I work in the interface of commutative algebra and algebraic geometry. I am interested in questions that aim to understand the local behavior of shapes or geometric objects that are solutions to polynomial equations. One can study such solutions in various algebraic objects called rings, like the ring of integers, the ring of real numbers, the ring of complex numbers or in more exotic rings like rings with a prime number of elements (for instance the binary numbers used in computer science). I often think about the local behavior or singularities of solutions of polynomial equations over rings with a finite number of elements.