T-Varieties via Combinatorics

Toric varieties have been a hot topic in recent years, finding applications in fields ranging from mirror symmetry to coding theory. $T$-varieties, that is, normal varieties with an effective action by some torus $T$, provide a natural generalization. In this talk, I will give a gentle introduction to $T$-varieties, focusing on the combinatorial approach started by K. Altmann and J. Hausen.