Higher teichmuller theory

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August undefined, 2024

WebIn this PhD thesis, we give a new geometric approach to higher Teichmuller theory. In particular we construct a geometric structure on surfaces, generalizing the complex structure, and we explore its link to Hitchin components. The construction of this structure, called higher complex structure, uses the punctual Hilbert scheme of the plane. Its … WebLENGTH ASYMPTOTICS IN HIGHER TEICHMULLER THEORY 3 The standard presentation of ˇ 1(S) of a surface of genus ghas generators a i, b i, where 1 i gand a relation Q 4 i=1 [a i;b i] = I. Starting from the canonical representation of a surface group ˇ 1(S) !SL(2;R) !SL(3;R) in Example 2.1 we can make a perturbation within the Hitchin …

An introduction to pressure metrics for higher Teichmüller spaces

WebP.I.C. M.–2024 RiodeJaneiro,Vol.2(1031–1058) ANINVITATIONTOHIGHERTEICHMÜLLERTHEORY AW Abstract … WebTeichmüller theory is the ever-expanding manual to this unique feature of mathematics. I'll indicate its broad lines in the next few paragraphs. The primary focus of Teichmüller theory is Riemann surfaces of finite topological type, thus surfaces with g handles, m punctures, and n holes, for some triple of non-negative integers (g,m,n). t shirt printing kirkcaldy

An invitation to higher Teichmüller theory – Anna Wienhard ...

Web25 de jan. de 2024 · This paper is a survey on the role of Higgs bundle theory in the study of higher Teichmuller spaces. Recall that the Teichmuller space of a compact surface can be identified with a certain connected component of the moduli space of representations of the fundamental group of the surface into $\mathrm {PSL} (2, {\mathbb {R}})$. Web10 de jun. de 2024 · In this PhD thesis, we give a new geometric approach to higher Teichmüller theory. In particular we construct a geometric structure on surfaces, generalizing the complex structure, and we... Web10 de jun. de 2024 · In this PhD thesis, we give a new geometric approach to higher Teichmüller theory. In particular we construct a geometric structure on surfaces, … philosophy song lyrics

Inter-universal Teichmüller theory - Wikipedia

Higher teichmuller theory

Galois–Teichmüller Theory and Arithmetic Geometry

Web2 de out. de 2013 · In this note, we recover a recent result of Sambarino by showing that certain length functions arising in higher Teichm¨uller theory satisfy a prime geodesic theorem analogous to that of Huber in the classical case. We also show that there are more sophisticated distributional and limiting results. WebFrom the 1980's, Grothendieck's “Esquisse d'un Programme” triggered tremendous developments in number theory and arithmetic geometry, extending from the studies of anabelian geometry and related Galois representations to those of polylogarithms and multiple zeta values, motives, rational points on arithmetic varieties, and effectiveness …

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WebIntroduction to Teichmu¨ller Theory Michael Kapovich August 31, 2008 1 Introduction This set of notes contains basic material on Riemann surfaces, Teichmu¨ller spaces and … WebI was a PhD student at Université de Paris-Sud between 2010-2014, under the direction of Prof. François Labourie. Research Interests Higher Teichmuller theory: low dimensional topology, and...

Web23 de mai. de 2016 · These include (but not limited to) the role of virtually special groups, representations of Kleinian groups in SL(2,C) and generalizations (e.g. Higher Teichmuller Theory), the Mapping Class Group and its recent role in low dimensional geometry and topology and group theoretic connections with Heegaard Floer theory through left … Webbraic geometry. In recent years, higher Teichmüller theory emerged as a new ﬁeld in mathematics. It builds as well on a combination of methods from diﬀerent areas of mathematics. The goal of this article is to invite the reader to get to know and to get …

WebIn mathematics, the Teichmüller space of a (real) topological (or differential) surface , is a space that parametrizes complex structures on up to the action of … WebAbout Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright ...

Web16 de abr. de 2010 · Higher Teichmüller Spaces: from SL (2,R) to other Lie groups Marc Burger, Alessandra Iozzi, Anna Wienhard The first part of this paper surveys several …

Web8 de mai. de 2024 · 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 … t shirt printing lakewood ohioWeb2 de out. de 2013 · In this note, we recover a recent result of Sambarino by showing that certain length functions arising in higher Teichm¨uller theory satisfy a prime geodesic … t-shirt printing kissimmee flWebOur higher Teichmüller spaces will be spaces of Anosov representations of a word-hyperbolic group into a semi-simple Lie group. We begin by discussing our construction in the classical setting of the Teichmüller space of a closed orientable surface of genus at least 2, then we explain the construction for Hitchin components and finally we treat the … philosophy sophie\u0027s worldWeb10 de nov. de 2003 · Their positive real points provide the two higher Teichmuller spaces related to G and S, while the points with values in the tropical semifields provide the … t-shirt printing lawrence ksWebGeometryInvited Lecture 5.11An invitation to higher Teichmüller theoryAnna Wienhard Abstract: Riemann surfaces are of fundamental importance in many areas of... philosophy songsWeb25 de jan. de 2024 · Higher Teichmüller spaces correspond to special components of the moduli space of representations when one replaces by a real non-compact semisimple Lie group of higher rank. Examples of these spaces are provided by the Hitchin components for split real groups, and maximal Toledo invariant components for groups of Hermitian type. t shirt printing lexington ncWebIn this note, we recover a recent result of Sambarino by showing that certain length functions arising in higher Teichm¨uller theory satisfy a prime geodesic theorem analogous to that of Huber in the classical case. We also show that there are more sophisticated distributional and limiting results. 1. t-shirt printing las vegas