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14h
comment How one can use a real math function on transaction in Hybrid Petri Net fundamental equation?
With a little more background, this question can be asked in an appropriate stackoverflow. This is not a research-level mathematics question.
Feb
4
revised Analytic continuation of the double sum $\sum_{n,m\ge0}x^ny^mt^{nm}$
math error makes this not an actual solution
Feb
4
comment Analytic continuation of the double sum $\sum_{n,m\ge0}x^ny^mt^{nm}$
That is a very good point. @WeatherReport, if you were interested in $f(x,y,t) + f(x^{-1}, y, t^{-1})$ then the above derivation should work (with $x$ replaced by $y$). Are you sure that what you want is $f(x,y,t) + f(x^{-1}, y, t)$?
Feb
3
answered Analytic continuation of the double sum $\sum_{n,m\ge0}x^ny^mt^{nm}$
Jan
26
revised What kind of geometric object is the Pauli spin matrix vector $\vec{\sigma} = (\sigma_1, \sigma_2, \sigma_3)$?
edited body
Jan
26
answered What kind of geometric object is the Pauli spin matrix vector $\vec{\sigma} = (\sigma_1, \sigma_2, \sigma_3)$?
Jan
20
comment What is modern algebraic topology(homotopy theory) about?
Give me an area of mathematics that doesn't care about K theory :)
Jan
19
revised What is modern algebraic topology(homotopy theory) about?
added paragraph on moduli spaces
Jan
19
answered What is modern algebraic topology(homotopy theory) about?
Jan
17
awarded  Popular Question
Jan
12
comment Geometric Interpretation of Trace
I want to bump up Sujit Nair's answer, which is how I think about it. Trace is the derivative of |1+tA|. This is the lie theoretical interpretation.
Dec
26
comment Algebraic K theory, Karoubi completion and splitting
Sure. Take complexes of vector spaces of even total dimension.
Dec
26
asked Algebraic K theory, Karoubi completion and splitting
Dec
24
comment When does algebraic K theory behave like a cohomology theory
What I want is an invariant of the ring $\text{Chains}\Omega(X)$, whose $\pi_0$ admits a map from the Grothendieck group of $\text{rep}\Omega(X)$, which I want to define as the category of (homologically) graded finite-dimensional $\mathbb{F}$ spaces with homotopy action by the group $\Omega(X)$ (a pre-triangulated DG category).
Dec
22
awarded  Citizen Patrol
Dec
22
asked When does algebraic K theory behave like a cohomology theory
Dec
12
accepted Does quantum mechanics ever really quantize classical mechanics?
Dec
12
awarded  Nice Question
Dec
11
comment Does quantum mechanics ever really quantize classical mechanics?
Thanks, your blog post was exactly what I was looking for.
Dec
11
comment Vector bundle $L$ admits connection if and only if degree of every direct summand of $L$ divisible by $\text{char}\,k$, intuition
Well, as you point out, the Frobenius pullback of a bundle always has a connection. So to prove the converse it would be enough to show that any indecomposable degree-zero bundle is a Frobenius pullback. Frobenius pullback is is the stacky frobenius applied to Bun_X(G) for $G = GL_n$, so (if this method works), you'd want to show that the behavior of the irreducible, degree-zero part of this stack is "geometric enough" that the Frobenius is invertible on points. You might try to do that using some stability filtration... this is just a guess.