BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nick Salter (Columbia University) DTSTART:20200415T200000Z DTEND:20200415T213000Z DTSTAMP:20260422T212708Z UID:InformalGD/1 DESCRIPTION:Title: Framed mapping class groups and strata of abelian differentials\nby Nick Salter (Columbia University) as part of Informal geometry and dynami cs seminar\n\n\nAbstract\nStrata of abelian differentials have long been o f interest for their dynamical and algebro-geometric properties\, but rela tively little is understood about their topology. I will describe a projec t aimed at understanding the (orbifold) fundamental groups of non-hyperell iptic stratum components. The centerpiece of this is the monodromy represe ntation valued in the mapping class group of the surface relative to the z eroes of the differential. For $g \\ge 5$\, we give a complete description of this as the stabilizer of the framing of the (punctured) surface arisi ng from the flat structure associated to the differential. This is joint w ork with Aaron Calderon.\n LOCATION:https://researchseminars.org/talk/InformalGD/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Dubi Kelmer (Boston College) DTSTART:20200408T200000Z DTEND:20200408T213000Z DTSTAMP:20260422T212708Z UID:InformalGD/2 DESCRIPTION:Title: Effective density for values of a generic quadratic form\nby Dubi K elmer (Boston College) as part of Informal geometry and dynamics seminar\n \n\nAbstract\nThe Oppenheim Conjecture\, proved by Margulis\, states that any irrational quadratic form\, has values (at integer coordinates) that a re dense on the real line. However\, obtaining effective estimates for any given form is a very difficult problem. In this talk I will discuss recen t results\, where such effective estimates are obtained for generic forms using a combination of methods from dynamics and analytic number theory. I will also discuss some results on analogous problems for inhomogenous for ms and more general higher degree polynomials.\n LOCATION:https://researchseminars.org/talk/InformalGD/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Rick Kenyon (Yale University) DTSTART:20200422T200000Z DTEND:20200422T213000Z DTSTAMP:20260422T212708Z UID:InformalGD/3 DESCRIPTION:Title: Pseudo-Anosov maps and toral automorphisms\nby Rick Kenyon (Yale Un iversity) as part of Informal geometry and dynamics seminar\n\n\nAbstract\ nWe give a construction of a pseudo-Anosov map of a surface starting from (and almost isomorphic to) a hyperbolic automorphism of an n-torus. The co nstruction arises from a peano curve based on an invariant space-filling t ree. This construction allows to confirm (for degree 3) a conjecture of Fr ied regarding stretch factors of pseudo-Anosov maps.\n LOCATION:https://researchseminars.org/talk/InformalGD/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Sahana Vasudevan (MIT) DTSTART:20200429T200000Z DTEND:20200429T213000Z DTSTAMP:20260422T212708Z UID:InformalGD/4 DESCRIPTION:Title: Large genus bounds for the distribution of triangulated surfaces in mod uli space\nby Sahana Vasudevan (MIT) as part of Informal geometry and dynamics seminar\n\n\nAbstract\nTriangulated surfaces are compact (hyperbo lic) Riemann surfaces that admit a conformal triangulation by equilateral triangles. Brooks and Makover started the study of the geometry of random large genus triangulated surfaces. Mirzakhani later proved analogous resul ts for random hyperbolic surfaces. These results\, along with many others\ , suggest that the geometry of triangulated surfaces mirrors the geometry of arbitrary hyperbolic surfaces especially in the case of large genus asy mptotics. In this talk\, I will describe an approach to show that triangul ated surfaces are asymptotically well-distributed in moduli space.\n LOCATION:https://researchseminars.org/talk/InformalGD/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Kathryn Lindsey (Boston College) DTSTART:20200603T200000Z DTEND:20200603T213000Z DTSTAMP:20260422T212708Z UID:InformalGD/5 DESCRIPTION:Title: Slices of Thurston's Master Teapot\nby Kathryn Lindsey (Boston Coll ege) as part of Informal geometry and dynamics seminar\n\n\nAbstract\nThur ston's Master Teapot is the closure of the set of all points $(z\,\\lambda ) \\in \\mathbb{C} \\times \\mathbb{R}$ such that $\\lambda$ is the growth rate of a critically periodic unimodal self-map of an interval and $z$ is a Galois conjugate of $\\lambda$. I will present a new characterization o f which points are in this set. This characterization gives a way to think of each horizontal slice of the Master Teapot as an analogy of the Mandel brot set for a "restricted iterated function system.'' An application of this characterization is that the Master Teapot is not invariant under the map $(z\,\\lambda) \\mapsto (-z\,\\lambda)$. This presentation is based o n joint work with Chenxi Wu.\n LOCATION:https://researchseminars.org/talk/InformalGD/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Ben Dozier (Stony Brook University) DTSTART:20200506T200000Z DTEND:20200506T213000Z DTSTAMP:20260422T212708Z UID:InformalGD/6 DESCRIPTION:Title: Coarse density of subsets of moduli space\nby Ben Dozier (Stony Bro ok University) as part of Informal geometry and dynamics seminar\n\n\nAbst ract\nI will discuss coarse geometric properties of algebraic subvarieties of the moduli space of Riemann surfaces. In joint work with Jenya Sapir\, we prove that such a subvariety is coarsely dense\, with respect to eithe r the Teichmuller or Thurston metric\, iff it has full dimension in the mo duli space. This work was motivated by an attempt to understand the geomet ry of the image of the projection map from a stratum of abelian or quadrat ic differentials to the moduli space of Riemann surfaces. As a corollary o f our theorem\, we characterize when this image is coarsely dense. A key p art of the proof of the theorem involves comparing analytic plumbing coord inates at the Deligne-Mumford boundary to hyperbolic/extremal lengths of c urves on nearby smooth surfaces.\n LOCATION:https://researchseminars.org/talk/InformalGD/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Apisa (Yale University) DTSTART:20200513T200000Z DTEND:20200513T213000Z DTSTAMP:20260422T212708Z UID:InformalGD/7 DESCRIPTION:Title: In the moduli space of Abelian differentials\, big invariant subvarieti es come from topology\nby Paul Apisa (Yale University) as part of Info rmal geometry and dynamics seminar\n\n\nAbstract\nIt is a beautiful fact t hat any holomorphic one-form on a genus g Riemann surface can be presented as a collection of polygons in the plane with sides identified by transla tion. Since GL(2\, R) acts on the plane (and polygons in it)\, it follows that there is an action of GL(2\, R) on the collection of holomorphic one- forms on Riemann surfaces. This GL(2\, R) action can also be described as the group action generated by scalar multiplication and Teichmuller geodes ic flow. By work of McMullen in genus two\, and Eskin\, Mirzakhani\, and M ohammadi in general\, given any holomorphic one-form\, the closure of its GL(2\, R) orbit is an algebraic variety. While McMullen classified these o rbit closures in genus two\, little is known in higher genus. \n\nIn the f irst part of the talk\, I will describe the Mirzakhani-Wright boundary of an invariant subvariety (using mostly pictures) and a new result about rec onstructing an orbit closure from its boundary. In the second part of the talk\, I will define the rank of an invariant subvariety - a measure of s ize related to dimension - and explain why invariant subvarieties of rank greater than g/2 are loci of branched covers of lower genus Riemann surfac es. This will address a question of Mirzakhani.\n\nNo background on Teichm uller theory or dynamics will be assumed. This material is work in progres s with Alex Wright.\n LOCATION:https://researchseminars.org/talk/InformalGD/7/ END:VEVENT END:VCALENDAR