Splitting fields of conics and sums of squares of rational functions

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Technology supporting meditation is a multimillion-dollar market that continues to grow. There is also strong academic interest to understand and improve the impact technology can have for the user experience of practitioners. However, little work investig ...

Let k be a field, and let L be an etale k-algebra of finite rank. If a is an element of k(x), let X-a be the affine variety defined by N-L/k(x) = a. Assuming that L has at least one factor that is a cyclic field extension of k, we give a combinatorial desc ...

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 ...

In this thesis we consider the problem of estimating the correlation of Hecke eigenvalues of GL2 automorphic forms with a class of functions of algebraic origin defined over finite fields called trace functions. The class of trace functions is vast and inc ...

We use birational geometry to show that the existence of rational points on proper rationally connected varieties over fields of characteristic 0 is a consequence of the existence of rational points on terminal Fano varieties. We discuss several consequenc ...

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 ...

Artificial Intelligence often relies on information obtained from others through crowdsourcing, federated learning, or data markets. It is crucial to ensure that this data is accurate. Over the past 20 years, a variety of incentive mechanisms have been dev ...

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

Ethynylbenziodoxolones (EBXs) have recently emerged as potent reagents for the alkynylation of radicals. Their combination with photocatalysis allows the synthesis of valuable alkynes at room temperature. Herein, we discuss two photomediated strategies for ...

Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (I) not naturally amenable to gradient-based optimization, and (II) incompatible with deep lear ...

We consider a least-squares/relaxation finite element method for the numerical solution of the prescribed Jacobian equation. We look for its solution via a least-squares approach. We introduce a relaxation algorithm that decouples this least-squares proble ...

The ab initio determination of electronic excited state (ES) properties is the cornerstone of theoretical photochemistry. Yet, traditional ES methods become impractical when applied to fairly large molecules, or when used on thousands of systems. Machine l ...

We provide an introduction to Gaussian process regression (GPR) machinelearning methods in computational materials science and chemistry. The focus of the present review is on the regression of atomistic properties: in particular, on the construction of in ...

We formulate a conjecture characterizing smooth projective varieties in positive characteristic whose Frobenius morphism can be lifted modulo p(2)-we expect that such varieties, after a finite stale cover, admit a toric fibration over an ordinary abelian v ...

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 ...

We prove that smooth, projective, K-trivial, weakly ordinary varieties over a perfect field of characteristic p>0 are not geometrically uniruled. We also show a singular version of our theorem, which is sharp in multiple aspects. Our work, together with La ...

The present work deals with monochromatic wavefront aberrations in optical systems without symmetries. The treatment begins with a class of systems characterized by misaligned spherical surfaces whose behavior is analyzed using the wavefront aberration exp ...

This thesis focuses on the numerical analysis of partial differential equations (PDEs) with an emphasis on first and second-order fully nonlinear PDEs. The main goal is the design of numerical methods to solve a variety of equations such as orthogonal maps ...

Abelian varieties are fascinating objects, combining the fields of geometry and arithmetic. While the interest in abelian varieties has long time been of purely theoretic nature, they saw their first real-world application in cryptography in the mid 1980's ...

The aerosol size distribution was measured with a custom made scanning mobility particle sizer (SMPS), range 18⁠ – ⁠660 nm. Aerosols are important for a variety of reasons, one of the most prominent is that a sub-set of the aerosol population can act as cl ...

Splitting fields of conics and sums of squares of rational functions

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Adapting Haptic Feedback for Guided Meditation

NORM TORI OF ETALE ALGEBRAS AND UNRAMIFIED BRAUER GROUPS

Lattice packings through division algebras

Algebraic twists of GL(2) automorphic forms

On rationally connected varieties over C1 fields of characteristic 0

On the projectivity of some moduli spaces of varieties

Game-theoretic Mechanisms for Eliciting Accurate Information

A Functional Perspective on Information Measures

Radical Alkynylations with EthynylBenziodoXolones: From Photocatalysis to Direct Excitation

Neural Set Function Extensions: Learning with Discrete Functions in High Dimensions

A Least-Squares Method for the Solution of the Non-smooth Prescribed Jacobian Equation

Learning the Exciton Properties of Azo-dyes

Gaussian Process Regression for Materials and Molecules

Global Frobenius liftability I

Serre-Tate theory for Calabi-Yau varieties

Ordinary varieties with trivial canonical bundle are not uniruled

ON WAVEFRONT ABERRATIONS IN ASYMMETRIC AND MULTIPLE APERTURE OPTICAL SYSTEMS

Numerical Methods for First and Second Order Fully Nonlinear Partial Differential Equations

Computing Cyclic Isogenies between Principally Polarized Abelian Varieties over Finite Fields

Size distribution of interstitial and total particles between 18 and 660 nm collected during the Arctic Ocean 2018 expedition