Publications related to Siegel modular variety

Birational characterization of abelian varieties and ordinary abelian varieties in characteristic p>0

Let k be an algebraically closed field of characteristic p > 0. We give a birational characterization of ordinary abelian varieties over k: a smooth projective variety X is birational to an ordinary abelian variety if and only if kappa(S)(X) = 0 and b(1)(X ...

DUKE UNIV PRESS2019

Enumeration of Border-Strip Decompositions and Weil-Petersson Volumes

Linus Jordan

We describe an injection from border-strip decompositions of certain diagrams to permutations. This allows us to provide enumeration results as well as q-analogues of enumeration formulas. Finally, we use this injection to prove a connection between the nu ...

2019

Arithmetic and geometric structures in cryptography

Benjamin Pierre Charles Wesolowski

We explore a few algebraic and geometric structures, through certain questions posed by modern cryptography. We focus on the cases of discrete logarithms in finite fields of small characteristic, the structure of isogeny graphs of ordinary abelian varietie ...

EPFL2018

On subadditivity of Kodaira dimension in positive characteristic over a general type base

Zsolt Patakfalvi

We show that for a surjective, separable morphism f of smooth projective varieties over a field of positive characteristic such that f(*) OX congruent to O-Y subadditivity of Kodaira dimension holds, provided the base is of general type and the Hasse-Witt ...

2018

Isogeny graphs of ordinary abelian varieties

Dimitar Petkov Jetchev, Benjamin Pierre Charles Wesolowski, Ernest Hunter Brooks

Fix a prime number l. Graphs of isogenies of degree a power of l are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ordinary abelian varieties over a finite field. We analyse gr ...

Springer Heidelberg2017

Mirror 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

SL_n

and

PGL_n

. More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generica ...

2017

On the mechanical characteristics of a self-setting calcium phosphate cement

John Botsis, Luis Pablo Canal Casado, Dimitrios Karalekas, Alexios Bimis

Objective: To perform a mechanical characterization of a self-setting calcium phosphate cement in function of the immersion time in Ringer solution. Materials and methods: Specimens of self-setting calcium phosphate cement were prepared from pure alpha-TCP ...

Elsevier2017

Motivic invariants of moduli spaces of rank 2 Bradlow-Higgs triples

Riccardo Grandi

In the present thesis we study the geometry of the moduli spaces of Bradlow-Higgs triples on a smooth projective curve C. There is a family of stability conditions for triples that depends on a positive real parameter Ï. The moduli spaces of Ï-semistable ...

EPFL2016

Motivic Classes of Nakajima Quiver Varieties

Dimitri Stelio Wyss

We prove that Hausel’s formula for the number of rational points of a Nakajima quiver variety over a finite field also holds in a suitable localization of the Grothendieck ring of varieties. In order to generalize the arithmetic harmonic analysis in his pr ...

2016

Computational Aspects of Jacobians of Hyperelliptic Curves

Alina Dudeanu

Nowadays, one area of research in cryptanalysis is solving the Discrete Logarithm Problem (DLP) in finite groups whose group representation is not yet exploited. For such groups, the best one can do is using a generic method to attack the DLP, the fastest ...

EPFL2016

Siegel modular variety

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Birational characterization of abelian varieties and ordinary abelian varieties in characteristic p>0

Enumeration of Border-Strip Decompositions and Weil-Petersson Volumes

Arithmetic and geometric structures in cryptography

On subadditivity of Kodaira dimension in positive characteristic over a general type base

Isogeny graphs of ordinary abelian varieties

Mirror symmetry for moduli spaces of Higgs bundles via $p$-adic integration

On the mechanical characteristics of a self-setting calcium phosphate cement

Motivic invariants of moduli spaces of rank 2 Bradlow-Higgs triples

Motivic Classes of Nakajima Quiver Varieties

Computational Aspects of Jacobians of Hyperelliptic Curves

Arithmetic and geometric structures in cryptography

Birational characterization of abelian varieties and ordinary abelian varieties in characteristic p>0

Enumeration of Border-Strip Decompositions and Weil-Petersson Volumes

Mirror symmetry for moduli spaces of Higgs bundles via $p$-adic integration

Computational Aspects of Jacobians of Hyperelliptic Curves

On the mechanical characteristics of a self-setting calcium phosphate cement

Motivic Classes of Nakajima Quiver Varieties

On subadditivity of Kodaira dimension in positive characteristic over a general type base

Isogeny graphs of ordinary abelian varieties

Motivic invariants of moduli spaces of rank 2 Bradlow-Higgs triples