Past Events
Following lecture notes by Michael Struwe, we will continue our exploration of 2+1-dimensional wave maps with symmetries. We will see that a co-rotational wave map into a surface of revolution which blows up necessarily does so in a self-similar way, with the profile given by a non-constant co-…
Let W be a complete finite type Liouville manifold. One can associate to each closed subset K of W that is conical at infinity an invariant SH_W(K). I will first explain the construction of SH_W(K) and note how it recovers known invariants through special choices of K. Then, I will prove a big…
In 1998, Smale published his `list of mathematical problems for the next century'. His 17th problem asked if a zero of d random complex polynomials in d unknowns can be found by an algorithm in polynomial time on average. Beltrán and Pardo proved the existence of an efficient randomized…
I will talk about singularities of special Lagrangian surfaces.
Semialgebraic graphs are a convenient way to encode many problems in discrete geometry. These include the Erdős unit distance problem and many of its variants, the point-line incidence problems studied by Szemerédi–Trotter and by Guth–Katz, more general problems about incidences of…
Moy-Prasad filtration subgroups are generalization of congruence subgroups for $GL_n(Q_p)$ to a general $p$-adic reductive group $G(F)$. Moy-Prasad proved that any irreducible smooth representation of $G(F)$ has its restriction to a Moy-Prasad subgroup given by an irreducible representation (…
The Vafa Witten equations on 4-manifolds are the variational equations of a functional that generalizes one of the Chern-Simons functionals for SL(2;C) connections on 3-manifolds (and it reduces to that on products of a 3-manifold with the circle). Being that the moduli space of solutions…
In this talk, we explore two classical image processing tasks motivated by cryo-electron microscopy imaging: tomographic image denoising and rigid image registration. Both tasks inherently involve operations of 2D rotations, where leveraging specific transforms can significantly enhance the…
Abstract: The existence of multi black hole solutions in asymptotically flat spacetimes is one of the expectations from the final state conjecture. In this talk, I will present preliminary works towards showing the existence of multi black hole solutions via a semilinear toy model in dimension 3…