Many real-world processes evolve in cascades over complex networks, whose topologies are often unobservable and change over time. However, the so-termed adoption times when blogs mention popular news items, individuals in a community catch an infectious disease, or consumers adopt a trendy electronics product are typically known, and are implicitly dependent on the underlying network. To infer the network topology, a dynamic structural equation model is adopted that captures the relationship between observed adoption times and the unknown edge weights. Assuming a slowly time-varying network and leveraging the sparse connectivity inherent to social networks, edge weights are estimated by minimizing a sparsity-regularized exponentially-weighted least-squares criterion. An alternating-direction method of multipliers solver is developed to this end, and preliminary tests on synthetic network data corroborate the effectiveness of the novel algorithm in unveiling the dynamically-evolving network topology.