Kenz Kallal, a mathematician at Princeton University, presents a joint IAS/Princeton number theory seminar on theta functions, arguing for a purely algebraic route to a fact usually proved analytically. Jacobi's theta function and its relatives associated to positive-definite quadratic forms are modular forms of half-integral weight, traditionally shown via the Poisson summation formula. Kallal instead ties the theta function to heat diffusion on a circle, recasting the heat equation as a flat connection on a bundle over a modular curve, which yields an algebraic proof of modularity. The talk builds on and refines earlier algebraic theories of theta functions due to Moret-Bailly, Faltings-Chai, and Candelori, extending the framework to indefinite quadratic forms and non-ample line bundles, cases the earlier theory could not reach. Kallal also describes how this generalizes the Kudla-Millson analytic theory to torsion coefficients, work in progress with Akshay Venkatesh. The seminar runs 67 minutes and assumes graduate-level background in modular forms and algebraic geometry.