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BEGIN:VEVENT
SUMMARY:Kasra Rafi (University of Toronto)
DTSTART;VALUE=DATE-TIME:20200423T160000Z
DTEND;VALUE=DATE-TIME:20200423T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/1
DESCRIPTION:Title: Absolutely continuous stationary measures for the mapping class gro
up\nby Kasra Rafi (University of Toronto) as part of BISTRO - Billiard
s and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\nWe p
rove a version of a Theorem of Furstenberg in the setting of Mapping class
groups. Thurston measure defines a smooth measure class on PML. For every
measure \\nu in this measure class\, we produce a measure \\mu with finit
e first moment on the mapping class group such that \\nu is the unique \\m
u-stationary measure. In particular\, this gives an coding-free proof of t
he already known result that the Lyapunov spectrum of Kontsevich-Zorich co
cycle on the principal stratum of quadratic differentials is simple.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Costantini (Universität Bonn)
DTSTART;VALUE=DATE-TIME:20200430T160000Z
DTEND;VALUE=DATE-TIME:20200430T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/2
DESCRIPTION:Title: The Chern classes and the Euler characteristic of the moduli spaces
of abelian differentials\nby Matteo Costantini (Universität Bonn) as
part of BISTRO - Billiards and Surfaces à la Teichmüller and Riemann\,
Online\n\n\nAbstract\nRecently\, Bainbridge-Chen-Gendron-Grushevsky-Mölle
r defined the moduli space of multi scaled differentials\, which is a comp
actification of the moduli spaces of abelian differentials with very simil
ar properties as the Deligne-Mumford compactification of the moduli space
of curves. During the talk I will explain how it is possible to develop in
tersection theory on this moduli space and how to use it\, together with a
twisted Euler sequence\, in order to compute its Chern classes. As a spec
ial case\, via Gauss-Bonnet\, we compute a formula for the Euler character
istic of the moduli spaces of abelian homolorphic and meromorphic differen
tials and obtain values in small genera. This is based on a joint work wit
h Martin Möller and Jonathan Zachhuber.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Curtis McMullen (Harvard)
DTSTART;VALUE=DATE-TIME:20200521T170000Z
DTEND;VALUE=DATE-TIME:20200521T180000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/3
DESCRIPTION:Title: Billiards\, heights and modular symbols\nby Curtis McMullen (Ha
rvard) as part of BISTRO - Billiards and Surfaces à la Teichmüller and R
iemann\, Online\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Calderon (Yale University)
DTSTART;VALUE=DATE-TIME:20200507T160000Z
DTEND;VALUE=DATE-TIME:20200507T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/4
DESCRIPTION:Title: Shear-shape coordinates for Teichmüller space and applications to
flat and hyperbolic geometry\nby Aaron Calderon (Yale University) as p
art of BISTRO - Billiards and Surfaces à la Teichmüller and Riemann\, On
line\n\n\nAbstract\nThere is a deep yet mysterious connection between the
hyperbolic and singular flat geometry of Riemann surfaces. Using Bonahon a
nd Thurston’s “shear coordinates” for maximal laminations\, Mirzakha
ni related the earthquake and horocycle flows on Teichmüller space\, two
notions of unipotent flow coming from hyperbolic\, respectively flat\, geo
metry. In this talk\, I will describe joint work (in progress) with James
Farre in which we construct new “shear-shape coordinates” for Teichmü
ller space adapted to any lamination. Using these coordinates\, we extend
Mirzakhani’s conjugacy to strata of quadratic differentials as well as p
roduce new examples of geodesics for the Lipschitz (asymmetric) metric wit
h given stretch locus. These coordinates also yield information about the
global structure of certain subloci in both Teichmüller space and its cot
angent bundle of quadratic differentials.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francisco Arana Herrera (Stanford)
DTSTART;VALUE=DATE-TIME:20200514T160000Z
DTEND;VALUE=DATE-TIME:20200514T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/5
DESCRIPTION:Title: Counting hyperbolic multi-geodesics with respect to the lengths of
individual components\nby Francisco Arana Herrera (Stanford) as part o
f BISTRO - Billiards and Surfaces à la Teichmüller and Riemann\, Online\
n\n\nAbstract\nIn her thesis\, Mirzakhani showed that on any closed hyperb
olic surface of genus g\, the number of simple closed geodesics of length
at most L is asymptotic to a polynomial in L of degree 6g-6. Wolpert conje
ctured that analogous results should hold for more general countings of mu
lti-geodesics that keep track of the lengths of individual components. In
this talk we will present a proof of this conjecture which combines techni
ques and results of Mirzakhani with ideas introduced by Margulis in his th
esis.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jane Wang (Indiana University)
DTSTART;VALUE=DATE-TIME:20200528T160000Z
DTEND;VALUE=DATE-TIME:20200528T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/6
DESCRIPTION:Title: The realization problem for twisted quadratic differentials (dilati
