Rigidity of maximal holomorphic representations of Kähler groups

20 pagesWe investigate representations of Kähler groups $\Gamma = \pi_1(X)$ to a semisimple non-compact Hermitian Lie group $G$ that are deformable to a representation admitting an (anti)-holomorphic equivariant map. Such representations obey a Milnor--Wood inequality similar to those found by Burger--Iozzi and Koziarz--Maubon. Thanks to the study of the case of equality in Royden's version of the Ahlfors--Schwarz Lemma, we can completely describe the case of maximal holomorphic representations. If \dim_{\C}X \geq 2, these appear if and only if $X$ is a ball quotient, and essentially reduce to the diagonal embedding \Gamma < \SU(n,1) \to \SU(nq,q) \hookrightarrow \SU(p,q). If $X$ is a Riemann surface, most representations are deformable to a holomorphic one. In that case, we give a complete classification of the maximal holomorphic representations, that thus appear as preferred elements of the respective maximal connected components

Deformations of harmonic mappings and variation of the energy

We study the deformations of twisted harmonic maps $f$ with respect to the representation $\rho$. After constructing a continuous "universal" twisted harmonic map, we give a construction of every first order deformation of $f$ in terms of Hodge theory; we apply this result to the moduli space of reductive representations of a K\"ahler group, to show that the critical points of the energy functional $E$ coincide with the monodromy representations of polarized complex variations of Hodge structure. We then proceed to second order deformations, where obstructions arise; we investigate the existence of such deformations, and give a method for constructing them, as well. Applying this to the energy functional as above, we prove (for every finitely presented group) that the energy functional is a potential for the K\"ahler form of the "Betti" moduli space; assuming furthermore that the group is K\"ahler, we study the eigenvalues of the Hessian of $E$ at critical points.Comment: 32 pages. Several typos have been corrected and some references have been added. To appear on Math.

Elliptic Surfaces

L'oggetto dello studio sono le superfici complesse compatte analitiche, con particolare riguardo per quelle proiettive. Nel primo capitolo vengono discusse generalità sulle superfici, e la classificazione di Enriques-Kodaira (senza dimostrazioni). Poi si trattano argomenti generali sulle fibrazioni di superfici, per affrontare nei capitoli 3 e 4 le fibrazioni di Weierstrass e le superfici ellittiche. Si mostra la naturale relazione tra le prime e le superfici ellittiche con sezione, e si discutono nei dettagli la classificazione delle fibre singolari, la monodromia, la classificazione delle curve ellittiche, la classificazione a-b-delta per le fibrazioni di Weierstrass e le forme normali, e infine il gruppo rivestimento doppio e il processo di trasferimento dello *. Nell'ultimo capitolo, seguendo lavori di R. Miranda, U. Persson e T. Shioda, si discute la classificazione delle configurazioni di fibre singolari che possono effettivamente esistere su una superficie ellittica di dato genere aritmetico

Adaptive potential of hybridization among malaria vectors: Introgression at the immune locus TEP1 between Anopheles coluzzii and A. gambiae in 'Far-West' Africa

“Far-West” Africa is known to be a secondary contact zone between the two major malaria vectors Anopheles coluzzii and A. gambiae.We investigated gene-flow and potentially adaptive introgression between these species along a west-to-east transect in Guinea Bissau, the putative core of this hybrid zone. To evaluate the extent and direction of gene flow, we genotyped site 702 in Intron-1 of the para Voltage-Gated SodiumChannel gene, a species-diagnostic nucleotide position throughout most of A. coluzzii and A. gambiae sympatric range. We also analyzed polymorphismin the thioester-binding domain (TED) of the innate immunity-linked thioester-containing protein 1 (TEP1) to investigate whether elevated hybridization might facilitate the exchange of variants linked to adaptive immunity and Plasmodium refractoriness. Our results confirm asymmetric introgression of genetic material from A. coluzzii to A. gambiae and disruption of linkage between the centromeric "genomic islands" of inter-specific divergence. We report that A. gambiae from the Guinean hybrid zone possesses an introgressed TEP1 resistant allelic class, found exclusively in A. coluzzii elsewhere and apparently swept to fixation inWest Africa (i.e. Mali and Burkina Faso). However, no detectable fixation of this allele was found in Guinea Bissau, which may suggest that ecological pressures driving segregation between the two species in larval habitats in this region may be different from those experienced in northern and more arid parts of the species’ range. Finally, our results also suggest a genetic subdivision between coastal and inland A. gambiae Guinean populations and provide clues on the importance of ecological factors in intra-specific differentiation processes

