Abstract We are poised to enter a new era of conformational biology. Genome conformation is critical for numerous cellular processes, including gene regulation, with certain alterations (translocations, fu- sions) being oncogenic. While recent assays, notably Hi-C, have already transformed understanding of chromatin architecture, even newer technologies have the potential to dramatically improve accuracy and resolution of three-dimensional (3D) genome reconstructions. However, to fully realize this potential, new statistical methods and algorithms will be required to operate on the resultant data and structures, and to integrate concomitant biomedical data. This project aims at developing such methods. A concrete example is provided by current findings identifying an instance of insulated neighborhood disruption as a novel oncogenic mechanism. Instead of an individual instance, we will develop methods to detect, and prioritize, genome-wide candidates, building on our previous work on 3D hotspot elicitation. In particular, we will devise original reconstruction-free approaches to avert uncertainties in inferring architecture. Despite these uncertainties, reconstructions confer several advantages. We will deploy newly devised assays, in conjunction with recent algorithmic advances, to improve reconstruction accuracy and resolution. Multiplexed FISH provides richer imaging of chromatin conformation, enabling refinement of transfer functions linking Hi-C contacts to distances, a precursor to reconstruction. Protein-centric HiChIP provides gains in informative reads, as does multi-read rescue. Combining these advances will produce enhanced approaches to 3D genome reconstruction. The very notion of ?a? 3D genome reconstruction has been questioned since the underlying Hi- C assays are based on large cell populations. Multiplexed in situ Hi-C has enabled generation of thousands of single-cell datasets which we will couple with a new multi-track reconstruction algorithm to dissect inter-cellular structural heterogeneity. We will also use this data to develop classifiers, based on structural differences, for between cell-type discrimination. Much downstream interpretation of Hi-C data has derived from spectral analysis of the contact matrix, especially delineation of chromatin compartments. Spectral summarization has limitations including compartment identification at high resolution, sensitivity to normalization, and extent of explained variation. We will evaluate spectral analysis of contact matrices with emphasis on the impact of approximations on 3D reconstructions, assessed via (i) inferred distance matrices, (ii) derived reconstructions, and (iii) subsequent hotspot detection.