algebraic topology, but for the beautiful interplay between them. I benefited greatly from reading it in graduate school, not least because it broadened my perspective on what techniques might be applied to what problems.
Jul
17
comment The evaluation fibration of a transitive, effective topological group action
Do you mean "fibration" or "fiber bundle"? en.wikipedia.org/wiki/Fibration en.wikipedia.org/wiki/Fiber_bundle
Jul
17
comment Properties of loop space functor from homotopy types to group objects in homotopy types
I'm not an expert in any of this material, but it seems to me that it might be helpful to learn about classifying spaces before jumping to $(\infty,1)$-categories.
Jul
17
comment When to postpone a proof?
Your Example 1 is dragging this discussion in the wrong direction, since everyone is going to agree with it: who would object to stating the main theorems in the introduction? The real question is about the structure of arguments within the body of the paper, and when it is appropriate to postpone a proof there. This is an important question, which too many authors neglect to think about when outlining their papers; I hope we'll get to hear a discussion on this point.
Jul
13
reviewed Approve Why is the fundamental group of a compact Riemann surface not free ?
May
27
reviewed Approve The possibility of a symmetric difference in a torsion-free group
May
24
comment Searching for $C^*$
This is clearly a question of interest to research mathematicians (indeed uniquely to research mathematicians).
May
21
comment Will this be a case of self plagiarism or will it annoy the referee?
I'm voting to close this question as off-topic because it belongs on academia.stackexchange.com (and was also asked there: academia.stackexchange.com/questions/45754/…)
May
16
comment Generalize $\pi_0(B\mathcal{C})\cong\{\text{objects}\}/\{\text{morphisms}\}$ to categories internal to topological spaces
The proof you give is not correct. Consider the category $x\rightarrow y\leftarrow z$. There is a path in $B\mathcal{C}$ from $x$ to $z$, but there is no morphism in $\mathcal{C}$ from $x$ to $z$. This contradicts your claim "which means that there is a morphism between x0 and x1"; the mistake seems to be in the earlier claim "yields a path ... but as $N_1(\mathcal{C})$ is discrete, it is constant". As Zhen Lin points out, the correct deduction is that there is a zigzag of morphisms from $x_0$ to $x_1$.
Apr
29
comment Continuous maps to fat geometric realizations of simplicial spaces
Note there is a typo in the statement of Segal's Proposition 4.1: it should say that $\text{pr}\colon BX_U\to X$ is a homotopy equivalence, not $BR_U\to X$.
Apr
28
awarded  Revival
Mar
25
reviewed Approve Can an abelian variety/Q have no non-trivial points over Q_sol?
Mar
24
reviewed Approve Mal'cev “rational equivalence” and model theory
Mar
18
reviewed Approve hyperbolic metrics
Mar
15
answered Does there exist a fibre bundle $K(\mathbb{Z}_4,1)\rightarrow K(\mathbb{Z}_2,1)$ with fiber $K(\mathbb{Z}_2,1)$?
Mar
6
answered Maryam Mirzakhani's works
Mar
6
reviewed Approve latex tag wiki