9 problems

Let $A_d$ denote the set of real algebraic numbers of degree $d$. A real number is badly approximable if its rational approximations do not achieve arbitrarily small errors relativ…

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 … These are the badly approximable real numbers. The conjecture on algebraic badly approximable numbers. The only algebraic numbers belonging to $\mathbf{Bad}$ are quadratic ir…

Winning criterion conjecture.

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

Schmidt's conjecture. For any $\alpha_1,\alpha_2,\beta_1,\beta_2\in[0,1]$ satisfying $\alpha_1+\beta_1=\alpha_2+\beta_2=1$, the intersection

Schmidt's conjecture. For any $alpha_1,alpha_2,beta_1,beta_2\in[0,1]$ satisfying $alpha_1+beta_1=alpha_2+beta_2=1$, the intersection

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…

Schmidt's conjecture. For any $calpha_1,calpha_2,cbeta_1,cbeta_2cin[0,1]$ satisfying $calpha_1+cbeta_1=calpha_2+cbeta_2=1$,