Given a grid diagram for a knot or link in the three-sphere, we
construct a spectrum whose homology is the knot Floer homology of .
We conjecture that the homotopy type of the spectrum is an
invariant of . Our construction does not use holomorphic...
In joint work in progress with Anschütz and Le Bras we aim to
construct a 6-functor formalism for quasicoherent sheaves on the
relative Fargues-Fontaine curve over rigid-analytic varieties (and
even general v-stacks), providing new insights into the...
The recent work of Drinfeld and Bhatt-Lurie led to a new
geometric approach to p-adic cohomology theories, analogously to
what was done earlier in Hodge theory by Simpson. This stacky
perspective gives in particular a new approach to p-adic non...
Despite the remarkable success of the standard model of
cosmology, the lambda CDM model, at predicting the observed
structure of the universe over many scales, very little is known
about the fundamental nature of its principal constituents:
dark...
With every bounded prism Bhatt and Scholze associated a
cohomology theory of formal p-adic schemes. The prismatic
cohomology comes equipped with the Nygaard filtration and the
Frobenius endomorphism. The Bhatt-Scholze construction has
been advanced...
I will talk about (very much in progress) joint work with Mark
Kisin on a Hodge—Newton style inequality for the mod p Breuil—Kisin
modules arising from crystalline Galois representations.
The minimal model program for 3-folds has been developed only in
characteristics p greater than or equal to 5. A key difficulty at
small primes is that the singularities occurring in the minimal
model program need not be Cohen-Macaulay, as they are...
Let f:Y→X be a finite covering map of complex algebraic
varieties. The essential dimension of f is the smallest integer e
such that, birationally, f arises as the pullback of a covering
Y′→X′
of dimension e, via a map X→X′. This invariant goes
back...
A theorem of Borel says that any holomorphic map from a complex
algebraic variety to a smooth arithmetic variety is automatically
an algebraic map. The key ingredient is to show that any
holomorphic map from the (poly) punctured disc to the Baily...