scholarly journals Quiver theories for moduli spaces of classical group nilpotent orbits

2016 ◽  
Vol 2016 (6) ◽  
Author(s):  
Amihay Hanany ◽  
Rudolph Kalveks
Keyword(s):  
Moduli Spaces ◽  
Classical Group ◽  
Nilpotent Orbits

scholarly journals CLUSTER STRUCTURES ON HIGHER TEICHMULLER SPACES FOR CLASSICAL GROUPS

2019 ◽  
Vol 7 ◽  
Author(s):  
IAN LE
Keyword(s):  
Moduli Spaces ◽  
Classical Group ◽  
Teichmüller Space ◽  
Classical Groups ◽  
Local Systems ◽  
Cluster Ensemble ◽  
Teichmüller Theory ◽  
Cluster Varieties ◽  
Simply Connected ◽  
Higher Teichmüller Theory

Let $S$ be a surface, $G$ a simply connected classical group, and $G^{\prime }$ the associated adjoint form of the group. We show that the moduli spaces of framed local systems ${\mathcal{X}}_{G^{\prime },S}$ and ${\mathcal{A}}_{G,S}$, which were constructed by Fock and Goncharov [‘Moduli spaces of local systems and higher Teichmuller theory’, Publ. Math. Inst. Hautes Études Sci.103 (2006), 1–212], have the structure of cluster varieties, and thus together form a cluster ensemble. This simplifies some of the proofs in that paper, and also allows one to quantize higher Teichmuller space, which was previously only possible when $G$ was of type $A$.

scholarly journals Folding orthosymplectic quivers

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Antoine Bourget ◽  
Julius F. Grimminger ◽  
Amihay Hanany ◽  
Rudolph Kalveks ◽  
Marcus Sperling ◽  
...  
Keyword(s):  
Phase Diagrams ◽  
Moduli Spaces ◽  
Nilpotent Orbits ◽  
Gauge Groups ◽  
Unitary Gauge ◽  
General Family ◽  
New Family ◽  
New Construction ◽  
Exceptional Algebras

Abstract Folding identical legs of a simply-laced quiver creates a quiver with a non-simply laced edge. So far, this has been explored for quivers containing unitary gauge groups. In this paper, orthosymplectic quivers are folded, giving rise to a new family of quivers. This is realised by intersecting orientifolds in the brane system. The monopole formula for these non-simply laced orthosymplectic quivers is introduced. Some of the folded quivers have Coulomb branches that are closures of minimal nilpotent orbits of exceptional algebras, thus providing a new construction of these fundamental moduli spaces. Moreover, a general family of folded orthosymplectic quivers is shown to be a new magnetic quiver realisation of Higgs branches of 4d $$ \mathcal{N} $$ N = 2 theories. The Hasse (phase) diagrams of certain families are derived via quiver subtraction as well as Kraft-Procesi transitions in the brane system.

Prolonging Nerve Grafts Using Chemical Extracted Muscle-in-vein with Vein Window Method Chemical acellular nerve grafts

2018 ◽  
Vol 68 (12) ◽  
pp. 2936-2940
Author(s):  
Irina Mihaela Jemnoschi Hreniuc ◽  
Camelia Tamas ◽  
Sorin Aurelian Pasca ◽  
Bogdan Ciuntu ◽  
Roxana Ciuntu ◽  
...  
Keyword(s):  
Classical Group ◽  
Donor Site ◽  
Good Alternative ◽  
Nerve Graft ◽  
Male Rats ◽  
Chemical Extraction ◽  
Nerve Grafting ◽  
Nerve Grafts ◽  
Local Resources ◽  
Window Method

Nerve injuries are a common pathology in hand trauma. The consequences are drastic both for patients and doctors/medical system. In many cases direct coaptation is impossible. A nerve graft should be used in the case of a neuroma, trauma or tumor, for restoration of nervous influx. The aim of this study is demonstrate that by grafting restant nerve stumps with muscle-in-vein nerve grafts we obtain good result in terms of functional and sensibility recovery and also our method �window-vein� is a good way of prolonging nerve grafts. The method of study is experimental. We worked in the laboratory in optimal conditions for carrying out of muscles-in-vein nerve grafts (nerve grafts size 1.5 cm-3 cm). We used acellular muscle grafts with the chemical extraction method.The study was conducted on experimental animals (Wistar male rats).We used 30 experience animals in 3 equal groups (classical group and muscle-in-vein nerve grafts-2 nerve grafts of 1,5 cm central sutured and the third group with muscle-in-vein nerve grafts, window-vein method, 3 cm). At 4 and respectively 6 weeks postoperative at the quality tests we observed the progress with the footprint test. The operated hind in comparison with the healthy hind was 86% recovered and similar with classic nerve grafts. Quantitatively the number of regenerated axons in the group with muscle-in-vein nerve grafts was significant bigger in comparison with the classical group (15%).The method using muscle-in-vein nerve graft with windows-vein it�s a good alternative for nerve grafting in comparison with classical nerve grafting. When the local possibilities are limited, this method is good for prolonging the grafts. The relationship between cost and benefit in this case it�s an advantage because we use the local resources of the affected area. The motor results of nerve grafting ingroup 2 in comparison with group 3 were similar and in some cases better in group 1. Grafting with MVNG offers a better alternative for donor site regeneration in comparison with classical nerve grafts. This method is useful to prolong nerve grafts without adding morbidity.

