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 ...
The paper presents a novel method to verify and debug gate-level arithmetic circuits implemented in Galois Field arithmetic. The method is based on forward reduction of the specification polynomials of the circuit in GF(2(m)) using GF(2) models of its logi ...
Findings from neuroscience are increasingly interwoven with architectural research (1,2). Understanding physiological responses to environmental stimuli in the built environment is critical when evaluating occupant health and wellbeing. Research in the fie ...
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 ...
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 ...
In this thesis we compute motivic classes of hypertoric varieties, Nakajima quiver varieties and open de Rham spaces in a certain localization of the Grothendieck ring of varieties. Furthermore we study the p-adic pushforward of the Haar measure under a ...
Let R be a semilocal Dedekind domain. Under certain assumptions, we show that two (not necessarily unimodular) hermitian forms over an R-algebra with involution, which are rationally isomorphic and have isomorphic semisimple coradicals, are in fact isomorp ...
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 ...
We use Masser's counting theorem to prove a lower bound for the canonical height in powers of elliptic curves. We also prove the Galois case of the elliptic Lehmer problem, combining Kummer theory and Masser's result with bounds on the rank and torsion of ...