on surfaces)\nby Jane Wang (Indiana University) as part of BISTRO - Bi
lliards and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract
\nTwisted quadratic differentials\, also known as dilation surfaces\, are
geometric structures that are in a way a generalization of translation sur
faces. We can define a dilation surface either as a quadratic differential
twisted by some real holonomy or as a collection of polygons with sides i
dentified by translations and dilations by nonzero real factors. This smal
l generalization is enough to introduce interesting new dynamical behavior
s on dilation surfaces that do not occur for translation surfaces. In this
talk\, we will introduce dilation surfaces and discuss some of the new an
d interesting dynamical behaviors that can occur on them. We will then mot
ivate and formulate the realization problem\, which asks which mapping cla
ss group elements and subgroups can be realized as affine automorphisms of
a dilation surfaces\, and discuss challenges and progress toward resolvin
g this problem.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barak Weiss (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20200604T170000Z
DTEND;VALUE=DATE-TIME:20200604T180000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/7
DESCRIPTION:Title: New bounds on the covering density of a lattice\nby Barak Weiss
(Tel Aviv University) as part of BISTRO - Billiards and Surfaces à la Te
ichmüller and Riemann\, Online\n\n\nAbstract\nWe obtain new upper bounds
on the minimal density of lattice coverings of R^n by dilates of a convex
body K. We also obtain bounds on the probability (with respect to the natu
ral Haar-Siegel measure on the space of lattices) that a randomly chosen l
attice L satisfies L+K=R^n. As a step in the proof\, we utilize and streng
then results on the discrete Kakeya problem. Joint work with Or Ordentlich
and Oded Regev.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Smith (Cambridge University)
DTSTART;VALUE=DATE-TIME:20200611T160000Z
DTEND;VALUE=DATE-TIME:20200611T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/8
DESCRIPTION:Title: Symplectic mapping class groups and flat surfaces\nby Ivan Smit
h (Cambridge University) as part of BISTRO - Billiards and Surfaces à la
Teichmüller and Riemann\, Online\n\n\nAbstract\nI will try to explain why
one particular approach to studying the mapping class groups of higher-di
mensional symplectic manifolds leads to thinking about flat surfaces and t
heir cousins\, and some of the open questions that arise in that context.
The talk will try to be reasonably self-contained\, but will therefore nec
essarily be somewhat impressionistic.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amol Aggarwal (Harvard University)
DTSTART;VALUE=DATE-TIME:20200618T160000Z
DTEND;VALUE=DATE-TIME:20200618T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/9
DESCRIPTION:Title: Large Genus Asymptotics for Intersection Numbers and Strata Volumes
\nby Amol Aggarwal (Harvard University) as part of BISTRO - Billiards
and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\nCorrel
ators\, or intersection numbers between psi-classes on the moduli space of
stable curves\, are fundamental invariants ubiquitous in mathematical phy
sics\, algebraic geometry\, geometric topology\, and dynamical systems. In
this talk\, we analyze the large genus asymptotics for these correlators
using a comparison between the recursive relations (Virasoro constraints)
that uniquely determine them with the jump probabilities of a certain asym
metric simple random walk. By combining this result with a combinatorial a
nalysis of recently proven formulas of Delecroix-Goujard-Zograf-Zorich\, w
e further provide the large genus limits for Masur-Veech volumes and area
Siegel-Veech constants associated with principal strata in the moduli spac
e of quadratic differentials.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Salter (Columbia University)
DTSTART;VALUE=DATE-TIME:20200625T160000Z
DTEND;VALUE=DATE-TIME:20200625T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/10
DESCRIPTION:Title: Framed mapping class groups and strata of abelian differentials\nby Nick Salter (Columbia University) as part of BISTRO - Billiards and
Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\nStrata of
abelian differentials have long been of interest for their dynamical and a
lgebro-geometric properties\, but relatively little is understood about th
eir topology. I will describe a project aimed at understanding the (orbifo
ld) fundamental groups of non-hyperelliptic stratum components. The center
piece of this is the monodromy representation valued in the mapping class
group of the surface relative to the zeroes of the differential. For g \\g
e 5\, we give a complete description of this as the stabilizer of the fram
ing of the (punctured) surface arising from the flat structure associated
to the differential. This is joint work with Aaron Calderon.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanni Forni (University of Maryland)
DTSTART;VALUE=DATE-TIME:20200702T160000Z
DTEND;VALUE=DATE-TIME:20200702T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/11
