Exotic Boundaries and Interfaces of Gapless Topological MatterWe study boundary and interface phenomena in symmetry-enriched critical matter, including gapless symmetry-protected topological (gSPT) phases, asking how critical correlations yield a richer bulk–boundary correspondence. First, we analyze boundaries at a transition between distinct SPT phases: incompatible edge modes lead to highly frustrated boundary behavior, including a non-Landau “deconfined quantum critical” transition. Second, motivated by the search for lower-dimensional signatures of gSPTs, we initiate a study of spatial interfaces between inequivalent gapless theories. The resulting non-invertible conformal defects, which are tightly constrained and may host localized degenerate modes or anomalies, provide both a defining indicator of symmetry-enriched criticality and a new window into the novel phenomena that gapless topological phases exhibit.