Nicolas M. Thiéry

Directed Nonabelian Sandpile Models on Trees

We define two general classes of nonabelian sandpile models on directed trees (or arborescences), as models of nonequilibrium statistical physics. Unlike usual applications of the well-known abelian sandpile model, these models have the property that sand grains can enter only through specified reservoirs.In the Trickle-down sandpile model, sand grains are allowed to move one at a time. For this model, we show that the stationary distribution is of product form. In the Landslide sandpile model, all the grains at a vertex topple at once, and here we prove formulas for all eigenvalues, their multiplicities, and the rate of convergence to stationarity. The proofs use wreath products and the representation theory of monoids.

Interoperability in the OpenDreamKit Project: The Math-in-the-Middle Approach

OpenDreamKit – “Open Digital Research Environment Toolkit for the Advancement of Mathematics” – is an H2020 EU Research Infrastructure project that aims at supporting, over the period 2015–2019, the ecosystem of open-source mathematical software systems. OpenDreamKit will deliver a flexible toolkit enabling research groups to set up Virtual Research Environments, customised to meet the varied needs of research projects in pure mathematics and applications.

On the uniqueness of promotion operators on tensor products of type A crystals

The affine Dynkin diagram of type An(1) has a cyclic symmetry. The analogue of this Dynkin diagram automorphism on the level of crystals is called a promotion operator. In this paper we show that the only irreducible type An crystals which admit a promotion operator are the highest weight crystals indexed by rectangles. In addition we prove that on the tensor product of two type An crystals labeled by rectangles, there is a single connected promotion operator. We conjecture this to be true for an arbitrary number of tensor factors. Our results are in agreement with Kashiwara’s conjecture that all ‘good’ affine crystals are tensor products of Kirillov-Reshetikhin crystals.

The biHecke monoid of a finite Coxeter group and its representations

The usual combinatorial model for the 0-Hecke algebra of the symmetric group is to consider the algebra (or monoid) generated by the bubble sort operators. This construction generalizes to any finite Coxeter group W. The authors previously introduced the Hecke group algebra, constructed as the algebra generated simultaneously by the bubble sort and antisort operators, and described its representation theory. In this paper, we consider instead the monoid generated by these operators. We prove that it has |W| simple and projective modules. In order to construct a combinatorial model for the simple modules, we introduce for each w in W a combinatorial module whose support is the interval [1,w] in right weak order. This module yields an algebra, whose representation theory generalizes that of the Hecke group algebra. This involves the introduction of a w-analogue of the combinatorics of descents of W and a generalization to finite Coxeter groups of blocks of permutation matrices.

Electrical properties of single crystal Yttrium Iron Garnet ultra-thin films at high temperatures

We report a study on the electrical properties of 19 nm thick Yttrium Iron Garnet (YIG) films grown by liquid phase epitaxy. The electrical conductivity and Hall coefficient are measured in the high temperature range [300,400]~K using a Van der Pauw four-point probe technique. We find that the electrical resistivity decreases exponentially with increasing temperature following an activated behavior corresponding to a band-gap of

EXPLORATION OF FINITE-DIMENSIONAL KAC ALGEBRAS AND LATTICES OF INTERMEDIATE SUBFACTORS OF IRREDUCIBLE INCLUSIONS

E_g\approx 2

Spin conductance of YIG thin films driven from thermal to subthermal magnons regime by large spin-orbit torque

eV, indicating that epitaxial YIG ultra-thin films behave as large gap semiconductor, and not as electrical insulator. The resistivity drops to about

Knowledge-based interoperability for mathematical software systems

5\times 10^3

Spectral Gap for Random-to-Random Shuffling on Linear Extensions

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Implementing Algebraic Combinatorics Some feedback from the development of MuPAD-Combinat (abstract only)

\Omega \cdot \text{cm}