5 problems

Consider the four-band Hamiltonian with parameters $(\alpha_0,\alpha_1,\alpha_2)$, and the four regions in this three-dimensional parameter space obtained by removing the exception…

The residue-class description. For $d \equiv 0,1,6,7 \pmod{8}$, the kinematic variety $\mathcal{K}^{(2)}_{d,n}$ consists of all symmetric $n\times n$ matrices with zero diagonal an…

Let ${\mathcal S}_{\mathbb C}^{1,1}$ denote the set of complex Hermitian matrices of rank at most one and signature $(1,1)$, and let…

Let $k$ be an algebraically closed field, let $r$ be a positive integer, let $N=2n$ be an even positive integer, and let $d=(d_1,\ldots,d_N)$ be an $N$-tuple of nonincreasing integ…

F-regularity conjecture for $\mathcal{P}(X)$. The quotient ring