Let π be a cuspidal automorphic representation of Sp_2n over Q
which is holomorphic discrete series at infinity, and χ a Dirichlet
character. Then one can attach to π an orthogonal p-adic Galois
representation ρ of dimension 2n+1. Assume ρ is...
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...
