Department of Mathematics - Geometry & Topology
https://math.yale.edu/seminars/geometry-topology
enSublinear Rigidity of Lattices in Semisimple Lie Groups
https://math.yale.edu/event/sublinear-rigidity-lattices-semisimple-lie-groups
<div class="label-inline">Time: </div><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2023-04-18T16:15:00-04:00">4:15pm</span><div class="label-above">Speaker: </div>Ido Grayevsky<div class="label-above">Abstract: </div><p>I will discuss metric deformations of lattices in semisimple Lie groups. The underlying question is whether the class of lattices is stable (rigid) under distortions of 'sublinear' nature. I will present work that settles this question in the affirmative in almost all settings. For groups without real rank 1 factors, this amounts to a sublinear generalization of the classical quasi-isometric rigidity results.<br />
The main focus of my talk will be the geometric structure of non-uniform lattices and its relation to the horospheres of the corresponding symmetric space. I aim to describe the proof of a key proposition, which is motivated by a lattice criterion conjectured by Margulis and proven by Oh and Benoist-Miquel.</p>
<div class="label-inline">Seminar: </div><a href="/seminars/geometry-topology">Geometry & Topology</a><div class="label-above">Undergraduate Event?: </div>FalseFri, 10 Mar 2023 18:05:02 +0000Subhadip Dey24699 at https://math.yale.eduhttps://math.yale.edu/event/sublinear-rigidity-lattices-semisimple-lie-groups#commentsSubgroups of SO(3,Q)
https://math.yale.edu/event/subgroups-so3q
<div class="label-inline">Time: </div><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2023-04-25T16:15:00-04:00">4:15pm</span><div class="label-above">Speaker: </div>Nic Brody<div class="label-inline">Location: </div><div class="location vcard">
<div class="adr">
<span class="fn">LOM 206</span>
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</div>
<div class="label-above">Abstract: </div><p>The classification of finite subgroups of SO(3) is a classical problem in geometry. In this talk, we will welcome in the much larger class of rational rotation groups and see what sense can be made of such groups. Call a subgroup G of SO(3,Q) primary if it is discrete in some p-adic topology. These groups are essentially free groups, and we’ll consider them well-understood. We entertain the possibility that any subgroup of SO(3,Q) which is not abelian or primary might be forced to be arithmetic, meaning that it looks a lot like SO(3,A) for a subring A of Q. We prove some results supporting this conjecture, including some special cases of the conjecture and a rigidity result. This conjecture has many analogues in the broader study of discrete subgroups of Lie groups, and has many consequences in geometry and group theory.</p>
<div class="label-inline">Seminar: </div><a href="/seminars/geometry-topology">Geometry & Topology</a><div class="label-above">Undergraduate Event?: </div>FalseThu, 26 Jan 2023 20:29:41 +0000Franco Vargas Pallete24676 at https://math.yale.eduhttps://math.yale.edu/event/subgroups-so3q#commentsOn the 1-loop conjecture of fundamental shadow link complements
https://math.yale.edu/event/1-loop-conjecture-fundamental-shadow-link-complements
<div class="label-inline">Time: </div><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2023-02-14T14:45:00-05:00">2:45pm</span><div class="label-above">Speaker: </div>Ka Ho Wong<div class="label-inline">Location: </div><div class="location vcard">
<div class="adr">
<span class="fn">LOM 200</span>
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</div>
<div class="label-above">Abstract: </div><p>The 1-loop conjecture proposed by Dimofte and Garoufalidis suggests a simple and explicit formula to compute the adjoint twisted Reidemeister torsion of hyperbolic 3-manifolds with toroidal boundary in terms of the shape parameters of any ideal triangulation of the manifolds. In this talk, I will give a brief overview of the conjecture and present our recent result on the 1-loop conjecture for fundamental shadow link complements. This is a joint work with Tushar Pandey.</p>
<div class="label-inline">Seminar: </div><a href="/seminars/geometry-topology">Geometry & Topology</a><div class="label-above">Undergraduate Event?: </div>FalseThu, 19 Jan 2023 18:01:42 +0000Franco Vargas Pallete24647 at https://math.yale.eduhttps://math.yale.edu/event/1-loop-conjecture-fundamental-shadow-link-complements#commentsHorocycle flow on the moduli space of translation surfaces
https://math.yale.edu/event/horocycle-flow-moduli-space-translation-surfaces
<div class="label-inline">Time: </div><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2023-04-11T16:15:00-04:00">4:15pm</span><div class="label-above">Speaker: </div>Barak Weiss<div class="label-inline">Location: </div><div class="location vcard">
<div class="adr">
<span class="fn">LOM 206</span>
</div>
</div>
