Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

An Introduction to Probability Theory and its Applications, Volume I

On the order of magnitude of the difference between consecutive prime numbers

Birational Geometry of Algebraic Varieties: Preface

We construct (cohomological) correspondences between mod $p$ fibers of different Shimura varieties and describe the fibers of these correspondences by studying irreducible components of affine Deligne-Lusztig varieties. In particular, in the case of correspondences from a Shimura set to a Shimura variety, we obtain a description of the basic Newton stratum of the latter, and show that the irreducible components of the basic Newton stratum generate all the Tate classes in the middle cohomology of the Shimura variety, under a certain genericity condition. Along the way, we also determine the set of irreducible components of the affine Deligne-Lusztig variety associated to an unramified twisted conjugacy class.

Cycles on Shimura varieties via geometric Satake

Hecke eigenvalues of Siegel modular forms (modp) and of algebraic modular forms

Co m pu ta tio na lM at he m at ic s w ith Sa ge M at h or Sage for short, is an open-source mathematical system based on the Python language. Sage is developed by an international community of hundreds of teachers and researchers, whose aim is to provide an alternative to the commercial products Magma, Maple, Mathematica and Matlab. To reach this goal, Sage relies on many open-source programs, including GAP, Maxima, PARI and various scientific libraries for Python, to which thousands of new functions are added. Sage is freely available and is supported by all modern operating systems.

Computational Mathematics with SageMath

We describe a computational approach to the verification of Maeda's conjecture for the Hecke operator $T_2$ on the space of cusp forms of level one. We provide experimental evidence for all weights less than 14000, as well as some applications of these results. The algorithm was implemented using the mathematical software Sage, and the code and resulting data were made freely available.

https://projecteuclid.org/download/pdf_1/euclid.tbilisi/1528768903

Experimental evidence for Maeda's conjecture on modular forms

We show that the systems of Hecke eigenvalues occurring in the spaces of Siegel modular forms (mod p) of fixed dimension g, fixed level N, and varying weight, are the same as the systems occurring in the spaces of Siegel cusp forms with the same parameters and varying weight. In particular, in the case g=1, this says that the Hecke eigensystems (mod p) coming from classical modular forms are the same as those coming from cusp forms. The proof uses restriction to the superspecial locus. We also give a comparison of cusp forms on the Satake compactification versus the toroidal compactifications of Siegel modular varieties.

https://www.intlpress.com/site/pub/files/_fulltext/journals/mrl/2006/0013/0005/MRL-2006-0013-0005-a011.pdf

All Siegel Hecke eigensystems (mod p) are cuspidal

We describe a computational approach to the verification of Maeda's conjecture for the Hecke operator T2 on the space of cusp forms of level one. We provide experimental evidence for all weights less than 12000, as well as some applications of these results. The algorithm was implemented using the mathematical software Sage, and the code and resulting data were made freely available.

Alexandru Ghitza

Papers

Hecke eigenvalues of Siegel modular forms (modp) and of algebraic modular forms

Computational Mathematics with SageMath

Experimental evidence for Maeda's conjecture on modular forms

All Siegel Hecke eigensystems (mod p) are cuspidal

Experimental evidence for Maeda's conjecture on modular forms