Concept
Hodge conjecture
Related publications (14)
Cochains are all you need
In this thesis, we apply cochain complexes as an algebraic model of space in a diverse range of mathematical and scientific settings. We begin with an algebraic-discrete Morse theory model of auto-encoding cochain data, connecting the homotopy theory of d ...
EPFL2024On rationally connected varieties over C1 fields of characteristic 0
We use birational geometry to show that the existence of rational points on proper rationally connected varieties over fields of characteristic 0 is a consequence of the existence of rational points on terminal Fano varieties. We discuss several consequenc ...
MATHEMATICAL SCIENCE PUBL2022Reduced representations of complexes, signals, and multifiltrations
The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...
EPFL2022Collapse-invariant properties of spaces equipped with signals or directions
Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...
EPFL2022Serre-Tate theory for Calabi-Yau varieties
Classical Serre-Tate theory describes deformations of ordinary abelian varieties. It implies that every such variety has a canonical lift to characteristic zero and equips the base of its universal deformation with a Frobenius lifting and canonical multipl ...
WALTER DE GRUYTER GMBH2021Global Frobenius liftability I
We formulate a conjecture characterizing smooth projective varieties in positive characteristic whose Frobenius morphism can be lifted modulo p(2)-we expect that such varieties, after a finite stale cover, admit a toric fibration over an ordinary abelian v ...
EUROPEAN MATHEMATICAL SOC-EMS2021Mirror symmetry for moduli spaces of Higgs bundles via $p$-adic integration
Dimitri Stelio Wyss, Michael Gröchenig
We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type and . More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generica ...
2017On the fundamental domain of affine Springer fibers
Let G be a connected reductive algebraic group over an algebraically closed field k,gamma is an element of g( k(( epsilon ))) a semisimple regular element, we introduce a fundamental domain F gamma for the affine Springer fibers X gamma. We show that the p ...
Springer Heidelberg2017Homology of the three flag Hilbert Scheme
We prove the existence of an affine paving for the three-step flag Hilbert scheme that parametrizes flag of three 0-dimensional subschemes of length, respectively, n, n+1 and n+2 that are supported at the origin of the affine plane. This is done by showing ...
EPFL2016L-2-cohomology and complete Hamiltonian manifolds
A classical theorem of Frankel for compact Kahler manifolds states that a Kahler S-1-action is Hamiltonian if and only if it has fixed points. We prove a metatheorem which says that when the Hodge theory holds on non-compact manifolds, Frankel's theorem st ...
Elsevier2015