# All Questions

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### The largest size of a boolean subgraph (a hypercube) of a given graph

Let $G(\mathbb{F}_2^n)$ denote the graph that represents the lattice of all subspaces of $\mathbb{F}_2^n$ (also called a Hasse diagram). I am interested in knowing if there exists a large hypercube ...
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### Chow ring of two varieties

Suppose we are given two smooth projective varieties $X$ and $Y$. Maybe this is elementary but what is the Chow ring $CH(X\times Y)$ in terms of $CH(X)$ and $CH(Y)$?
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### Direct image of an ideal sheaf along a blow-up

Suppose that $I\subseteq\mathbb{C}[x_0,\ldots,x_n]$ is a saturated homogeneous ideal. Let $\mathcal{I}\subseteq\mathcal{O}_{\mathbb{P}^n}$ denote the corresponding coherent ideal sheaf, and then let ...
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### Number of representations of an integer as an (arbitrary) sum of products

If $n$ is a positive integer, let $r(n)$ denote the number of representations of $n$ as a sum of products of positive integers. (Here, the order of the terms in the sum does not matter, but products ...
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### endomorphisms of the Jacobian of a curve

Let $C$ be a smooth, projective curve over the complex numbers and let $J(C)$ be its Jacobian. The Torelli theorem relates the automorphisms of $C$ to the automorphisms of $J(C)$. Precisely, ...
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### Are finite-dimensional representations of groups of type $\text{FP}_{\infty}$?

Let $G$ be a group (possibly infinite) and $k$ be a field. A module $M$ over $k[G]$ is said to be of type $\text{FP}_{\infty}(k)$ if it has a projective resolution each of whose terms is finitely ...
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### Connectedness properties of groups of homeomorphisms

Denote by $H(X)$ the group of homeomorphisms of a topological space $X$. Assume further that $X$ is either compact or locally compact and locally connected. In both cases $H(X)$ becomes a topological ...
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### Lie Group Isomorphisms

I'm not sure of the difficulty of the question I'm about to ask. If it does not fit the criteria for this site then I apologize in advance, I'm rather new here. So here it goes: Let $G$ be a Lie ...
Let $G$ be any algebraic subgroup of $\mathrm{GL}_n$ over an algebraically closed field of any characteristic. If $s$ is a semisimple element of $G$, can the $G$-conjugacy class of $s$ fail to be ...