Research Institute for Mathematical Sciences (RIMS), Kyoto University
My research is in arithmetic geometry and number theory. I work on p-adic Hodge theory, Galois representations, and Langlands Correspondence.
A Lean 4 formalization of Langlands’s Second Main Lemma following the companion local proof. The First Main Lemma gives only a power relation; the formalization verifies the further ramification analysis, including the mathematically new wild dyadic case.
PDF · arXiv / full text · HAL · Lean code
A local proof of Langlands’s Second Main Lemma in mixed and equal characteristic. The new point is the wild dyadic case, where the remaining sign is determined by comparing the finite sums in Lamprecht’s formula.
PDF · arXiv / full text · HAL · Langlands’s comments on the Second Main Lemma
A Lean 4 formalization of the First Main Lemma following the companion local proof, including local constants, ramification and finite-field identities, stationary classes, and the full case analysis.
A complete purely local proof of Langlands’s First Main Lemma in both mixed and equal characteristic, reconstructing the Dwork–Langlands method and completing the missing endpoint, non-stable wild, and quadratic calculations.
Constructs crystalline comparison isomorphisms for proper smooth formal schemes over an absolutely unramified base, allowing nontrivial coefficients and a relative version, using the pro-étale site.
Proves the Breuil–Mézard conjecture for split non-scalar residual representations of the local Galois group by local methods; together with earlier cases this completes the conjecture for p ≥ 5. As a consequence, it removes the remaining local restriction in Kisin’s proof of the Fontaine–Mazur conjecture, yielding the corresponding two-dimensional modularity theorem.
Constructs one-parameter families of overconvergent Siegel–Hilbert modular forms, with applications to Galois representations attached to automorphic forms of non-cohomological weights.
Studies modularity of Calabi–Yau varieties from the viewpoint of conformal field theory, expressing the modular forms of one-dimensional Calabi–Yau orbifolds as products of Dedekind eta functions.
Generalizes Kisin’s theory of finite-slope subspaces to arbitrary p-adic fields and studies finite-slope deformation rings, local Galois eigenvarieties, their geometry near de Rham points, and an infinite fern in local Galois deformation space.