DESCRIPTION:Title: On weak mixing for translation flows and billiards in polygons
\nby Giovanni Forni (University of Maryland) as part of BISTRO - Billiards
and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\nHow c
haotic can a polygonal billiard be? We will present a recent joint result
with Jon Chaika that the set of weak mixing (non-rational) polygons is den
se (hence a dense G_delta). Along the way we will discuss results and ope
n questions on weak mixing and effective weak mixing of translation flows
and interval exchange transformations.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Kontsevich (IHES)
DTSTART;VALUE=DATE-TIME:20200716T160000Z
DTEND;VALUE=DATE-TIME:20200716T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/12
DESCRIPTION:Title: Integral PL actions from birational geometry\nby Maxim Kontsev
ich (IHES) as part of BISTRO - Billiards and Surfaces à la Teichmüller a
nd Riemann\, Online\n\n\nAbstract\nTheory of flat surfaces provides a seri
es of interesting actions of SL2(Z) on finite sets (isomorphism classes of
square-tiled surfaces with a given integer area). I will talk on a differ
ent construction\, with the origin in mirror symmetry/tropical geometry\,
producing somewhat similar actions. For example\, in the case of K3-surfac
es\, an arithmetic subgroup of SO(1\,18) acts on S2 by Z-piecewise-linear
transformations\, inducing a tower of non-trivial finite actions. I will d
escribe a general construction\, and give numerous examples which could be
interesting from the dynamical point of view.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincent Delecroix and Elise Goujard (University of Bordeaux)
DTSTART;VALUE=DATE-TIME:20200709T160000Z
DTEND;VALUE=DATE-TIME:20200709T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/13
DESCRIPTION:Title: The number of components of a multicurve in large genus\nby Vi
ncent Delecroix and Elise Goujard (University of Bordeaux) as part of BIST
RO - Billiards and Surfaces à la Teichmüller and Riemann\, Online\n\n\nA
bstract\nA multicurve on a closed surface S of genus g >= 2 is a homotopy
class of a disjoint collection of simple closed curves on S. A hyperbolic
metric on S allows to measure the length of a multicurve. We study the num
ber of components of a multicurve taken at random among all multicurves of
length at most L on S. We then let L tend to infinity and talk about a ra
ndom multicurve on S. M. Mirzakhani proved that the number of components
of a random multicurve on S only depends on the topology of S and not on t
he specific hyperbolic metric. It hence makes sense to talk about the numb
er of components of a random multicurve of genus g. Furthermore M. Mirzakh
ani provided explicit formulas for this distribution involving the Kontsev
ich-Witten correlators. Thanks to the recent work of A. Aggarwal on the as
ymptotics of these correlators we describe its behavior as the genus g ten
d to infinity. We show that it asymptotically behaves as the number of cyc
les of a random permutation in Sym_{3g-3} taken with respect to a very exp
licit probability distribution.\nThe number of components of a random mult
icurve of genus g coincide with the number of cylinders of a random square
-tiled surface in genus g. Hence our work equivalently provides results on
the geometry of random square-tiled surfaces.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Apisa (Yale University)
DTSTART;VALUE=DATE-TIME:20200914T160000Z
DTEND;VALUE=DATE-TIME:20200914T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/14
DESCRIPTION:Title: Reconstructing an orbit closure from its boundary\, holomorphic re
tracts of Teichmuller space\, and new Eierlegende-Wollmilchsau-like orbit
closures!\nby Paul Apisa (Yale University) as part of BISTRO - Billiar
ds and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\nWor
k of McMullen in genus two and Eskin\, Mirzakhani\, Mohammadi\, and Filip
in general established that the GL(2\, R) orbit closure of any translation
surface is an affine invariant subvariety (AIS). Myriad questions abound
about AIS. We focus on the following - how does the boundary of an AIS co
nstrain the AIS? \n\nWe will begin by explaining how different boundary c
omponents of an AIS can be accessed by cylinder degenerations. While consi
dering one degeneration is often insufficient to completely determine an A
IS\, we will show that one can often identify the AIS from two degeneratio
ns that form what will be called a diamond. These results are key to work
in progress showing that any sufficiently large orbit closure of a genus g
translation surface is a locus of covers (sufficiently large means that t
he rank is greater than g/2). To explain the connection\, we take a seemin
g detour. \n\nThe Eierlegende-Wollmilchsau square-tiled surface has the pr
operty that every cylinder is parallel to exactly one other cylinder\, whi
ch is isometric to it. In this talk\, we will generalize this property to
AIS beyond those generated by square-tiled surfaces\, saying\, roughly\, t
hat an AIS on which every cylinder on every surface has an isometric “tw
in” is called geminal. Loci of double covers are examples of geminal AIS
