31,033 reputation
364141
bio website math.tsukuba.ac.jp/~carnahan
location 筑波市, Japan
age
visits member for 5 years, 11 months
seen 29 mins ago
I think this is a neat project.

1d
comment Are there open problems for primes which are known for probable primes?
@TerryTao I had been a bit hesitant to post this answer because it seemed rather trivial, but your observation makes it look much more interesting.
2d
answered Are there open problems for primes which are known for probable primes?
2d
comment Most dense subset of numbers that avoids arbitrarily long arithmetic progressions
The two links seem to go to the same place.
2d
comment A road to inter-universal Teichmuller theory
One of Mochizuki's progress reports has a list of what parts of which earlier papers you need to read to understand the IUT series.
Sep
1
comment Encyclopedia of Mathematics?(non-Alphabetical)
The Princeton Companion is not a bad substitute.
Aug
31
comment Decomposition of orthogonal matrix into 2 orthogonal matrices
Am I allowed to set $Q$ to be identity?
Aug
31
comment Does an element in the center of universal enveloping algebra becomes a scalar in irreducible representations?
@JunekeyJeon Yes, if $G$ is connected, then $G$ is generated by exponentials of elements in the Lie algebra. This implies the two versions of invariance are the same.
Aug
29
answered Does an element in the center of universal enveloping algebra becomes a scalar in irreducible representations?
Aug
29
answered Non-standard numbers and exponential form of Zeta function
Aug
28
comment Tangent space of Hilbert scheme
A normal vector field on $Y$ lets you wiggle $Y$ in $X$ (infinitesimally) without changing the Hilbert polynomial.
Aug
21
answered Any representation is a sub representation of direct sum of regular representation
Aug
17
comment Important formulas in Combinatorics
I wish I knew a good reference that described the physical picture in detail, with $z$ giving momentum and $q$ giving energy. For the mathematical side, I would first suggest "Bombay lectures" by Kac, Raina, and Rozhkovskaya. Then there is the last chapter of Kac's "Infinite dimensional Lie algebras". Finally, there is section 5.3 of Frenkel and Ben-Zvi's "Vertex Algebras on Algebraic curves".
Aug
17
comment Important formulas in Combinatorics
This has a more-or-less equivalent interpretation in terms of boson-fermion correspondence. The left side is the character of an infinite dimensional spinor representation, while the right side is the character of bosonic strings compactified on a circle. There is an isomorphism of the respective vertex superalgebras, and this yields an equality of characters.
Aug
15
answered Classification of finite group schemes over a field
Aug
15
comment “set of all irreducible representations of a group”, set-theoretic issues
This is more or less answered in the second paragraph of Borcherds's reply to the "Wiles's theorem uses inaccessible cardinals" question mathoverflow.net/a/35762/121 Your reasoning also eliminates the possibility of classifying groups of order 4 up to isomorphism.
Aug
13
comment The formal p-adic numbers
@DavidRoberts I've never read Coq before, but it looks like they simply define $p$-adic integers as infinite sequences of integers between 0 and p-1, equipped with an add-with-carry rule.
Aug
12
comment Topological Subset Take-Away
I don't see why, in Gale's original game, the same player wins for both $|S|=1$ and $|S|=2$.
Aug
11
comment Reference for higher categorical analogue of algebraic cycle?
-1: You really need to be more specific.
Aug
9
comment Kac moody algebras and Weyl groups
When you say "doubt", do you mean "question"?
Aug
8
comment reference for “Topological algebra of Grothendieck”
The bottom of this page: pages.bangor.ac.uk/~mas010/pstacks.htm suggests that "Pursuing stacks" is a good first step.