7 problems

Let $alpha,beta$ be Schmidt-game parameters, and let $gamma_A$ and $gamma_B$ denote the auxiliary constants associated with Alice's and Bob's moves. Let…

Let $D^-_{c}$ denote the set of real numbers whose lower frequency of the digit $0$ is greater than $c$, and let $D(D^-_{c})$ denote its set of Schmidt-game parameters…

Let real two-dimensional weighted badly approximable vectors be defined with respect to two weightings of the approximation problem. Schmidt's intersection conjecture. Any two sets…

Let $d,n\in\mathbb{N}$ and let a weight specify the exponents used to measure simultaneous rational approximation of real $d\times n$ matrices. A set of matrices is weighted badly…

Winning criterion conjecture.

HAW conjecture on $H$. The set

Winning conjecture. For every $m\in\mathbb{Q}$, the set $BA_{\partial X}^{\psi}(X_m(\mathbb{Z}))$ is a (strong) winning subset of $\partial X$.