Sex-sorted canine sperm cryopreservation: Limits and procedural considerations

The aim of this study was to define a protocol to store dog sperm before and after sorting to obtain an insemination dose sufficient to allow the conception by artificial insemination. Experiment 1 and 2 were performed to evaluate the more appropriate extender for preserving at room temperature dog sperm before and after sorting. Four extenders were tested: (1) Tris-fructose-citrate (TFC), (2) Tris-glucose-citrate (TGC), (3) modified Tyrode\u2019s albumin lactate pyruvate medium (mTALP), and (4) third fraction of the ejaculate (after centrifugation at 5000 g for 10 minutes; III FRAC). Experiment 3 and 4 were performed to evaluate the ability of dog semen to withstand sex sorting and freezing/thawing. Modified Tyrode\u2019s albumin lactate pyruvate medium was the best extender for canine sperm storage at room temperature (20 C\u201325 C) before (total motility: TFC, 8.3 1.7; TGC, 50.0 11.5; mTALP, 70.0 0.1; III FRAC, 25.0 1 0.4; P &lt; 0.05) and after sorting (total motility: TFC, 7.3 1.5; TGC, 10.3 1.5; mTALP, 33.3 6.7; III FRAC, 8.7 5.8; P &lt; 0.05), even if at 24- hour sorted sperm quality was impaired in all extenders tested herein. Sperm quality decreased after sorting (total motility: control, 92.5 0.9; sorted, 52.9 6.0; P &lt; 0.05) and, especially, after freezing/thawing (total motility: frozen control, 25.7 4.1; frozen sorted, 2.4 1.2; P &lt; 0.05). In conclusion, mTALP is an appropriate medium for canine sperm storage before and soon after sorting (hours), but a long storage period of sexed sperm at room temperature is not adequate. Cryopreservation greatly impaired sperm quality, and further studies are needed to optimize the freezing protocol for sexed dog sperm

A systematic analysis of the memory term in coarse-grained models: The case of the Markovian approximation

The systematic development of coarse-grained (CG) models via the Mori–Zwanzig projector operator formalism requires the explicit description of a deterministic drift term, a dissipative memory term and a random fluctuation term. The memory and fluctuating terms are related by the fluctuation–dissipation relation and are more challenging to sample and describe than the drift term due to complex dependence on space and time. This work proposes a rational basis for a Markovian data-driven approach to approximating the memory and fluctuating terms. We assumed a functional form for the memory kernel and under broad regularity hypothesis, we derived bounds for the error committed in replacing the original term with an approximation obtained by its asymptotic expansions. These error bounds depend on the characteristic time scale of the atomistic model, representing the decay of the autocorrelation function of the fluctuating force; and the characteristic time scale of the CG model, representing the decay of the autocorrelation function of the momenta of the beads. Using appropriate parameters to describe these time scales, we provide a quantitative meaning to the observation that the Markovian approximation improves as they separate. We then proceed to show how the leading-order term of such expansion can be identified with the Markovian approximation usually considered in the CG theory. We also show that, while the error of the approximation involving time can be controlled, the Markovian term usually considered in CG simulations may exhibit significant spatial variation. It follows that assuming a spatially constant memory term is an uncontrolled approximation which should be carefully checked. We complement our analysis with an application to the estimation of the memory in the CG model of a one-dimensional Lennard–Jones chain with different masses and interactions, showing that even for such a simple case, a non-negligible spatial dependence for the memory term exists

