Endow the edges of the ZD lattice with positive weights, sampled
independently from a suitable distribution (e.g., uniformly
distributed on [a,b] for some b greater than a greater than 0). We
wish to study the geometric properties of the resulting...
p-adic heights have been a rich source of explicit functions
vanishing on rational points on a curve. In this talk, we will
outline a new construction of canonical p-adic heights on abelian
varieties from p-adic adelic metrics, using p-adic Arakelov...
Any non-negative univariate polynomial over the reals can be
written as a sum of squares. This gives a simple-to-verify
certificate of non-negativity of the polynomial. Rooted in
Hilbert's 17th problem, there's now more than a century's work
that...
We discuss the shape invariant, a sort of set valued symplectic
capacity defined by the Lagrangian tori inside a domain of R4.
Partial computations for convex toric domains are sometimes enough
to give sharp obstructions to symplectic embeddings...
In distributed certification, our goal is to certify that a
network has a certain desired property, e.g., the network is
connected, or the internal states of its nodes encode a valid
spanning tree of the network. To this end, a prover
generates...
I'll give an exposition of the theory of "multiplicative
polynomial laws," introduced by Roby, and how (following a
suggestion of Scholze) they can be applied to the theory of
commutative (flat) group schemes. This talk will feature more
questions...
I will discuss how much the choice of coefficients impacts the
quantitative information of Floer theory, especially spectral
invariants. In particular, I will present some phenomena that are
specific to integer coefficients, including an answer to a...
The key principle in Grothendieck's algebraic geometry is that
every commutative ring be considered as the ring of functions on
some geometric object. Clausen and Scholze have introduced a
categorification of algebraic and analytic geometry, where...
For a reductive group G, its BdR+-affine Grassmannian is defined
as the étale (equivalently, v-) sheafification of the presheaf
quotient LG/L+G of the BdR-loop group LG by the BdR+ -loop subgroup
L+G. We combine algebraization and approximation...
In 1970, Allan Sandage famously described Cosmology as "A search
for two numbers". In the half-century since that description of the
field was penned, as Stage III cosmic surveys come to an end and
Stage-IV surveys begin taking data, the field finds...