<div class="label-above">Abstract: </div><p>I will discuss the dynamics of the horocycle flow on a stratum of translation surfaces (which is an invariant subvariety of the bundle Omega M_g of holomorphic one forms over the moduli space of genus g Riemann surfaces). This flow can be defined as the action of upper triangular matrices with eigenvalue 1, acting linearly on flat charts. Work of Ratner on unipotent flows on homogeneous spaces leads to the question of whether the orbit-closures and invariant measures for this action can be meaningfully classified. I will quickly survey both positive and negative results in this direction. The talk will be based on joint work with Bainbridge, Chaika, Smillie, and Ygouf (in various combinations).</p>
<div class="label-inline">Seminar: </div><a href="/seminars/geometry-topology">Geometry & Topology</a><div class="label-above">Undergraduate Event?: </div>FalseSat, 24 Dec 2022 14:38:11 +0000Franco Vargas Pallete24635 at https://math.yale.eduhttps://math.yale.edu/event/horocycle-flow-moduli-space-translation-surfaces#commentsCircle homeomorphisms with square summable diamond shears
https://math.yale.edu/event/circle-homeomorphisms-square-summable-diamond-shears
<div class="label-inline">Time: </div><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2023-04-04T16:15:00-04:00">4:15pm</span><div class="label-above">Speaker: </div>Yilin Wang<div class="label-inline">Location: </div><div class="location vcard">
<div class="adr">
<span class="fn">LOM 206</span>
</div>
</div>
<div class="label-above">Abstract: </div><p>The shear coordinate is a countable coordinate system to describe increasing self-maps of the unit circle, which is furthermore invariant under modular transformations. Characterizations of circle homeomorphism, quasisymmetric homeomorphisms were obtained by D.Šarić. We are interested in characterizing Weil-Petersson circle homeomorphisms using shears. This class of homeomorphisms arises from the study of Kähler geometry on the universal Teichmüller space and connects various distant fields that will be mentioned briefly. </p>
<p>For this, we introduce diamond shear which is the minimal combination of shears producing WP homeomorphisms. Diamond shears are closely related to log-Lambda length introduced by R. Penner. We obtain sharp results comparing the class of circle homeomorphisms with square summable diamond shears with the Weil-Petersson class and Hölder classes. We also express the Weil-Petersson metric tensor and symplectic form in terms of infinitesimal shears and diamond shears. </p>
<p>This talk is based on joint work with Dragomir Šarić and Catherine Wolfram. See <a href="https://arxiv.org/abs/2211.11497">https://arxiv.org/abs/2211.11497</a>.</p>
<div class="label-inline">Seminar: </div><a href="/seminars/geometry-topology">Geometry & Topology</a><div class="label-above">Undergraduate Event?: </div>FalseTue, 13 Dec 2022 22:12:17 +0000Franco Vargas Pallete24633 at https://math.yale.eduhttps://math.yale.edu/event/circle-homeomorphisms-square-summable-diamond-shears#commentsHomogeneous Riemann surfaces
https://math.yale.edu/event/homogeneous-riemann-surfaces
<div class="label-inline">Time: </div><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2023-02-21T16:15:00-05:00">4:15pm</span><div class="label-above">Speaker: </div>Ara Basmajian<div class="label-inline">Location: </div><div class="location vcard">
<div class="adr">
<span class="fn">LOM 206</span>
</div>
</div>
<div class="label-above">Abstract: </div><p>We are interested in spaces that look the same from any point of the space (that is, ``homogeneous spaces"). Of course the notion of looking the same is dependent on the context. For example, the simply connected Riemann surfaces, namely the Riemann sphere, complex plane, and unit disc are conformally homogeneous Riemann surfaces. In fact, along with the punctured plane and the torus these are the only ones. On the other hand, given any surface it is not difficult to cook up a diffeomorphism between any two points of the surface. Hence one needs a notion that is not as strong as conformality and not as weak as differentiability. The key observation is that while smooth maps can distort infinitesimal circles to ellipses with unbounded eccentricity (the ratio of the major to the minor axis can be arbitrarily large), conformal maps do not distort infinitesimal circles at all. This leads to the notion of a homeomorphism being K-quasiconformal (has eccentricity bounded by K). Conformal homeomorphisms are 1-quasiconformal. </p>
<p>A Riemann Surface X is said to be K-quasiconformally homogeneous if for any two points x and y on it, there exists a K-quasiconformal self-mapping taking x to y. If such a K exists we say that X is a QCH Riemann surface. After introducing the basics, the focus of this talk will be on Riemann surface structures that are QCH, and their connections to the topology and hyperbolic geometry of the surface.</p>
<div class="label-inline">Seminar: </div><a href="/seminars/geometry-topology">Geometry & Topology</a><div class="label-above">Undergraduate Event?: </div>FalseMon, 05 Dec 2022 11:08:19 +0000Franco Vargas Pallete24631 at https://math.yale.eduhttps://math.yale.edu/event/homogeneous-riemann-surfaces#commentsThe symplectic structure of the SL_n(R)-Hitchin component
