Let K be an algebraically closed field of characteristic zero, and let G be a connected reductive algebraic group over K. We address the problem of classifying triples (G, H, V ), where H is a proper connected subgroup of G, and V is a finitedimensional ir ...
A spinal cord injury (SCI) triggers a cascade of molecular and cellular responses involving inflammatory cell infiltration and cytokine release, apoptosis, demyelination, excitotoxicity, ischemia, and the formation of a fibrotic scar surrounded by an astro ...
Type inference in the presence of first-class or "impredicative" second-order polymorphism a la System F has been an active research area for several decades, with original works dating back to the end of the 80s. Yet, until now many basic problems remain ...
The category of linear algebraic groups admits non-surjective epimorphisms. For simple algebraic groups of rank 2 defined over algebraically closed fields, we show that the minimal dimension of a closed epimorphic subgroup is 3. ...
Ulam asked whether all Lie groups can be represented faithfully on a countable set. We establish a reduction of Ulam's problem to the case of simple Lie groups. In particular, we solve the problem for all solvable Lie groups and more generally Lie groups w ...
The arise of disagreement is an emergent phenomenon that can be observed within a growing social group and, beyond a certain threshold, can lead to group fragmentation. To better understand how disagreement emerges, we introduce an analytically tractable m ...
We investigate generalizations along the lines of the Mordell-Lang conjecture of the author's p-adic formal Manin-Mumford results for n-dimensional p-divisible formal groups F. In particular, given a finitely generated subgroup (sic) of F(Q(p)) and a close ...
Historically speaking, the notion of the type was reintroduced to the larger architectural discourse as a direct consequence of the crisis of the Modern. The task of revisiting the forms of the past also dictated the return of architectural methods that ha ...
Activin-A is a Transforming Growth Factor-B (TGFB)-related cytokine that regulates various biological processes including cell proliferation and differentiation through autocrine, paracrine or endocrine signaling. Activin-A expression is upregulated in mul ...
Let k be an algebraically closed field of arbitrary characteristic, let G be a simple simply connected linear algebraic group and let V be a rational irreducible tensor-indecomposable finite-dimensional kG-module. For an element g of G we denote by $V_{g}( ...
Let G be a simple algebraic group over an algebraically closed field F of characteristic p >= h, the Coxeter number of G. We observe an easy 'recursion formula' for computing the Jantzen sum formula of a Weyl module with p-regular highest weight. We also d ...
We investigate finite torsors over big opens of spectra of strongly F-regular germs that do not extend to torsors over the whole spectrum. Let (R, m, k, K) be a strongly F-regular k-germ where k is an algebraically closed field of characteristic p > 0. We ...
Let G be either a simple linear algebraic group over an algebraically closed field of characteristic l>0 or a quantum group at an l-th root of unity. The category Rep(G) of finite-dimensional G-modules is non-semisimple. In this thesis, we develop new tech ...
We continue our work, started in [9], on the program of classifying triples (X, Y, V), where X, Yare simple algebraic groups over an algebraically closed field of characteristic zero with X < Y, and Vis an irreducible module for Y such that the restriction ...
Ulam asked whether every connected Lie group can be represented on a countable structure. This is known in the linear case. We establish it for the first family of non-linear groups, namely in the nilpotent case. Further context is discussed to illustrate ...
We generalize the fixed-point property for discrete groups acting on convex cones given by Monod in [23] to topological groups. At first, we focus on describing this fixed-point property from a functional point of view, and then we look at the class of gro ...
Concepts of type and typology are not specific to architecture. Rather they represent an interdisciplinary approach to ordering knowledge and gaining insight. In the field of architecture, the study of types and typology offers a didactic perspective that ...
The widespread use of bots to support software development makes social coding platforms such as GitHub a particularly rich source of data for the study of human-bot interaction. Software development bots are used to automate repetitive tasks, interacting ...
It is generally assumed that the parent-twin interface is a fully invariant plane. The calculations of the rational interfaces of the type I twins and irrational interfaces of the type II twins are based on this hypothesis. Recently, some asymmetric facets ...
The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...