. Less trivially\, every sufficiently large AIS (with rel zero) is geminal
. Moreover\, work of Markovic and Gekhtman showed that if M is the collect
ion of points\, in a stratum of quadratic differentials\, whose correspond
ing Teichmuller disk is a holomorphic retract of Teichmuller space\, then
the locus of holonomy double covers of elements of M is geminal. \n\nUsing
the “reconstructing an AIS from its boundary” technique described abo
ve\, we will show that geminal AIS are loci of covers. This result has imp
lications for the complex geometry of Teichmuller space and is a key step
in the aforementioned work showing that sufficiently large AIS are loci of
covers. Finally\, we will sketch the construction of new geminal AIS. Th
ese examples negatively resolve two questions of Mirzakhani and Wright and
illustrate new behavior in the finite blocking problem. This work is join
t with Alex Wright.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bram Petri (IMG-PRG)
DTSTART;VALUE=DATE-TIME:20200921T160000Z
DTEND;VALUE=DATE-TIME:20200921T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/15
DESCRIPTION:Title: The minimal diameter of a hyperbolic surface.\nby Bram Petri (
IMG-PRG) as part of BISTRO - Billiards and Surfaces à la Teichmüller and
Riemann\, Online\n\n\nAbstract\nThe main question in this talk is what th
e "most connected" closed hyperbolic surface of a given genus is. There ar
e multiple measures of the connectivity of a hyperbolic surface\, but as t
he title suggests\, we will focus on their diameter. I will explain how ra
ndom constructions of hyperbolic surfaces help with this question. This is
joint work with Thomas Budzinski and Nicolas Curien.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaëtan Borot (Humboldt-Universität zu Berlin)
DTSTART;VALUE=DATE-TIME:20200928T160000Z
DTEND;VALUE=DATE-TIME:20200928T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/16
DESCRIPTION:Title: Geometry of combinatorial moduli spaces and multicurve counts\
nby Gaëtan Borot (Humboldt-Universität zu Berlin) as part of BISTRO - Bi
lliards and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract
\nThe Teichmuller space of bordered surfaces can be described via metric r
ibbon graphs\, leading to a natural geometry (the symplectic form introduc
ed by Kontsevich in his proof of Witten's conjecture). I will show that ma
ny tools of hyperbolic geometry can be adapted to this combinatorial geome
try: there are Fenchel-Nielsen coordinates that are Darboux\, Mirzakhani-M
cShane type identity\, integration formulas\, recursions for volume and st
atistics of multicurves\, etc. Besides\, combinatorial geometry is hyperbo
lic geometry for large boundary lengths converges to combinatorial geometr
y: we extend some results of Mondello in this direction\, but also stress
some non-uniformity than manifests itself in a different integrability beh
avior of the Thurston measure of unit balls wrt combinatorial length in th
e space of measured foliations than the one found in the hyperbolic settin
g by Arana-Herrera and Athreya.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junho Peter Whang (MIT)
DTSTART;VALUE=DATE-TIME:20201005T160000Z
DTEND;VALUE=DATE-TIME:20201005T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/17
DESCRIPTION:Title: Integral points on moduli of local systems\nby Junho Peter Wha
ng (MIT) as part of BISTRO - Billiards and Surfaces à la Teichmüller and
Riemann\, Online\n\n\nAbstract\nModuli spaces for special linear rank two
local systems on topological surfaces are basic objects in geometry. The
study of integer points on these algebraic varieties can be traced back to
1880 work of Markoff\, in the case where the surface is the once-puncture
d torus. In the first part of the talk\, we describe a structure theorem f
or the integral points on these moduli spaces for general surfaces\, prove
d using mapping class group dynamics and differential geometric tools. In
the second part (based on joint work with Fan)\, we discuss exceptional is
omorphisms between these varieties and moduli spaces of points on (algebra
ic) 3-spheres. Using this connection and the previous structure theorem fo
r the twice-punctured torus\, we can deduce a Diophantine finiteness resul
t for integral Stokes matrices of rank 4.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karl Winsor (Harvard)
DTSTART;VALUE=DATE-TIME:20201012T160000Z
DTEND;VALUE=DATE-TIME:20201012T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/18
DESCRIPTION:Title: Navigating absolute period leaves and the Arnoux-Yoccoz surface in
genus 3\nby Karl Winsor (Harvard) as part of BISTRO - Billiards and S
urfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\nThe moduli
space of holomorphic 1-forms on genus g Riemann surfaces has a foliation w
hose leaves consist of 1-forms with locally constant absolute periods. Ind
ividual leaves have a natural flat structure\, recording changes in relati
ve periods along paths between the zeros. In genus 2\, a typical leaf is t
opologically a disk\, after being completed. One can also restrict this fo
liation to strata of 1-forms with given zero orders\, and we will mainly f
ocus on strata in genus greater than 2. We will describe closed geodesics
