Salim Tayou, speaking in the joint IAS/Princeton University Number Theory seminar, presents new progress on a conjecture posed by Stephen Kudla about special cycles in Shimura varieties. He opens with the 1980s theorem of Kudla and Millson showing that generating series built from special cycles in orthogonal and unitary Shimura varieties are modular forms, then turns to Kudla's open question of whether this modularity extends to toroidal compactifications of these spaces. Tayou reports joint work with Francois Greer and Philip Engel that answers the conjecture for divisors in O(p,2) and for cycles in U(n,1) up to the middle degree, working in cohomology. The talk is aimed at specialists and moves through the cohomological machinery needed to extend the classical Kudla-Millson result, situating the new theorem within the broader program connecting arithmetic geometry, automorphic forms, and the structure of special cycles on locally symmetric spaces.