My group studies probabilistic graphical models and develops theory, methodology and algorithms to allow application of these models to scientifically important novel problems. In particular, our work to date has broken new grounds on providing a systematic approach to studying graphical models. We use a holistic approach that combines ideas from applied algebraic geometry, combinatorics, convex optimization, mathematical statistics, and machine learning. By leveraging the inherent algebraic structure in graphical models, we have uncovered statistical and computational limitations for learning directed graphical models to perform causal inference. In addition, my group develops scalable algorithms with provable guarantees for learning graphical models in genomics, in particular for learning gene regulatory networks. Gene regulation is inherently linked to the spatial organization of the DNA in the cell nucleus. In order to understand the mechanisms underlying gene regulation, my group works towards deciphering the codes that link the packing of the DNA with gene expression. Towards this goal, my group has introduced a new geometric model for the organization of chromosomes that is based on the theory of packing in mathematics: we view a chromosome configuration  as a minimal overlap configuration of ellipsoids. My group has successfully applied this model to predict the reorganization of chromosomes that happen during changes of cell shape as they occur for example during reprogramming. We envision that such models will provide important insights into processes such as differentiation, trans-differentiation or reprogramming, where it is essential to understand the coupling between cell shape, chromosome organization and gene regulation.