on these leaves\, give an example of a leaf with infinite genus\, and show
how to upgrade this to a statement about a typical leaf in the ambient st
ratum component.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Monk (IRMA)
DTSTART;VALUE=DATE-TIME:20201026T170000Z
DTEND;VALUE=DATE-TIME:20201026T180000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/19
DESCRIPTION:Title: Geometry and spectrum of random hyperbolic surfaces\nby Laura
Monk (IRMA) as part of BISTRO - Billiards and Surfaces à la Teichmüller
and Riemann\, Online\n\n\nAbstract\nThe aim of this talk is to describe th
e geometry and spectrum of most random hyperbolic surfaces\, picked with t
he Weil-Petersson probability measure.\n\nIn this model\, one can get a go
od understanding of the geometry of a typical surface: Cheeger constant\,
diameter (Mirzakhani)\, injectivity radius\, number of short closed geodes
ics (Mirzakhani-Petri)\, length of the shortest non-simple closed geodesic
\, improved collar theorem (joint work with Joe Thomas)\, Benjamini-Schram
m convergence.\n\nI will explain how these geometric properties\, together
with the Selberg trace formula\, lead to precise estimates on the distrib
ution of the eigenvalues of the Laplacian on a typical surface.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yilin Wang (MIT)
DTSTART;VALUE=DATE-TIME:20201102T170000Z
DTEND;VALUE=DATE-TIME:20201102T180000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/20
DESCRIPTION:Title: SLE\, energy duality\, and foliations by Weil-Petersson quasicircl
es\nby Yilin Wang (MIT) as part of BISTRO - Billiards and Surfaces à
la Teichmüller and Riemann\, Online\n\n\nAbstract\nSchramm-Loewner evolut
ion (SLE) is a one-parameter family of random simple planar curve. It firs
t arises as interfaces in scaling limits of 2D statistical mechanics latti
ce models which exhibit conformal invariance. The small-parameter asymptot
ic behaviors give rise to the Loewner energy for Jordan curves\, which is
finite if and only if the curve is a Weil-Petersson quasicircle\, and is m
oreover a Kahler potential on the Weil-Petersson Teichmuller space. I will
survey the link between SLE and Weil-Petersson quasicircles\, then show t
he large-parameter asymptotic behaviors of SLE giving rise to Loewner-Kufa
rev energy\, provides a further duality via foliations of the Riemann sphe
re by Weil-Petersson quasicircles.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Serge Cantat (IRMAR)
DTSTART;VALUE=DATE-TIME:20201207T170000Z
DTEND;VALUE=DATE-TIME:20201207T180000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/21
DESCRIPTION:Title: Stationary measures on real projective surface\nby Serge Canta
t (IRMAR) as part of BISTRO - Billiards and Surfaces à la Teichmüller an
d Riemann\, Online\n\n\nAbstract\nConsider a real projective surface $X(\\
R)$\, and a group $\\Gamma$ acting by algebraic diffeomorphisms on $X(\\R)
$. If $\\nu$ is a probability measure on $\\Gamma$\, one can randomly and
independently choose elements $f_j$ in $\\Gamma$ and look at the random or
bits $x$\, $f_1(x)$\, $f_2(f_1(x))$\, $\\ldots$ How do these orbits distri
bute on the surface ? This is directly related to the classification of st
ationary measures on $X(\\R)$. I will describe recent results on this prob
lem\, all obtained in collaboration with Romain Dujardin. The main ingredi
ents will be ergodic theory\, notably the work of Brown and Rodriguez-Hert
z\, algebraic geometry\, and complex analysis. Concrete geometric examples
will be given.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Chung (UChicago)
DTSTART;VALUE=DATE-TIME:20201019T160000Z
DTEND;VALUE=DATE-TIME:20201019T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/22
DESCRIPTION:Title: Stationary measure and orbit closure classification for random wal
ks on surfaces\nby Brian Chung (UChicago) as part of BISTRO - Billiard
s and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\nWe s
tudy the problem of classifying stationary measures and orbit closures for
non-abelian action on surfaces. Using a result of Brown and Rodriguez Her
tz\, we show that under a certain average growth condition\, the orbit clo
sures are either finite or dense. Moreover\, every infinite orbit equidist
ributes on the surface. This is analogous to the results of Benoist-Quint
and Eskin-Lindenstrauss in the homogeneous setting\, and the result of Esk
in-Mirzakhani in the setting of moduli spaces of translation surfaces.\n\n
We then consider the problem of verifying this growth condition in concret
e settings. In particular\, we apply the theorem to two settings\, namely
discrete perturbations of the standard map and the Out(F2)-action on a cer
tain character variety. We verify the growth condition analytically in the
former setting\, and verify numerically in the latter setting.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frederik Benirschke (Stony Brook)
DTSTART;VALUE=DATE-TIME:20201109T170000Z
DTEND;VALUE=DATE-TIME:20201109T180000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/23
DESCRIPTION:Title: The boundary of orbit closures\nby Frederik Benirschke (Stony
Brook) as part of BISTRO - Billiards and Surfaces à la Teichmüller and R
