6 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 an $n$-dimensional weight be a vector $\boldsymbol{\mathbf{r}}=(r_1,\dots,r_n)$ with $r_i\geq 0$ and $r_1+\cdots+r_n=1$. A vector $\mathbf{x}\in\mathbb{R}^n$ is…

Winning criterion conjecture.

Schmidt's conjecture.

Folklore conjecture. The only algebraic irrationals that belong to $\mathbf{Bad}$ are the quadratic irrationals.

Let $\mathcal{D}$ be as above. For triples satisfying … let $\mathbf{Bad}_{\mathcal{D}}(i,j,k)$ be the set of $(x,y)\in\mathbb{R}^2$ for which there exists $c(x,y)>0$ such that … w…