Isomonodromic deformations of logarithmic connections and stability

Let X_0 be a compact connected Riemann surface of genus g with D_0\subset X_0 an ordered subset of cardinality n, and let E_G be a holomorphic principal G-bundle on X_0, where G is a complex reductive affine algebraic group, that admits a logarithmic connection \nabla_0 with polar divisor D_0. Let (\cal{E}_G, \nabla) be the universal isomonodromic deformation of (E_G,\nabla_0) over the universal Teichm\"uller curve (\cal{X}, \cal{D})\rightarrow {Teich}_{g,n}, where {Teich}_{g,n} is the Teichm\"uller space for genus g Riemann surfaces with n-marked points. We prove the following: Assume that g>1 and n= 0. Then there is a closed complex analytic subset \cal{Y} \subset {Teich}_{(g,n)}, of codimension at least $g$, such that for any t\in {Teich}_{(g,n)} \setminus \mathcal{Y}, the principal G-bundle \cal{E}_G\vert_{{\cal X}_t} is semistable, where {\cal X}_t is the compact Riemann surface over $t$. Assume that g>0, and if g= 1, then n >0. Also, assume that the monodromy representation for \nabla_0 does not factor through some proper parabolic subgroup of G. Then there is a closed complex analytic subset $\cal{Y}' \subset {Teich}_{(g,n)}, of codimension at least g, such that for any t\in {Teich}_{(g,n)} \setminus \cal{Y}', the principal G-bundle$\cal{E}_G\vert_{{\cal X}_t}$ is semistable. Assume that g>1. Assume that the monodromy representation for \nabla_0 does not factor through some proper parabolic subgroup of G. Then there is a closed complex analytic subset \cal{Y}" \subset {Teich}_{(g,n)}, of codimension at least g-1, such that for any t\in {Teich}_{(g,n)} \setminus \cal{Y}', the principal G-bundle \cal{E}_G\vert_{{\cal X}_t} is stable.Comment: Final version; to appear in Math Annale

Universal isomonodromic deformations of meromorphic rank 2 connections on curves

International audienceWe consider tracefree meromorphic rank 2 connections over compact Riemann surfaces of arbitrary genus. By deforming the curve, the position of the poles and the connection, we construct the global universal isomonodromic deformation of such a connection. Our construction, which is specific to the tracefree rank 2 case, does not need any Stokes analysis for irregular singularities. It is thereby more elementary than the construction in arbitrary rank due to B. Malgrange and I. Krichever and it includes the case of resonant singularities in a natural way

Solving the Cultural Paradox of Loneliness

Are members of individualistic societies more likely to feel lonely? This seems intuitive because more people in such societies, for instance, renounce family life or live alone. However, although solitude and social isolation seem to increase loneliness, average loneliness tends to be lower in more individualistic, rather than more collectivistic, cultures. In this dissertation, we aim to resolve this “cultural paradox of loneliness” by examining how risk factors for loneliness may be influenced by cultural norms about social relationships (i.e., rules about what is commonly done in, or what should [not] be done in relationships). These define the standards that people compare their relationships to and steer how they relate to others, which can both influence loneliness. We report quantitative and qualitative studies among young and middle-aged adults in altogether 30 countries (e.g., Sweden, Portugal, Egypt, India), on which we base our theoretical explanation for the cultural paradox of loneliness. In the novel culture-loneliness framework, we suggest that, through less strict and less demanding cultural norms about social relationships, higher individualism may indeed make some people lonely because they end up alone or socially isolated. However, through stricter and more demanding norms about relationships, higher collectivism may, on average, make people even lonelier because they can less freely select fulfilling relationships, may more often feel that their relationships cannot meet expectations, or may experience social sanctions if their relationships do not conform to norms. These insights into culture- specific risks may help to develop culture-sensitive interventions against loneliness in the future

Challenges of Volunteerism within a Cultural Community: Case Study of Young Hmong Adults in Kitchener-Waterloo

Volunteering is an act of civic participation where members of a community engage in a social process of performing activities to assist in achieving a certain goal. This study looks at volunteerism in the context of a cultural voluntary organization within the Hmong community in Southern Ontario. The study presents findings of a case study conducted with young Hmong adult members about their perspectives of volunteering within a non-profit organization, which incorporates three generations of members. The study reveals intergenerational and cross-cultural challenges and discusses how these challenges impact the volunteer experiences of the participants. The study advances our knowledge of volunteerism among minority populations in the context of their cultural communities and informs society of the experiences that may need to be considered when developing strategies to increase volunteer participation within Canadian society

Transition ordre-désordre induite thermiquement dans les systèmes cellulaires fluides bidimensionnels

International audienceMany systems, including biological tissues and foams, are made of highly packed units having high deformability but low compressibility. At two dimensions, these systems offer natural tesselations of plane with fixed density, in which transitions from ordered to disordered patterns are often observed, in both directions. Using a modified Cellular Potts Model algorithm that allows rapid thermalization of extensive systems, we numerically explore the order-disorder transition of monodisperse, two-dimensional cellular systems driven by thermal agitation. We show that the transition follows most of the predictions of Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory developed for melting of 2D solids, extending the validity of this theory to systems with many-body interactions. In particular, we show the existence of an intermediate hexatic phase, which preserves the orientational order of the regular hexagonal tiling, but looses its positional order. In addition to shedding light on the structural changes observed in experimental systems, our study shows that soft cellular systems offer macroscopic systems in which KTHNY melting scenario can be explored, in the continuation of Bragg's experiments on bubble rafts