iemann\, Online\n\n\nAbstract\nModuli spaces of translation surfaces carry
a natural GL(2\,R)-action by acting linearly on the periods of the transl
ation surface.\nRecent breakthroughs by Eskin\, Mirazakhani\, Mohammadi an
d Filip\, which extend results of McMullen in genus 2\, show that orbit
closures for the GL(2\,R)-action are surprisingly well behaved: Orbit clos
ures are algebraic varieties that are locally defined by linear equations
among periods. Orbit closures are never compact and it is natural to searc
h for "nice" compactifications. One simple way of compactifying orbit clos
ures is by taking the closure inside the moduli space of multi-scale diffe
rentials\, which was constructed recently by Bainbridge-Chen-Gendron-Grush
evsky-Möller. Our main result is a description of the boundary of an orbi
t closure inside the moduli space of multi-scale differentials. In particu
lar the boundary is again given by linear equations among periods. Time pe
rmitting\, we explain how our description of the boundary can be used to e
xtend Wrights cylinder deformation theorem to the case of meromorphic stra
ta\, which is partially joint work with Benjamin Dozier and Samuel Grushe
vsky.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Mullane (Frankfurt)
DTSTART;VALUE=DATE-TIME:20201116T170000Z
DTEND;VALUE=DATE-TIME:20201116T180000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/24
DESCRIPTION:Title: Strata of exact differentials and the birational geometry of Hurwi
tz spaces\nby Scott Mullane (Frankfurt) as part of BISTRO - Billiards
and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\nThe st
rata of exact differentials are obtained from Hurwitz spaces of covers of
the rational line with specified branching profiles and form linear manifo
lds inside the strata of meromorphic differentials. Despite the utility of
Hurwitz spaces in the study of a number of the birational aspects of the
moduli space of curves\, many open questions on Hurwitz spaces persist. I'
ll show how the perspective of the strata of exact differentials can be us
ed to prove\, that as conjectured\, the rational Picard group of the modul
i space of simply branched degree d covers of the rational line by smooth
genus g curves is trivial for d>g-1. \nFurther\, this perspective yields r
esults on open questions on the irreducibility of non-simple Hurwitz space
s and has applications to the birational geometry of moduli spaces of poin
ted rational curves.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Marshall-Maldonado (Marseille)
DTSTART;VALUE=DATE-TIME:20201123T170000Z
DTEND;VALUE=DATE-TIME:20201123T180000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/25
DESCRIPTION:Title: Quantitative weakly mixing of flows over Salem type substitutions<
/a>\nby Juan Marshall-Maldonado (Marseille) as part of BISTRO - Billiards
and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\nSuspen
sion flows over Vershik automorphisms provide a powerful symbolic frame fo
r study linear flows over translation surfaces. The simplest case is the p
eriodic one\, which leads us to substitutions. Spectral properties depend
strongly on the algebraic nature of the Perron eigenvalue of the adjacency
matrix of the substitution\, as shown in the work of Bufetov and Solomyak
. In this talk I will consider the "border case" in which this eigenvalue
is a Salem number and I will show a modulus of continuity for spectral mea
sures in a family of algebraic points.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chaya Norton (UMich)
DTSTART;VALUE=DATE-TIME:20201130T170000Z
DTEND;VALUE=DATE-TIME:20201130T180000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/26
DESCRIPTION:Title: Obtuse Veech Triangles\nby Chaya Norton (UMich) as part of BIS
TRO - Billiards and Surfaces à la Teichmüller and Riemann\, Online\n\n\n
Abstract\nThe question of which obtuse triangles ufold to Veech surfaces h
as been open since Kenyon and Smillie's results on acute and right triangl
es. There are two known infinite families of obtuse Veech triangles due to
Veech and Ward. More recently Hooper showed that the unfolding of the spo
radic example (pi/12\, pi/3\, 7*pi/12) generates a Teichmuller curve\, and
he conjectures that these are all the obtuse Veech triangles. We prove th
is conjecture when the largest angle is at least 135 degrees. Our method r
elies on a criterion of Mirzakhani and Wright which builds on work of Moel
ler and McMullen studying the variation of the period matrix along the GL(
2\,R) action. This is joint work with Anne Larsen and Bradley Zykoski comp
leted during the 2020 University of Michigan REU.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olga Paris-Romaskevich (CNRS)
DTSTART;VALUE=DATE-TIME:20210201T170000Z
DTEND;VALUE=DATE-TIME:20210201T180000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/27
DESCRIPTION:by Olga Paris-Romaskevich (CNRS) as part of BISTRO - Billiards
and Surfaces à la Teichmüller and Riemann\, Online\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Howard Masur (UChicago)
DTSTART;VALUE=DATE-TIME:20210208T170000Z
DTEND;VALUE=DATE-TIME:20210208T180000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/28
