Open Problems in Diophantine Approximation and Geometry of Numbers

Explore several specialized open problems in Diophantine Approximation and Geometry of Numbers in this 1-hour 8-minute lecture. Delve into intriguing mathematical challenges that, while not widely known, have connections to various mathematical fields and may lead to counterintuitive results. Focus on the approximation of linear or affine subspaces in $\mathbb{R}^d$ by rational subspaces, including the case of approximating a single irrational number $\alpha$ (case $d=2$). Examine key topics such as coprime inhomogeneous approximation, problems related to Minkowski function, Diophantine spectra, exponents of growth and Diophantine exponents, and approximation in terms of angles of inclination. Gain insights into these complex mathematical concepts and their potential implications for broader mathematical understanding.