Algebraic geometry is a branch of mathematics that studies geometric objects defined by polynomial equations, such as algebraic curves and algebraic surfaces. It combines techniques from algebra and geometry to understand the underlying structure and properties of these objects. Algebraic geometry has applications in diverse fields such as physics, computer science, and cryptography, and has deep connections to number theory and topology. Researchers in algebraic geometry study various topics including varieties, schemes, sheaves, cohomology, and moduli spaces.