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...
Let p be a prime number. Emerton introduced the p-adically
completed cohomology, which admits a representation of some p-adic
group and can be thought of as some spaces of p-adic automorphic
forms. In this talk, I want to explain that for Shimura...
I will discuss the formulation and sketch the proofs of duality
theorems for the geometric and arithmetic p-adic pro-étale
cohomology of Stein spaces. This is based on a joint work with
Pierre Colmez and Sally Gilles.
We will explain how to construct a Kirillov model for Emerton's
completed cohomology of the tower of modular curves. The trickiest
part is to prove injectivity of this model. This is joint
work with Shanwen Wang.