DESCRIPTION:Title: Counting finite order elements in the mapping class group\nby
Howard Masur (UChicago) as part of BISTRO - Billiards and Surfaces à la T
eichmüller and Riemann\, Online\n\n\nAbstract\nLet S be a closed surface
of genus g at least 2 and Mod(S) the mapping class group. Mod(S) acts by i
sometries on the Teichmuller space of S with respect to the Teichmuller me
tric. The lattice counting problem was considered in a paper by Athreya\,
Bufetov\, Eskin\, Mirzakhani. They showed that for any pair of points x an
d y\, the number of orbit points of y under the action of Mod(S) that lie
in a ball of radius R about x has an asymptotic growth rate of the form C
exp((6g-6)R)\, as R goes to infinity\, for a constant C. In this talk I w
ill discuss estimates for the number of finite order elements in this lat
tice counting problem. This is joint work with Spencer Dowdall.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunhui Wu (Tsinghua University\, Beijing)
DTSTART;VALUE=DATE-TIME:20210222T160000Z
DTEND;VALUE=DATE-TIME:20210222T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/29
DESCRIPTION:Title: Random hyperbolic surfaces of large genus have first eigenvalues g
reater than $\\frac{3}{16}-\\epsilon$\nby Yunhui Wu (Tsinghua Universi
ty\, Beijing) as part of BISTRO - Billiards and Surfaces à la Teichmülle
r and Riemann\, Online\n\n\nAbstract\nLet M_g be the moduli space of hyper
bolic surfaces of genus g endowed with the Weil-Petersson metric. In this
paper\, we show that for any $\\epsilon>0$\, as genus g goes to infinity\,
a generic surface $X\\in M_g$ satisfies that the first eigenvalue $\\lamb
da_1(X)>\\frac{3}{16}-\\epsilon$. This is a joint work with Yuhao Xue.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dawei Chen (Boston College)
DTSTART;VALUE=DATE-TIME:20210301T170000Z
DTEND;VALUE=DATE-TIME:20210301T180000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/30
DESCRIPTION:Title: Connected components of the strata of k-differentials\nby Dawe
i Chen (Boston College) as part of BISTRO - Billiards and Surfaces à la T
eichmüller and Riemann\, Online\n\n\nAbstract\nk-differentials on Riemann
surfaces correspond to (1/k)-translation structures. The moduli space of
k-differentials can be stratified according to the multiplicities of zeros
and poles of k-differentials. While these strata are smooth\, some of the
m can be disconnected. In this talk I will review known results and open p
roblems regarding the classification of their connected components\, with
a focus on geometric structures that can help distinguish different compon
ents. This is joint work with Quentin Gendron. (https://arxiv.org/abs/2101
.01650)\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Osama Khalil (University of Utah)
DTSTART;VALUE=DATE-TIME:20210308T170000Z
DTEND;VALUE=DATE-TIME:20210308T180000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/31
DESCRIPTION:Title: On the Mozes-Shah phenomenon for horocycle flows on moduli spaces<
/a>\nby Osama Khalil (University of Utah) as part of BISTRO - Billiards an
d Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\nThe Moze
s-Shah phenomenon on homogeneous spaces of Lie groups asserts that the spa
ce of ergodic measures under the action by subgroups generated by unipoten
ts is closed. A key input to their work is Ratner's fundamental rigidity t
heorems. Beyond its intrinsic interest\, this result has many applications
to counting problems in number theory. The problem of counting saddle con
nections on flat surfaces has motivated the search for analogous phenomena
for horocycle flows on moduli spaces of flat structures. In this setting\
, Eskin\, Mirzakhani\, and Mohammadi showed that this property is enjoyed
by the space of ergodic measures under the action of (the full upper trian
gular subgroup of) SL(2\,R). We will discuss joint work with Jon Chaika an
d John Smillie showing that this phenomenon fails to hold for the horocycl
e flow on the stratum of genus two flat surfaces with one cone point. As a
corollary\, we show that a dense set of horocycle flow orbits are not gen
eric for any measure\; in contrast with Ratner's genericity theorem.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viveka Erlandsson (University of Bristol)
DTSTART;VALUE=DATE-TIME:20210215T170000Z
DTEND;VALUE=DATE-TIME:20210215T180000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/32
DESCRIPTION:Title: Mirzakhani’s curve counting theorem\nby Viveka Erlandsson (U
niversity of Bristol) as part of BISTRO - Billiards and Surfaces à la Tei
chmüller and Riemann\, Online\n\n\nAbstract\nIn her thesis\, Mirzakhani e
stablished the asymptotic behavior of the number of simple closed geodesic
s of a given type in a hyperbolic surface. Here we say that two geodesics
are of the same type if they differ by a homeomorphism. In this talk I wil
l discuss this theorem\, the extension to geodesics which are not simple\,
and some applications.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedram Safaee (Universität Zürich)
DTSTART;VALUE=DATE-TIME:20210315T160000Z
DTEND;VALUE=DATE-TIME:20210315T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/33
