Related papers: On Gauss Calendar Formula: An Application of Modul…
We introduce a new diagrammatic notation for representing the result of (algebraic) effectful computations. Our notation explicitly separates the effects produced during a computation from the possible values returned, this way simplifying…
The ability to read, write, and speak mathematics is critical to students becoming comfortable with statistical models and skills. Faster development of those skills may act as encouragement to further engage with the discipline. Vocabulary…
In this paper we present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any cases. This approach allows to give a notion of divisibility…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
We report on a course project in which students submit weekly probabilistic forecasts of two weather variables and one financial variable. This real-time format allows students to engage in practical forecasting, which requires a diverse…
Expository paper discussing AG or Goppa codes arising from curves, first from an abstract general perspective then turning to concrete examples associated to modular curves. We will try to explain these extremely technical ideas using a…
We give an account of the complex Arithmetic-Geometric Mean (AGM), as first studied by Gauss, together with details of its relationship with the theory of elliptic curves over $\C$, their period lattices and complex parametrisation. As an…
We study the topological $\mu$-calculus, based on both Cantor derivative and closure modalities, proving completeness, decidability and FMP over general topological spaces, as well as over $T_0$ and $T_D$ spaces. We also investigate…
By extending the framework of the gravitational clock compass we show how a suitably prepared set of clocks can be used to extract information about the gravitational field in the context of General Relativity. Conceptual differences…
Two general methods for establishing the logarithmic behavior of recursively defined sequences of real numbers are presented. One is the interlacing method, and the other one is based on calculus. Both methods are used to prove logarithmic…
We introduce a method for calculating individual elements of matrix functions. Our technique makes use of a novel series expansion for the action of matrix functions on basis vectors that is memory efficient even for very large matrices. We…
The present notes are the expanded and polished version of three lectures given in Stanford, concerning the analytic and arithmetic properties of weight one modular forms. The author tried to write them in a style accessible to…
In this paper we connect classical differential geometry with the concepts from geometric calculus. Moreover, we introduce and analyze a more general Laplacian for multivector-valued functions on manifolds. This allows us to formulate a…
We reduce some key calculations of compositions of morphisms between Soergel bimodules ("Soergel calculus") to calculations in the nil Hecke ring ("Schubert calculus"). This formula has several applications in modular representation theory.
Context. Due to our increasing knowledge on the Galactic and stellar neighborhood of the Solar System, modern long-period comet motion studies have to take into account both stellar perturbations and the overall Galactic potential. Aims.…
Let KG be a group algebra of a finite p-group G over a finite field K of characteristic p. We compute the order of the unitary subgroup of the group of units when G is either an extraspecial 2-group or the central product of such a group…
We propose a presentation of classical propositional tableaux elaborated by application of methods that are noteworthy in program design, namely program derivation with separation of concerns. We start by deriving from a straightforward…
This short expository paper outlines applications of computer algebra to the implication problem of conditional independence for Gaussian random variables. We touch on certificates for validity and invalidity of inference rules from the…
This article accompanies my lecture at the 2015 AMS summer institute in algebraic geometry in Salt Lake City. I survey the recent advances in the study of tautological classes on the moduli spaces of curves. After discussing the…
The computation of triangular decompositions are based on two fundamental operations: polynomial GCDs modulo regular chains and regularity test modulo saturated ideals. We propose new algorithms for these core operations relying on modular…