Geometry and Physics: Volume II

2018 ◽  
Keyword(s):  
Moduli Spaces ◽  
Mirror Symmetry ◽  
Geometric Analysis ◽  
Mathematical Physics ◽  
Poisson Geometry ◽  
Special Holonomy ◽  
Low Dimensional Topology ◽  
Generalized Complex Structures ◽  
Wide Range ◽  
Low Dimensional

These volumes contain the proceedings of the conference held at Aarhus, Oxford and Madrid in September 2016 to mark the seventieth birthday of Nigel Hitchin, one of the world’s foremost geometers and Savilian Professor of Geometry at Oxford. The proceedings contain twenty-nine articles, including three by Fields medallists (Donaldson, Mori and Yau). The articles cover a wide range of topics in geometry and mathematical physics, including the following: Riemannian geometry, geometric analysis, special holonomy, integrable systems, dynamical systems, generalized complex structures, symplectic and Poisson geometry, low-dimensional topology, algebraic geometry, moduli spaces, Higgs bundles, geometric Langlands programme, mirror symmetry and string theory. These volumes will be of interest to researchers and graduate students both in geometry and mathematical physics.

scholarly journals On the Voevodsky motive of the moduli space of Higgs bundles on a curve

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Victoria Hoskins ◽  
Simon Pepin Lehalleur
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Characteristic Zero ◽  
Rational Point ◽  
Triangulated Category ◽  
Higgs Bundles ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
De Rham

AbstractWe study the motive of the moduli space of semistable Higgs bundles of coprime rank and degree on a smooth projective curve C over a field k under the assumption that C has a rational point. We show this motive is contained in the thick tensor subcategory of Voevodsky’s triangulated category of motives with rational coefficients generated by the motive of C. Moreover, over a field of characteristic zero, we prove a motivic non-abelian Hodge correspondence: the integral motives of the Higgs and de Rham moduli spaces are isomorphic.

scholarly journals EXTREMAL CASES OF RAPOPORT–ZINK SPACES

2021 ◽  
pp. 1-56
Author(s):  
Ulrich Görtz ◽  
Xuhua He ◽  
Michael Rapoport
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Complete List ◽  
Qualitative Properties ◽  
Model Case ◽  
Divisible Groups

Abstract We investigate qualitative properties of the underlying scheme of Rapoport–Zink formal moduli spaces of p-divisible groups (resp., shtukas). We single out those cases where the dimension of this underlying scheme is zero (resp., those where the dimension is the maximal possible). The model case for the first alternative is the Lubin–Tate moduli space, and the model case for the second alternative is the Drinfeld moduli space. We exhibit a complete list in both cases.

scholarly journals Holomorphic anomaly equation for and the Nekrasov-Shatashvili limit of local

2021 ◽  
Vol 9 ◽  
Author(s):  
Pierrick Bousseau ◽  
Honglu Fan ◽  
Shuai Guo ◽  
Longting Wu
Keyword(s):  
Elliptic Curve ◽  
Moduli Spaces ◽  
Topological String ◽  
Holomorphic Anomaly ◽  
Holomorphic Anomaly Equation ◽  
Anomaly Equation ◽  
Witten Theory ◽  
Generating Series ◽  
Maximal Contact ◽  
Higher Genus

Abstract We prove a higher genus version of the genus $0$ local-relative correspondence of van Garrel-Graber-Ruddat: for $(X,D)$ a pair with X a smooth projective variety and D a nef smooth divisor, maximal contact Gromov-Witten theory of $(X,D)$ with $\lambda _g$ -insertion is related to Gromov-Witten theory of the total space of ${\mathcal O}_X(-D)$ and local Gromov-Witten theory of D. Specializing to $(X,D)=(S,E)$ for S a del Pezzo surface or a rational elliptic surface and E a smooth anticanonical divisor, we show that maximal contact Gromov-Witten theory of $(S,E)$ is determined by the Gromov-Witten theory of the Calabi-Yau 3-fold ${\mathcal O}_S(-E)$ and the stationary Gromov-Witten theory of the elliptic curve E. Specializing further to $S={\mathbb P}^2$ , we prove that higher genus generating series of maximal contact Gromov-Witten invariants of $({\mathbb P}^2,E)$ are quasimodular and satisfy a holomorphic anomaly equation. The proof combines the quasimodularity results and the holomorphic anomaly equations previously known for local ${\mathbb P}^2$ and the elliptic curve. Furthermore, using the connection between maximal contact Gromov-Witten invariants of $({\mathbb P}^2,E)$ and Betti numbers of moduli spaces of semistable one-dimensional sheaves on ${\mathbb P}^2$ , we obtain a proof of the quasimodularity and holomorphic anomaly equation predicted in the physics literature for the refined topological string free energy of local ${\mathbb P}^2$ in the Nekrasov-Shatashvili limit.

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