https://math.yale.edu/event/symplectic-structure-slnr-hitchin-component
<div class="label-inline">Time: </div><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2023-02-07T16:15:00-05:00">4:15pm</span><div class="label-above">Speaker: </div>Francis Bonahon<div class="label-inline">Location: </div><div class="location vcard">
<div class="adr">
<span class="fn">LOM 206</span>
</div>
</div>
<div class="label-above">Abstract: </div><p>The SL_n(R)-Hitchin component of a closed surface is a special component in the character variety consisting of homomorphisms from the fundamental group of the surface to the Lie group SL_n(R). It carries a symplectic structure, defined by the Atiyah-Bott-Goldman form. I will provide an explicit computation of this symplectic form in terms of the generalized Fock-Goncharov coordinates of the Hitchin component (associated to a geodesic lamination on the surface).</p>
<div class="label-inline">Seminar: </div><a href="/seminars/geometry-topology">Geometry & Topology</a><div class="label-above">Undergraduate Event?: </div>FalseMon, 28 Nov 2022 19:32:38 +0000Franco Vargas Pallete24628 at https://math.yale.eduhttps://math.yale.edu/event/symplectic-structure-slnr-hitchin-component#commentsOrientable maps and polynomial invariants of free-by-cyclic groups
https://math.yale.edu/event/orientable-maps-and-polynomial-invariants-free-cyclic-groups
<div class="label-inline">Time: </div><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2023-03-28T16:15:00-04:00">4:15pm</span><div class="label-above">Speaker: </div>Samuel Taylor<div class="label-inline">Location: </div><div class="location vcard">
<div class="adr">
<span class="fn">LOM 206</span>
</div>
</div>
<div class="label-above">Abstract: </div><p>We relate the McMullen polynomial of a free-by-cyclic group to its Alexander polynomial. To do so, we introduce the notion of an orientable fully irreducible outer automorphism F and use it to characterize when the homological stretch factor of F is equal to its geometric stretch factor. This is joint work with Spencer Dowdall and Radhika Gupta.</p>
<div class="label-inline">Seminar: </div><a href="/seminars/geometry-topology">Geometry & Topology</a><div class="label-above">Undergraduate Event?: </div>FalseMon, 28 Nov 2022 15:48:01 +0000Franco Vargas Pallete24626 at https://math.yale.eduhttps://math.yale.edu/event/orientable-maps-and-polynomial-invariants-free-cyclic-groups#commentsHitchin representations and minimal surfaces
https://math.yale.edu/event/hitchin-representations-and-minimal-surfaces
<div class="label-inline">Time: </div><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2023-01-24T16:15:00-05:00">4:15pm</span><div class="label-above">Speaker: </div>Nathaniel Sagman<div class="label-inline">Location: </div><div class="location vcard">
<div class="adr">
<span class="fn">LOM 206</span>
</div>
</div>
<div class="label-above">Abstract: </div><p>Abstract: Labourie proved that every Hitchin representation into PSL(n,R) gives rise to an equivariant minimal surface in the corresponding symmetric space. He conjectured that uniqueness holds as well (this was known for n=2,3) and explained that if true, then the Hitchin component admits a mapping class group equivariant parametrization as a holomorphic vector bundle over Teichmüller space. After giving the relevant background, we will explain that Labourie’s conjecture fails for n at least 4, and point to some future questions.</p>
<div class="label-inline">Seminar: </div><a href="/seminars/geometry-topology">Geometry & Topology</a><div class="label-above">Undergraduate Event?: </div>FalseSun, 27 Nov 2022 18:39:12 +0000Franco Vargas Pallete24625 at https://math.yale.eduhttps://math.yale.edu/event/hitchin-representations-and-minimal-surfaces#commentsAnosov Flows on 3-manifolds
https://math.yale.edu/event/anosov-flows-3-manifolds
<div class="label-inline">Time: </div><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2023-02-28T16:15:00-05:00">4:15pm</span><div class="label-above">Speaker: </div>Katie Mann<div class="label-inline">Location: </div><div class="location vcard">
<div class="adr">
<span class="fn">LOM 206</span>
</div>
</div>
<div class="label-above">Abstract: </div><p>Anosov flows are rich examples of dynamical systems, they include the geodesic flows on unit tangent bundles of hyperbolic surfaces, and many other examples. This talk is about how dynamics, geometry and topology interact in dimension 3 via some longstanding open questions: Which 3-manifolds support Anosov flows? Which 3-manifolds support many topologically distinct Anosov flows? What invariants can be used to distinguish them? I will describe some of the state of the art, and recent work with Thomas Barthelmé, Steven Frankel, and Sergio Fenley that provides new topological invariants towards this classification problem.</p>
<div class="label-inline">Seminar: </div><a href="/seminars/geometry-topology">Geometry & Topology</a><div class="label-above">Undergraduate Event?: </div>FalseMon, 17 Oct 2022 18:00:19 +0000Sebastian Hurtado - Salazar24603 at https://math.yale.eduhttps://math.yale.edu/event/anosov-flows-3-manifolds#comments