Michael Albanese
Reputation
91/100 score
 Apr18 accepted Does a complex manifold always admit an acyclic cover for the sheaf of holomorphic functions? Dec1 accepted When is a vector field on a manifold restricted to a submanifold $X$ a vector field on $X$? Aug25 accepted Can we measure how close a vector bundle is to being trivial? Aug25 accepted The number of connected components of $SL(2, \mathbb{R})$ which keep $x^2 - y^2$ invariant Aug23 accepted Given an $(n-1)$-form $\varphi$ on a smooth orientable $n$-manifold, there is a vector field $v$ such that $i_v\varphi = 0$. Aug22 accepted Conformal map between $\mathbb{C}\setminus((-\infty, -1]\cup[1,\infty))$ and $\{z \in \mathbb{C} \mid 0 < \operatorname{Im}(z) < 7\}$ Aug18 accepted Show that $S = \{f \in L^1(\mathbb{R}) \mid \int_{\mathbb{R}}f dm = 0\}$ is closed in $L^1(\mathbb{R})$. Aug17 accepted Show that the set of one-to-one holomorphic maps $\Bbb{C}\setminus\{a,b,c\} \to \Bbb{C}\setminus\{a,b,c\}$ forms a finite group. Aug17 accepted Show that the kernel of the map $SL(n, \mathbb{Z}) \to SL(n, \mathbb{Z}/3\mathbb{Z})$ has no torsion. Aug16 accepted Let $A$ be an $n\times n$ invertible complex matrix such that $A^7 = A^*$. Show that $A^8 = I$. Aug16 accepted If $E, F \subset [0, 1]$, $m(E), m(F) > 0$, and $E_n = \{x \in [0, 1] : nx \bmod 1 \in E\}$, show $m(F\cap E_n) > 0$ for sufficiently large $n$ Aug16 accepted Exercise on Radon measures, constructing a convergent sequence Jul22 accepted $E \subseteq [0, 1]$, $m(E) > 0$. Show that there are $\alpha$ and $\beta$ such that $\alpha, \alpha + \beta, \alpha + 2\beta \in E$. Jun17 accepted Every non-trivial holomorphic involution on the open unit disc has a unique fixed point Jun13 accepted What is elliptic bootstrapping? Jun13 accepted What is a Kählerian variety? Jun13 accepted If $\omega^k$ is exact, is $\omega$ exact? Jun10 accepted Basic questions about $E[E[X \mid Y]]$ Jan4 accepted Is every almost complex structure tame up to sign? Dec27 accepted Showing a group is isomorphic to a group with known presentation