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:20260404T100033Z UID:InformalGD/1 DESCRIPTION:Title: Framed mapping class groups and strata of abelian differentials< /a>\nby Nick Salter (Columbia University) as part of Informal geometry and dynamics seminar\n\n\nAbstract\nStrata of abelian differentials have long been of interest for their dynamical and algebro-geometric properties\, b ut relatively little is understood about their topology. I will describe a project aimed at understanding the (orbifold) fundamental groups of non-h yperelliptic stratum components. The centerpiece of this is the monodromy representation valued in the mapping class group of the surface relative t o the zeroes of the differential. For $g \\ge 5$\, we give a complete desc ription of this as the stabilizer of the framing of the (punctured) surfac e arising from the flat structure associated to the differential. This is joint work with Aaron Calderon.\n LOCATION:https://stable.researchseminars.org/talk/InformalGD/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Dubi Kelmer (Boston College) DTSTART:20200408T200000Z DTEND:20200408T213000Z DTSTAMP:20260404T100033Z UID:InformalGD/2 DESCRIPTION:Title: Effective density for values of a generic quadratic form\nby Dubi Kelmer (Boston College) as part of Informal geometry and dynamics se minar\n\n\nAbstract\nThe Oppenheim Conjecture\, proved by Margulis\, state s that any irrational quadratic form\, has values (at integer coordinates) that are dense on the real line. However\, obtaining effective estimates for any given form is a very difficult problem. In this talk I will discus s recent results\, where such effective estimates are obtained for generic forms using a combination of methods from dynamics and analytic number th eory. I will also discuss some results on analogous problems for inhomogen ous forms and more general higher degree polynomials.\n LOCATION:https://stable.researchseminars.org/talk/InformalGD/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Rick Kenyon (Yale University) DTSTART:20200422T200000Z DTEND:20200422T213000Z DTSTAMP:20260404T100033Z UID:InformalGD/3 DESCRIPTION:Title: Pseudo-Anosov maps and toral automorphisms\nby Rick Kenyon ( Yale University) as part of Informal geometry and dynamics seminar\n\n\nAb stract\nWe give a construction of a pseudo-Anosov map of a surface startin g from (and almost isomorphic to) a hyperbolic automorphism of an n-torus. The construction arises from a peano curve based on an invariant space-fi lling tree. This construction allows to confirm (for degree 3) a conjectur e of Fried regarding stretch factors of pseudo-Anosov maps.\n LOCATION:https://stable.researchseminars.org/talk/InformalGD/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Sahana Vasudevan (MIT) DTSTART:20200429T200000Z DTEND:20200429T213000Z DTSTAMP:20260404T100033Z UID:InformalGD/4 DESCRIPTION:Title: Large genus bounds for the distribution of triangulated surfaces in moduli space\nby Sahana Vasudevan (MIT) as part of Informal geomet ry and dynamics seminar\n\n\nAbstract\nTriangulated surfaces are compact ( hyperbolic) Riemann surfaces that admit a conformal triangulation by equil ateral triangles. Brooks and Makover started the study of the geometry of random large genus triangulated surfaces. Mirzakhani later proved analogou s results for random hyperbolic surfaces. These results\, along with many others\, suggest that the geometry of triangulated surfaces mirrors the ge ometry of arbitrary hyperbolic surfaces especially in the case of large ge nus asymptotics. In this talk\, I will describe an approach to show that t riangulated surfaces are asymptotically well-distributed in moduli space.\ n LOCATION:https://stable.researchseminars.org/talk/InformalGD/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Kathryn Lindsey (Boston College) DTSTART:20200603T200000Z DTEND:20200603T213000Z DTSTAMP:20260404T100033Z UID:InformalGD/5 DESCRIPTION:Title: Slices of Thurston's Master Teapot\nby Kathryn Lindsey (Bost on College) as part of Informal geometry and dynamics seminar\n\n\nAbstrac t\nThurston'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 characteriz ation of which points are in this set. This characterization gives a way t o think of each horizontal slice of the Master Teapot as an analogy of the Mandelbrot set for a "restricted iterated function system.'' An applicat ion of this characterization is that the Master Teapot is not invariant un der the map $(z\,\\lambda) \\mapsto (-z\,\\lambda)$. This presentation is based on joint work with Chenxi Wu.\n LOCATION:https://stable.researchseminars.org/talk/InformalGD/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Ben Dozier (Stony Brook University) DTSTART:20200506T200000Z DTEND:20200506T213000Z DTSTAMP:20260404T100033Z UID:InformalGD/6 DESCRIPTION:Title: Coarse density of subsets of moduli space\nby Ben Dozier (St ony Brook University) as part of Informal geometry and dynamics seminar\n\ n\nAbstract\nI will discuss coarse geometric properties of algebraic subva rieties of the moduli space of Riemann surfaces. In joint work with Jenya Sapir\, we prove that such a subvariety is coarsely dense\, with respect t o either the Teichmuller or Thurston metric\, iff it has full dimension in the moduli space. This work was motivated by an attempt to understand the geometry of the image of the projection map from a stratum of abelian or quadratic differentials to the moduli space of Riemann surfaces. As a coro llary of our theorem\, we characterize when this image is coarsely dense. A key part of the proof of the theorem involves comparing analytic plumbin g coordinates at the Deligne-Mumford boundary to hyperbolic/extremal lengt hs of curves on nearby smooth surfaces.\n LOCATION:https://stable.researchseminars.org/talk/InformalGD/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Apisa (Yale University) DTSTART:20200513T200000Z DTEND:20200513T213000Z DTSTAMP:20260404T100033Z UID:InformalGD/7 DESCRIPTION:Title: In the moduli space of Abelian differentials\, big invariant sub varieties come from topology\nby Paul Apisa (Yale University) as part of Informal geometry and dynamics seminar\n\n\nAbstract\nIt is a beautiful fact that any holomorphic one-form on a genus g Riemann surface can be pr esented as a collection of polygons in the plane with sides identified by translation. Since GL(2\, R) acts on the plane (and polygons in it)\, it f ollows that there is an action of GL(2\, R) on the collection of holomorph ic one-forms on Riemann surfaces. This GL(2\, R) action can also be descri bed as the group action generated by scalar multiplication and Teichmuller geodesic flow. By work of McMullen in genus two\, and Eskin\, Mirzakhani\ , and Mohammadi in general\, given any holomorphic one-form\, the closure of its GL(2\, R) orbit is an algebraic variety. While McMullen classified these orbit closures in genus two\, little is known in higher genus. \n\nI n the first part of the talk\, I will describe the Mirzakhani-Wright bound ary of an invariant subvariety (using mostly pictures) and a new result ab out reconstructing an orbit closure from its boundary. In the second part of the talk\, I will define the rank of an invariant subvariety - a measu re of size related to dimension - and explain why invariant subvarieties o f rank greater than g/2 are loci of branched covers of lower genus Riemann surfaces. This will address a question of Mirzakhani.\n\nNo background on Teichmuller theory or dynamics will be assumed. This material is work in progress with Alex Wright.\n LOCATION:https://stable.researchseminars.org/talk/InformalGD/7/ END:VEVENT END:VCALENDAR