Please join the Department of Mathematics for the Brown/MIT Joint Geometric Analysis Seminar on April 13, 2026.

Register to Participate

• Registration/Check in will be in the Kassar House Common Room, 151 Thayer Street
• Talks will be in MacMillan Hall, Room 115, 167 Thayer Street

View the poster for full seminar schedule details.

Chao Li Courant Institute (NYC) 3:00-4:00pm, MacMillan Hall 115 Immersions of small normal curvature Given a closed manifold and a sufficiently large integer N, we study the smallest possible normal curvature, C_N(X), of all immersions of X into the unit ball of the N dimensional Euclidean space. This question was recently initiated by Gromov, who studied the case when X is the n-dimensional torus via Hilbert’s rational spherical design. In this talk, we will discuss small-curvature immersions of products of spheres via minimal Veronese mappings, and prove the optimality of such immersions in some cases via intrinsic comparison geometry.

Antoine Song California Institute of Technology 4:30-5:30pm, MacMillan Hall 115 Harmonic maps into high-dimensional spheres I will survey recent developments related to harmonic maps from surfaces to Euclidean spheres. Given a closed Riemann surface and a unitary representation of its fundamental group, classicalvariational theory produces a corresponding equivariant harmonic map from the Poincaré disk to a Euclidean sphere. In general not much can be said about the geometry of such maps. However, I will explain that by leveraging the theory of random matrices, if the representation is sufficiently generic, then the corresponding harmonic map becomes very close to an immersed hyperbolic plane inside a sphere. Moreover, the asymptotic limit is essentially unique. As one application, Ancona & Labourie & Roig Sanchis & Toulisse found a strong solution to a problem of S.T. Yau’s 1982 list about the existence of negatively curved minimal surfaces in spheres. Partly joint with Riccardo Caniato and Xingzhe Li.