Department of Mathematics - Geometry & Topology
https://math.yale.edu/seminars/geometry-topology
enMorse boundaries of CAT(0) cubical groups
https://math.yale.edu/event/morse-boundaries-cat0-cubical-groups
<div class="label-inline">Time: </div><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2024-04-30T16:00:00-04:00">4:00pm</span><div class="label-above">Speaker: </div>Carolyn Abbott<div class="label-inline">Location: </div><div class="location vcard">
<div class="adr">
<span class="fn">KT 205</span>
</div>
</div>
<div class="label-above">Abstract: </div><p>The visual boundary of a hyperbolic space is a quasi-isometry invariant that has proven to be a very useful tool in geometric group theory. When one considers CAT(0) spaces, however, the situation is more complicated, because the visual boundary is not a quasi-isometry invariant. Instead, one can consider a natural subspace of the visual boundary, called the (sublinearly) Morse boundary. In this talk, I will describe a new topology on this boundary and use it to show that the Morse boundary with the restriction of the visual topology is a quasi-isometry invariant in the case of (nice) CAT(0) cube complexes. This result is in contrast to Cashen’s result that the Morse boundary with the visual topology is not a quasi-isometry invariant of CAT(0) spaces in general. This is joint work with Merlin Incerti-Medici.</p>
<div class="label-inline">Seminar: </div><a href="/seminars/geometry-topology">Geometry & Topology</a><div class="label-above">Undergraduate Event?: </div>FalseTue, 23 Jan 2024 01:28:06 +0000Franco Vargas Pallete24847 at https://math.yale.eduhttps://math.yale.edu/event/morse-boundaries-cat0-cubical-groups#commentsIsoperimetry and volume preserving stability under symmetry constraint in space forms.
https://math.yale.edu/event/isoperimetry-and-volume-preserving-stability-under-symmetry-constraint-space-forms
<div class="label-inline">Time: </div><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2024-04-23T16:00:00-04:00">4:00pm</span><div class="label-above">Speaker: </div>Celso Viana<div class="label-inline">Location: </div><div class="location vcard">
<div class="adr">
<span class="fn">KT 205</span>
</div>
</div>
<div class="label-above">Abstract: </div><p>In this talk we will discuss the isoperimetric problem and volume preserving stability under additional restriction of symmetry from the ambient space. The scenarios of interest include the Euclidean ball, the round sphere, and the Gaussian space. Among other partial results, we show an isoperimetric characterization for slabs bounded by two parallel planes for a certain range of the Gaussian volume.</p>
<div class="label-inline">Seminar: </div><a href="/seminars/geometry-topology">Geometry & Topology</a><div class="label-above">Undergraduate Event?: </div>FalseFri, 19 Jan 2024 15:15:36 +0000Subhadip Dey24845 at https://math.yale.eduhttps://math.yale.edu/event/isoperimetry-and-volume-preserving-stability-under-symmetry-constraint-space-forms#commentsShort curves of end-periodic mapping tori
https://math.yale.edu/event/short-curves-end-periodic-mapping-tori
<div class="label-inline">Time: </div><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2024-04-16T16:00:00-04:00">4:00pm</span><div class="label-above">Speaker: </div>Brandis Whitfield<div class="label-inline">Location: </div><div class="location vcard">
<div class="adr">
<span class="fn">KT 205</span>
</div>
</div>
<div class="label-above">Abstract: </div><p>Let $S$ be a boundaryless infinite-type surface with finitely many ends and consider an end-periodic homeomorphism $f$ of S. The end-periodicity of $f$ ensures that $M_f$, its associated mapping torus, has a compactification as a $3$-manifold with boundary; and further, if $f$ is atoroidal, then $M_f$ admits a hyperbolic metric.</p>
<p>As an end-periodic analogy to work of Minsky in the finite-type setting, we show that given a subsurface $Y\subset S$, the subsurface projections between the ``positive" and ``negative" Handel-Miller laminations provide bounds for the geodesic length of the boundary of $Y$ as it resides in $M_f$.</p>
<p>In this talk, we'll discuss the motivating theory for finite-type surfaces and closed fibered hyperbolic $3$-manifolds, and how these techniques may be used in the infinite-type setting.</p>
