We develop the spectral analysis of the Jacobi operator on the
interfaces of soap-bubble clusters. By Plateau's laws, these always
meet in threes at $120^{\circ}$-angles, and thus naturally interact
via 3 linearly independent "conformal" boundary...
I will discuss the quantum resource known as magic and its
analysis in many-fermion systems such as the Sachdev-Ye-Kitaev
model. I will show that the SYK calculation of magic can be
quantitatively modeled with a gravity calculation
involving...
Singularities are local properties of algebraic varieties. For
example, the solution set of a polynomial in several variables such
as $y^2=x^3$ has a singularity at the origin $(0,0)$. In algebra,
one often studies singularities through the quotient...
We define and study an extension of the notion of the
VC-dimension of a hypergraph and apply it to establish a Tverberg
type theorem for unions of convex sets. We also prove a new Radon
type theorem for unions of convex sets, settling an open...
Hilbert, motivating his list of 23 problems, mentions the
arithmetical formulation of the concept of the continuum in the
works of Cauchy, Bolzano and Cantor, and the discovery of
non-Euclidean geometry by Gauss, Bolyai and Lobachevsky, as...
In a previous work with Felix Schlenk, we showed that an
analogue of the phenomenon of Lagrangian barriers holds in the
contact framework in S3 : there exist (explicit) Legendrian
complexes of arcs in S3 that have short Reeb chords to many...