Deformations of twisted harmonic maps

On étudie les déformations des applications harmoniques f tordues par rapport à une représentation. Après avoir construit une application harmonique tordue "universelle", on donne une construction de toute déformations du premier ordre de f en termes de la théorie de Hodge ; on applique ce résultat à l'espace de modules des représentations réductives d'un groupe de Kähler, pour démontrer que les points critiques de la fonctionnelle de l'énergie E coïncident avec les représentations de monodromie des variations complexes de structures de Hodge. Ensuite, on procède aux déformations du second ordre, où des obstructions surviennent ; on enquête sur l'existence de ces déformations et on donne une méthode pour le construire. En appliquant ce résultat à la fonctionnelle de l'énergie comme ci-dessus, on démontre (pour n'importe quel groupe de présentation finie) que la fonctionnelle de l'énergie est strictement pluri sous-harmonique sur l'espace des modules des représentations. En assumant de plus que le groupe soit de Kähler, on étudie les valeurs propres de la matrice hessienne de E dans les points critiques.We study the deformations of twisted harmonic maps f with respect to a representation. After constructing a continuous "universal" twisted harmonic map, we give a construction of every first order deformation of f in terms of Hodge theory; we apply this result to the moduli space of reductive representations of a Kähler group, to show that the critical points of the energy functional E coincide with the monodromy representations of polarized complex variations of Hodge structure. We then proceed to second order deformations, where obstructions arise; we investigate the existence of such deformations, and give a method for constructing them, as well. Applying this to the energy functional as above, we prove (for every finitely presented group) that the energy functional is strictly pluri sub-harmonic on the moduli space of representations; assuming furthermore that the group is Kähler, we study the eigenvalues of the Hessian of E at critical points

Déformations des applications harmoniques tordues

We study the deformations of twisted harmonic maps f with respect to a representation. After constructing a continuous "universal" twisted harmonic map, we give a construction of every first order deformation of f in terms of Hodge theory; we apply this result to the moduli space of reductive representations of a Kähler group, to show that the critical points of the energy functional E coincide with the monodromy representations of polarized complex variations of Hodge structure. We then proceed to second order deformations, where obstructions arise; we investigate the existence of such deformations, and give a method for constructing them, as well. Applying this to the energy functional as above, we prove (for every finitely presented group) that the energy functional is strictly pluri sub-harmonic on the moduli space of representations; assuming furthermore that the group is Kähler, we study the eigenvalues of the Hessian of E at critical points.On étudie les déformations des applications harmoniques f tordues par rapport à une représentation. Après avoir construit une application harmonique tordue "universelle", on donne une construction de toute déformations du premier ordre de f en termes de la théorie de Hodge ; on applique ce résultat à l'espace de modules des représentations réductives d'un groupe de Kähler, pour démontrer que les points critiques de la fonctionnelle de l'énergie E coïncident avec les représentations de monodromie des variations complexes de structures de Hodge. Ensuite, on procède aux déformations du second ordre, où des obstructions surviennent ; on enquête sur l'existence de ces déformations et on donne une méthode pour le construire. En appliquant ce résultat à la fonctionnelle de l'énergie comme ci-dessus, on démontre (pour n'importe quel groupe de présentation finie) que la fonctionnelle de l'énergie est strictement pluri sous-harmonique sur l'espace des modules des représentations. En assumant de plus que le groupe soit de Kähler, on étudie les valeurs propres de la matrice hessienne de E dans les points critiques

Déformations des applications harmoniques tordues

We study the deformations of twisted harmonic maps f with respect to a representation. After constructing a continuous "universal" twisted harmonic map, we give a construction of every first order deformation of f in terms of Hodge theory; we apply this result to the moduli space of reductive representations of a Kähler group, to show that the critical points of the energy functional E coincide with the monodromy representations of polarized complex variations of Hodge structure. We then proceed to second order deformations, where obstructions arise; we investigate the existence of such deformations, and give a method for constructing them, as well. Applying this to the energy functional as above, we prove (for every finitely presented group) that the energy functional is strictly pluri sub-harmonic on the moduli space of representations; assuming furthermore that the group is Kähler, we study the eigenvalues of the Hessian of E at critical points.On étudie les déformations des applications harmoniques f tordues par rapport à une représentation. Après avoir construit une application harmonique tordue "universelle", on donne une construction de toute déformations du premier ordre de f en termes de la théorie de Hodge ; on applique ce résultat à l'espace de modules des représentations réductives d'un groupe de Kähler, pour démontrer que les points critiques de la fonctionnelle de l'énergie E coïncident avec les représentations de monodromie des variations complexes de structures de Hodge. Ensuite, on procède aux déformations du second ordre, où des obstructions surviennent ; on enquête sur l'existence de ces déformations et on donne une méthode pour le construire. En appliquant ce résultat à la fonctionnelle de l'énergie comme ci-dessus, on démontre (pour n'importe quel groupe de présentation finie) que la fonctionnelle de l'énergie est strictement pluri sous-harmonique sur l'espace des modules des représentations. En assumant de plus que le groupe soit de Kähler, on étudie les valeurs propres de la matrice hessienne de E dans les points critiques