<div class="label-inline">Seminar: </div><a href="/seminars/geometry-topology">Geometry & Topology</a><div class="label-above">Undergraduate Event?: </div>FalseFri, 19 Jan 2024 15:14:44 +0000Subhadip Dey24844 at https://math.yale.eduhttps://math.yale.edu/event/short-curves-end-periodic-mapping-tori#commentsHorocycle orbit closures in periodic surfaces
https://math.yale.edu/event/horocycle-orbit-closures-periodic-surfaces
<div class="label-inline">Time: </div><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2024-01-30T16:00:00-05:00">4:00pm</span><div class="label-above">Speaker: </div>Yair Minsky<div class="label-inline">Location: </div><div class="location vcard">
<div class="adr">
<span class="fn">KT 205</span>
</div>
</div>
<div class="label-above">Abstract: </div><p>(Joint work with James Farre and Or Landesberg) </p>
<p>Horocyclic (and generally horospherical) orbit closures in hyperbolic manifolds are not very well understood in the infinite-volume setting. For finite volume it is classical that they are either closed (associated to cusps) or dense. In the case of Z-covers of compact manifolds there is an interesting connection between such closures and the geometry of "tight" circle valued functions on the compact manifolds and their maximal-stretch laminations. In dimension 2, this makes it possible to describe the orbit closures in great detail. In particular, although nontrivial orbit closures are fractal in some sense, they always have integral Hausdorff dimension.</p>
<div class="label-inline">Seminar: </div><a href="/seminars/geometry-topology">Geometry & Topology</a><div class="label-above">Undergraduate Event?: </div>FalseFri, 19 Jan 2024 15:13:56 +0000Subhadip Dey24843 at https://math.yale.eduhttps://math.yale.edu/event/horocycle-orbit-closures-periodic-surfaces#commentsTBA
https://math.yale.edu/event/tba-72
<div class="label-inline">Time: </div><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2024-03-05T16:00:00-05:00">4:00pm</span><div class="label-inline">Seminar: </div><a href="/seminars/geometry-topology">Geometry & Topology</a><div class="label-above">Undergraduate Event?: </div>FalseFri, 19 Jan 2024 15:12:54 +0000Subhadip Dey24842 at https://math.yale.eduhttps://math.yale.edu/event/tba-72#commentsExistence of quasigeodesic Anosov flows in hyperbolic 3-manifolds
https://math.yale.edu/event/existence-quasigeodesic-anosov-flows-hyperbolic-3-manifolds
<div class="label-inline">Time: </div><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2024-02-20T16:00:00-05:00">4:00pm</span><div class="label-above">Speaker: </div>Sergio Fenley<div class="label-inline">Location: </div><div class="location vcard">
<div class="adr">
<span class="fn">KT 205</span>
</div>
</div>
<div class="label-above">Abstract: </div><p>A quasigeodesic in a manifold is a curve so that when lifted to the universal cover is uniformly efficient up to a bounded multiplicative and added error in measuring length. A flow is quasigeodesic if all flow lines are quasigeodesics. We prove that an Anosov flow in a closed hyperbolic manifold is quasigeodesic if and only if it is not R-covered. Here R-covered means that the stable 2-dim foliation of the flow, lifts to a foliation in the universal cover whose leaf space is homeomorphic to the real numbers. There are many examples of quasigeodesic Anosov flows in closed hyperbolic 3-manifolds. There are consequences for the continuous extension property of Anosov foliations, and the existence of group invariant Peano curves associated with Anosov flows.</p>
<div class="label-inline">Seminar: </div><a href="/seminars/geometry-topology">Geometry & Topology</a><div class="label-above">Undergraduate Event?: </div>FalseFri, 19 Jan 2024 15:11:53 +0000Subhadip Dey24841 at https://math.yale.eduhttps://math.yale.edu/event/existence-quasigeodesic-anosov-flows-hyperbolic-3-manifolds#commentsPeriodic points of Prym eigenforms
https://math.yale.edu/event/periodic-points-prym-eigenforms
<div class="label-inline">Time: </div><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2024-02-06T16:00:00-05:00">4:00pm</span><div class="label-above">Speaker: </div>Sam Freedman<div class="label-inline">Location: </div><div class="location vcard">
<div class="adr">
<span class="fn">KT 205</span>
</div>
</div>
