Notice
R. Gutierrez - Quaternionic monodromies of the Kontsevich–Zorich cocycle
- document 1 document 2 document 3
- niveau 1 niveau 2 niveau 3
Descriptif
The monodromy group of a translation surface M is the Lie group spanned by all symplectic matrices arising from the homological action of closed loops at M (inside its embodying orbit closure). In the presence of zero Lyapunov exponents, Filip showed that these groups are —up to compact factors and finite-index b groups— constrained at the level of Lie groups presentations: they are either special quaternionic orthogonal groups SO*(2n) for odd n, special unitary groups SU (p,q) for p superior q, or exterior powers of SU(p,1). Nevertheless, it does not follow from these constraints that every group in this list is realizable as the monodromy group of some translation surface.
By the work of Avila–Matheus–Yoccoz, it is known that every SU (p,q) is realizable. Moreover, the work of Filip–Forni–Matheus shows an example that realizes SO *(6), which coincides with the second exterior power of SU( 3 , 1 ). In this talk, we show that the groups SO *( 2 n ) are realizable as monodromy groups for infinitely many odd values of n . To this end, we find concrete examples of square-tiled surfaces constructed as quaternionic covers —generalizing the construction by Filip–Forni–Matheus— having such groups as their monodromies (up to compact factors and finite-index subgroups). Our construction is valid for every n in the congruence class of 3 mod 8, up to a zero-density set.
Dans la même collection
-
A. Zorich - Counting simple closed geodesics and volumes of moduli spaces (Part 1)
ZorichAntonIn the first two lectures I will try to tell (or, rather, to give an idea) of how Maryam Mirzakhani has counted simple closed geodesics on hyperbolic surfaces. I plan to briefly mention her
-
Ö. Yurttas - Algorithms for multicurves with Dynnikov coordinates
YurttasÖyküMulticurves have played a fundamental role in the study of mapping class groups of surfaces since the work of Dehn. A beautiful method of describing such systems on the n-punctured disk is given by
-
A. Zorich - Counting simple closed geodesics and volumes of moduli spaces (Part 3)
ZorichAntonIn the first two lectures I will try to tell (or, rather, to give an idea) of how Maryam Mirzakhani has counted simple closed geodesics on hyperbolic surfaces. I plan to briefly mention her
-
A. Wright - Mirzakhani's work on Earthquakes (Part 3)
WrightAlexanderWe will give the proof of Mirzakhani's theorem that the earthquake flow and Teichmuller unipotent flow are measurably isomorphic. We will assume some familiarity with quadratic differentials, but no
-
-
B. Deroin - Monodromy of algebraic families of curves (Part 2)
DeroinBertrandThe mini-course will focus on the properties of the monodromies of algebraic families of curves defined over the complex numbers. One of the goal will be to prove the irreducibility of those
-
J. Smillie - Horocycle dynamics (Part 2)
SmillieJohnA major challenge in dynamics on moduli spaces is to understand the behavior of the horocycle flow. We will motivate this problem and discuss what is known and what is not known about it, focusing on
-
P. Hubert - Rauzy gasket, Arnoux-Yoccoz interval exchange map, Novikov's problem (Part 2)
HubertPascal1. Symbolic dynamics: Arnoux - Rauzy words and Rauzy gasket 2. Topology: Arnoux - Yoccoz example and its generalization 3. Novikov’s problem: how dynamics meets topology and together they help to
-
J. Aramayona - MCG and infinite MCG (Part 2)
AramayonaJavierThe first part of the course will be devoted to some of the classical results about mapping class groups of finite-type surfaces. Topics may include: generation by twists, Nielsen-Thurston
-
-
G. Forni - Cohomological equation and Ruelle resonnences (Part 2)
In these lectures we summarized results on the cohomological equation for translation flows on translation surfaces (myself, Marmi, Moussa and Yoccoz, Marmi and Yoccoz) and apply these results to the
-
A. Wright - Mirzakhani's work on Earthquakes (Part 2)
WrightAlexanderWe will give the proof of Mirzakhani's theorem that the earthquake flow and Teichmuller unipotent flow are measurably isomorphic. We will assume some familiarity with quadratic differentials, but no
Sur le même thème
-
"Le mathématicien Petre (Pierre) Sergescu, historien des sciences, personnalité du XXe siècle"
HerléaAlexandreAlexandre HERLEA est membre de la section « Sciences, histoire des sciences et des techniques et archéologie industrielle » du CTHS. Professeur émérite des universités, membre effectif de l'Académie
-
Webinaire sur la rédaction des PGD
LouvetViolaineRédaction des Plans de Gestion de Données (PGD) sous l’angle des besoins de la communauté mathématique.
-
Alexandre Booms : « Usage de matériel pédagogique adapté en géométrie : une transposition à interro…
« Usage de matériel pédagogique adapté en géométrie : une transposition à interroger ». Alexandre Booms, doctorant (Université de Reims Champagne-Ardenne - Cérep UR 4692)
-
J. Wang - Topological rigidity and positive scalar curvature
WangJianIn this talk, we shall describe some topological rigidity and its relationship with positive scalar curvature. Precisely, we will present a proof that a complete contractible 3-manifold with
-
R. Perales - Recent Intrinsic Flat Convergence Theorems
PeralesRaquelThéorèmes récents de convergence plane intrinsèque
-
J. Fine - Knots, minimal surfaces and J-holomorphic curves
FineJoëlI will describe work in progress, parts of which are joint with Marcelo Alves. Let L be a knot or link in the 3-sphere. I will explain how one can count minimal surfaces in hyperbolic 4-space
-
D. Semola - Boundary regularity and stability under lower Ricci bounds
SemolaDanieleThe theory of non smooth spaces with lower Ricci Curvature bounds has undergone huge developments in the last thirty years. On the one hand the impetus came from Gromov’s precompactness theorem
-
D. Stern - Harmonic map methods in spectral geometry
SternDanielOver the last fifty years, the problem of finding sharp upper bounds for area-normalized Laplacian eigenvalues on closed surfaces has attracted the attention of many geometers, due in part to
-
P. Burkhardt - Pointwise lower scalar curvature bounds for C0 metrics via regularizing Ricci flow
Burkhardt-GuimPaulaWe propose a class of local definitions of weak lower scalar curvature bounds that is well defined for C0 metrics. We show the following: that our definitions are stable under greater-than-second
-
R. Bamler - Compactness and partial regularity theory of Ricci flows in higher dimensions
BamlerRichard H.We present a new compactness theory of Ricci flows. This theory states that any sequence of Ricci flows that is pointed in an appropriate sense, subsequentially converges to a synthetic flow.
-
C. Li - Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions
LiChaoIn this talk, I will discuss some recent developments on the topology of closed manifolds admitting Riemannian metrics of positive scalar curvature. In particular, we will prove if a closed PSC
-
Y. Lai - A family of 3d steady gradient Ricci solitons that are flying wings
LaiYiWe find a family of 3d steady gradient Ricci solitons that are flying wings. This verifies a conjecture by Hamilton. For a 3d flying wing, we show that the scalar curvature does not vanish at
