Singularities of general fibers and the LMMP

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Given a hyperelliptic hyperbolic surface S of genus g >= 2, we find bounds on the lengths of homologically independent loops on S. As a consequence, we show that for any lambda is an element of (0, 1) there exists a constant N(lambda) such that every such ...

We show that mixed-characteristic and equicharacteristic small deformations of 3-dimensional canonical (resp., terminal) singularities with perfect residue field of characteristic p>5 are canonical (resp., terminal). We discuss applications to arithmetic a ...

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The topic of this thesis is vanishing theorems in positive characteristic. In particular, we use "the covering trick of Ekedahl" to investigate the vanishing of

H^1(X, \mathcal{O}_X(-D))

for a big and nef Weil divisor

D

on a normal projective variety w ...

Logic resynthesis is the problem of finding a dependency function to re-express a given Boolean function in terms of a given set of divisor functions. In this paper, we study logic resynthesis of majority-based circuits, which is motivated by the increasin ...

We present a bootstrapping procedure for the full-RNS variant of the approximate homomorphic-encryption scheme of Cheon et al., CKKS (Asiacrypt 17, SAC 18). Compared to the previously proposed procedures (Eurocrypt 18 & 19, CT-RSA 20), our bootstrapping pr ...

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 ...

Combining diffusion strategies with complementary properties enables enhanced performance when they can be run simultaneously. In this article, we first propose two schemes for the convex combination of two diffusion strategies, namely, the power-normalize ...

Algebraic network information theory is an emerging facet of network information theory, studying the achievable rates of random code ensembles that have algebraic structure, such as random linear codes. A distinguishing feature is that linear combinations ...

We propose a novel sparse dictionary learning method for planar shapes in the sense of Kendall, namely configurations of landmarks in the plane considered up to similitudes. Our shape dictionary method provides a good trade-off between algorithmic simplici ...

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 ...

We study the notions of mild solution and generalized solution to a linear stochastic partial differential equation driven by a pure jump symmetric Levy white noise, with symmetric alpha-stable Levy white noise as an important special case. We identify con ...

We prove that one can run the log minimal model program for log canonical 3-fold pairs in characteristic p > 5. In particular, we prove the cone theorem, contraction theorem, the existence of flips and the existence of log minimal models for pairs with log ...

We prove an asymptotic formula for the shifted convolution of the divisor functions d(k)(n) and d(n) with k >= 4, which is uniform in the shift parameter and which has a power saving error term, improving results obtained previously by Fouvry and Tenenbaum ...

The present thesis deals with problems arising from discrete mathematics, whose proofs make use of tools from algebraic geometry and topology. The thesis is based on four papers that I have co-authored, three of which have been published in journals, and o ...

Recent work has employed joint typicality encoding and decoding of nested linear code ensembles to generalize the compute-forward strategy to discrete memoryless multiple-access channels (MACs). An appealing feature of these nested linear code ensembles is ...

We review combinational results to enumerate and classify reversible functions and investigate the application to circuit complexity. In particularly, we consider the effect of negating and permuting input and output variables and the effect of applying li ...

In this paper, we propose a novel algorithm for dimensionality reduction that uses as a criterion the mutual information (MI) between the transformed data and their cor- responding class labels. The MI is a powerful criterion that can be used as a proxy to ...

A novel technique is proposed for obtaining unwrapped phase estimation from a highly noisy exponential phase field. In this technique, the interference phase is represented as a linear combination of linearly independent and pre-defined basis functions alo ...

Singularities of general fibers and the LMMP

Chattez avec Graph Search

Valerie Chavez-Demoulin, Anthony C Davison and Erwan Koch's contribution to the Discussion of 'The First Discussion Meeting on Statistical aspects of climate change'

Short homology bases for hyperelliptic hyperbolic surfaces

Arithmetic and geometric deformations of threefolds

Stochastic distributed learning with gradient quantization and double-variance reduction

Vanishing theorems in positive characteristic

Logic Resynthesis of Majority-Based Circuits by Top-Down Decomposition

Efficient Bootstrapping for Approximate Homomorphic Encryption with Non-sparse Keys

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

Convex Combination of Diffusion Strategies Over Networks

Compute-Forward for DMCs: Simultaneous Decoding of Multiple Combinations

Dictionary Learning for Two-Dimensional Kendall Shapes

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

Random field solutions to linear SPDEs driven by symmetric pure jump Levy space-time white noises

THE LMMP FOR LOG CANONICAL 3-FOLDS IN CHARACTERISTIC p > 5

The Shifted Convolution of Generalized Divisor Functions

Algebraic and topological methods in combinatorics

Towards an algebraic network information theory: Simultaneous joint typicality decoding

Enumeration of reversible functions and its application to circuit complexity

Graph Embedded Nonparametric Mutual Information For Supervised Dimensionality Reduction

Phase estimation from noisy phase fringe patterns using linearly independent basis functions