<div class="label-above">Abstract: </div><p>We will consider the dynamics of affine automorphisms acting on highly symmetric translation surfaces called Veech surfaces. Specifically, we’ll examine the points of the surface that are periodic, i.e., have a finite orbit under the whole automorphism group. While this set is known to be finite for primitive Veech surfaces, for applications it is desirable to determine the periodic points explicitly. In this talk we will discuss our classification of periodic points in the case of minimal Prym eigenforms, certain primitive Veech surfaces in genera 2, 3, and 4.</p>
<div class="label-inline">Seminar: </div><a href="/seminars/geometry-topology">Geometry & Topology</a><div class="label-above">Undergraduate Event?: </div>FalseFri, 19 Jan 2024 15:10:59 +0000Subhadip Dey24840 at https://math.yale.eduhttps://math.yale.edu/event/periodic-points-prym-eigenforms#commentsSystoles of hyperbolic hybrids
https://math.yale.edu/event/systoles-hyperbolic-hybrids
<div class="label-inline">Time: </div><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2024-03-26T16:00:00-04:00">4:00pm</span><div class="label-above">Speaker: </div>Sami Douba<div class="label-inline">Location: </div><div class="location vcard">
<div class="adr">
<span class="fn">KT 205</span>
</div>
</div>
<div class="label-above">Abstract: </div><p>We exhibit in any dimension n>2 and for any positive integer m a collection of m pairwise incommensurable closed hyperbolic n-manifolds of the same volume each possessing a unique shortest closed geodesic of the same length less than 1/m.</p>
<div class="label-inline">Seminar: </div><a href="/seminars/geometry-topology">Geometry & Topology</a><div class="label-above">Undergraduate Event?: </div>FalseThu, 18 Jan 2024 14:07:40 +0000Franco Vargas Pallete24827 at https://math.yale.eduhttps://math.yale.edu/event/systoles-hyperbolic-hybrids#commentsHessian estimates, monotonicity formulae, and applications
https://math.yale.edu/event/hessian-estimates-monotonicity-formulae-and-applications
<div class="label-inline">Time: </div><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2024-01-16T16:00:00-05:00">4:00pm</span><div class="label-above">Speaker: </div>Jiewon Park<div class="label-inline">Location: </div><div class="location vcard">
<div class="adr">
<span class="fn">KT 205</span>
</div>
</div>
<div class="label-above">Abstract: </div><p>Monotonicity formulae in geometric analysis have profound applications in many different problems. Quite often these formulae can be derived from Hessian estimates, also known as Li-Yau-Hamilton estimates. These estimates are often called differential Harnack estimates as well, since they imply Harnack estimates by integration along space or spacetime paths. In this talk we will focus on this connection, as well as a novel monotonicity formulae on Einstein manifolds.</p>
<div class="label-inline">Seminar: </div><a href="/seminars/geometry-topology">Geometry & Topology</a><div class="label-above">Undergraduate Event?: </div>FalseWed, 10 Jan 2024 18:18:18 +0000Franco Vargas Pallete24819 at https://math.yale.eduhttps://math.yale.edu/event/hessian-estimates-monotonicity-formulae-and-applications#commentsCounting arcs of the same type
https://math.yale.edu/event/counting-arcs-same-type
<div class="label-inline">Time: </div><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2024-02-13T16:00:00-05:00">4:00pm</span><div class="label-above">Speaker: </div>Marie Trin<div class="label-inline">Location: </div><div class="location vcard">
<div class="adr">
<span class="fn">KT 205</span>
</div>
</div>
<div class="label-above">Abstract: </div><p>Two closed curves on a hyperbolic surface are said to be of the same type if they differ from a mapping class. The question of counting curves of the same type with bounded length has been studied by M.Mirzakhani who showed that the counting is polynomial into the lenght. Mirzakhani's results were recovered and extended by Erlandsson-Souto proving convergence theorems for certain sequences of measures. In 2022, N.Bell obtained results similar to those of Mirzakhani for arcs of the same type in surfaces with boundary. We will introduce the method based on the convergence of measured for curves counting and then look at a way to adapt it to the case of arcs.</p>
<div class="label-inline">Seminar: </div><a href="/seminars/geometry-topology">Geometry & Topology</a><div class="label-above">Undergraduate Event?: </div>FalseMon, 01 Jan 2024 22:18:53 +0000Franco Vargas Pallete24816 at https://math.yale.eduhttps://math.yale.edu/event/counting-arcs-same-type#comments