### DIMACS Theoretical Computer Science Seminar

Title: Unconditionally Differentially Private Mechanisms for Linear Queries

I will talk about the problem of designing differentially private mechanisms for a set of $d$ linear queries over a database represented as a vector, while adding as little error as possible. Hardt and Talwar~\cite{HT} related this problem to geometric properties of a convex body defined by the set of queries and gave a $O(\log^3 d)$-approximation to the minimum $\ell_2^2$ error, assuming a conjecture from convex geometry called the {\em Slicing} or the {\em Hyperplane} conjecture. I will show a mechanism that works unconditionally, and also gives an improved $O(\log^2 d)$ approximation to the expected $\ell_2^2$ error.