Publication

Trace coordinates of Teichmüller spaces of Riemann surfaces

Publications associées (28)

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Univ Press Inc2024

BPS invariants from p-adic integrals

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We define p-adic BPS or pBPS invariants for moduli spaces M-beta,M-chi of one-dimensional sheaves on del Pezzo and K3 surfaces by means of integration over a non-archimedean local field F. Our definition relies on a canonical measure mu can on the F-analyt ...

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We introduce an algorithm to reconstruct a mesh from discrete samples of a shape's Signed Distance Function (SDF). A simple geometric reinterpretation of the SDF lets us formulate the problem through a point cloud, from which a surface can be extracted wit ...

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The unipotent mixing conjecture

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We show that shifted pairs of discrete or continuous low-lying horocycles equidistribute in the product space of two modular curves. ...

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In this text, we will show the existence of lattice packings in a family of dimensions by employing division algebras. This construction is a generalization of Venkatesh's lattice packing result Venkatesh (Int Math Res Notices 2013(7): 1628-1642, 2013). In ...

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Atomic-Level and Surface Structure of Calcium Silicate Hydrate Nanofoils

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Deciphering the calcium silicate hydrate (C-S-H) surface is crucial for unraveling the mechanisms of cement hydration and property development. Experimental observations of C-S-H in cement systems suggest a surface termination which is fundamentally differ ...

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On the projectivity of some moduli spaces of varieties

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This thesis is constituted of one article and three preprints that I wrote during my PhD thesis. Their common theme is the moduli theory of algebraic varieties. In the first article I study the Chow--Mumford line bundle for families of uniformly K-stable F ...

EPFL2022

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The design and construction of doubly-curved structures often reveals to be challenging and can result in complex manufacturing and assembly. A recent strategy to tackle this difficulty consists in exploiting the connection between discrete differential ge ...

2022

Geometrical Treatise on the Modelling of 3D Particulate Inclusion-Matrix Microstructures with an Application to Historical Stone Masonry Walls

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As historical stone masonry structures are vulnerable and prone to damage in earthquakes, investigating their structural integrity is important to reduce injuries and casualties while preserving their historical value. Stone masonry is a composite material ...

EPFL2022

Algebra and geometry of link homology Lecture notes from the IHES 2021 Summer School

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These notes cover the lectures of the first named author at 2021 IHES Summer School on "Enumerative Geometry, Physics and Representation Theory" with additional details and references. They cover the definition of Khovanov-Rozansky triply graded homology, ...

WILEY2022

Hybrid Flock - Formation Control Algorithms

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Two prominent categories for achieving coordinated multirobot displacement are flocking and navigation in formation. Both categories have their own body of literature and characteristics, including their respective advantages and disadvantages. While typic ...

Springer Nature Switzerland2022

Serre-Tate theory for Calabi-Yau varieties

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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 ...

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Let f(z)=q+∑n≥2a(n)qn be a weight k normalized newform with integer coefficients and trivial residual mod 2 Galois representation. We extend the results of Amir and Hong in Amir and Hong (On L-functions of modular elliptic curves and certain K3 surfaces, R ...

2021

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The design of envelopes with complex geometries often leads to construction challenges. To overcome these difficulties, resorting to discrete differential geometry proved successful by establishing close links between mesh properties and the existence of g ...

2021

A method to numerically determine the secondary electron yield considering effects of the surface morphology

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Secondary electron emission (SEE) of solid materials due to electron bombardment is influenced by numerous properties of materials, where the surface condition plays a critical role in the value of secondary electron yield (SEY). Here, a 3D random microstr ...

2021

Energy distribution of harmonic 1-forms and Jacobians of Riemann surfaces with a short closed geodesic

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We study the energy distribution of harmonic 1-forms on a compact hyperbolic Riemann surface S where a short closed geodesic is pinched. If the geodesic separates the surface into two parts, then the Jacobian variety of S develops into a variety that split ...

2021

Positivity of the CM line bundle for families of K-stable klt Fano varieties

Zsolt Patakfalvi, Giulio Codogni

The Chow-Mumford (CM) line bundle is a functorial line bundle on the base of any family of klt Fano varieties. It is conjectured that it yields a polarization on the moduli space of K-poly-stable klt Fano varieties. Proving ampleness of the CM line bundle ...

2021

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Tolerancing is an important step toward the fabrication of high-quality and cost-effective lens surfaces. It is critical for wafer-level optics, when up to tens of thousands microlenses are fabricated in parallel and whose surfaces cannot be formed individ ...

OPTICAL SOC AMER2020

Simple groups of birational transformations in dimension two

Christian Lucius Urech

We classify simple groups that act by birational transformations on compact complex Kahler surfaces. Moreover, we show that every finitely generated simple group that acts non-trivially by birational transformations on a projective surface over an arbitrar ...

2020

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2020