A parabollic flow of coclosed G2-structures with torsion-free fixed points 

15:30 - 15:15

Abstract: We introduce a geometric flow of conformally coclosed G2-structures, whose fixed points on a compact manifold correspond to metrics with holonomy contained in the exceptional Lie group G2. Our main results establish fundamental short-time existence and Shi-type smoothing properties of this flow. Thus, we establish in the affirmative a folklore question in the special holonomy community, about the existence of a well-posed flow for coclosed G2-structures with fixed points given by torsion-free G2-structures. The flow also satisfies a monotonicity formula for the G2-dilaton functional (volume scale in string theory), which leads to a general result on the convergence of nonsingular solutions. Joint work with Andres J. Moreno, Alec Payne, and Jeffrey Streets, in arxiv:2512.14317. 

Grad conjecture for isodynamic flows. A (last?) human-only proof

16:30 - 17:15

Abstract: A steady Euler flow is isodynamic (aka localizable) if the pressure function is constant along its streamlines. This property was used to construct the first smooth compactly supported steady states of 3D Euler. I will sketch the main steps of the proof that an analytic isodynamic 3D Euler flow in a bounded domain must be axisymmetric (in a rotationally symmetric toroidal domain with convex section).

Splitting and Merging of Stagnation Points for the 2D Navier-Stokes Equations

17:15 - 18:00

Abstract: The two-dimensional Navier-Stokes equations model the behavior of viscous fluids whose motion is restricted to a surface. Their solution, starting from a given initial condition, is the velocity field of the particles making up the fluid, assumed here to be incompressible. A bifurcation happens when its stagnation points, i.e. the zeroes of the velocity field, change their number or type.

In this talk, I will discuss a new result proving the existence of solutions to the two-dimensional Navier-Stokes equations, both in $\mathbb{R}^2$ and $\mathbb{T}^2$, with an arbitrary number of stagnation points that merge or split along prescribed trajectories, up to a small deformation. The proof combines ideas from the geometric theory of dynamical systems and recent techniques on the approximation of parabolic partial differential equations. This is joint work with A. Enciso and D. Peralta-Salas, as the speaker's PhD supervisors.