DESCRIPTION:Title: Quantitative Weak Mixing For Interval Exchange Transformations
\nby Pedram Safaee (Universität Zürich) as part of BISTRO - Billiards an
d Surfaces à la Teichmüller and Riemann\, Online\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Umberto Zannier (Scuola Normale Superiore di Pisa)
DTSTART;VALUE=DATE-TIME:20210412T160000Z
DTEND;VALUE=DATE-TIME:20210412T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/34
DESCRIPTION:Title: Torsion values of sections\, elliptical billiards and diophantine
problems in dynamics\nby Umberto Zannier (Scuola Normale Superiore di
Pisa) as part of BISTRO - Billiards and Surfaces à la Teichmüller and Ri
emann\, Online\n\n\nAbstract\nWe shall consider sections of (products of)
elliptic schemes\, and their "torsion values". For instance\, what can be
said of the complex numbers b for which (2\, \\sqrt{2(2-b)}) is torsion on
y^2=x(x-1)(x-b)? In particular\, we shall recall results of "Manin-Mumfor
d type" and illustrate some applications to elliptical billiards. Finally\
, we shall frame these issues as special cases of a general question in ar
ithmetic dynamics\, which can be treated with different methods\, dependin
g on the context. (Most results refer to work with Pietro Corvaja and Davi
d Masser.)\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Corinna Ulcigrai (Universität Zürich)
DTSTART;VALUE=DATE-TIME:20210503T160000Z
DTEND;VALUE=DATE-TIME:20210503T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/35
DESCRIPTION:Title: Rigidity of foliations in genus two and renormalization of general
ized IETs\nby Corinna Ulcigrai (Universität Zürich) as part of BISTR
O - Billiards and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAb
stract\nIt follows from a celebrated result by Michel Herman on circle dif
feomorphisms (later improved by Yoccoz) that minimal smooth orientable fol
iations on surfaces of genus one\, under a full measure arithmetic conditi
on on\, are geometrically rigid\, namely: if they are topologically conjug
ated to a linear flow\, then they are actually differentiably conjugated t
o it.\n\nIn very recent joint work with Selim Ghazouani\, we prove a gener
alization of this result to genus two\, in particular by showing that smoo
th\, orientable foliations with non-degenerate (Morse) singularities on su
rfaces of genus two\, under a full measure arithmetic condition\, are geom
etrically rigid.\n\nAt the level of Poincare maps\, this can be translated
in a statement about generalized interval exchange transformations (or GI
ETs\, for short) and answers a conjecture by Marmi\, Moussa and Yoccoz in
genus two.\n\nThe result is based on the study of the dynamics of a renorm
alization operator on the space of GIETs (which is a suitable acceleration
of Rauzy-Veech induction). We prove in particular a dynamical dichotomy f
or orbits under renormalization which is valid in any genus.\n\nIn the tal
k we will motivate and explain the result\, by giving a brief survey of so
me of the key results in the theory of circle diffeos and in the study of
GIETs and then an brief overview the main steps of the proof.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Payne (University of Texas)
DTSTART;VALUE=DATE-TIME:20210524T160000Z
DTEND;VALUE=DATE-TIME:20210524T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/36
DESCRIPTION:Title: The moduli space of tropical curves and top weight cohomology of M
_g\nby Sam Payne (University of Texas) as part of BISTRO - Billiards a
nd Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\nI will
discuss a natural proper and surjective map from the moduli space of Riema
nn surfaces of genus g to the moduli space of tropical curves of genus g a
nd its applications. In joint work with Chan and Galatius\, we show that
the pullback on compactly supported cohomology is an injection and that th
e compactly supported cohomology of the tropical moduli space is isomorphi
c to the cohomology of Kontsevich’s commutative graph complex. Combining
this with deep results of Brown and Willwacher from Grothendieck-Teichmü
ller theory\, we deduce that the dimension of H^{4g-6}(M_g\, Q) grows expo
nentially with g. This growth was unexpected and disproves conjectures of
Church-Farb-Putman and Kontsevich.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nalini Anantharaman (IRMA)
DTSTART;VALUE=DATE-TIME:20210607T160000Z
DTEND;VALUE=DATE-TIME:20210607T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/37
DESCRIPTION:by Nalini Anantharaman (IRMA) as part of BISTRO - Billiards an
d Surfaces à la Teichmüller and Riemann\, Online\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Fougeron (Université de Paris)
DTSTART;VALUE=DATE-TIME:20210419T160000Z
DTEND;VALUE=DATE-TIME:20210419T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/38
DESCRIPTION:Title: A cyclotomic family of thin groups\nby Charles Fougeron (Unive
rsité de Paris) as part of BISTRO - Billiards and Surfaces à la Teichmü
ller and Riemann\, Online\n\n\nAbstract\nThin matrix groups are a delicate
object: they are by definition a sparse subgroup of a lattice but Zariski
-dense in the ambient Lie group. Despite much recent work\, a lot remains
to be understood about these groups and explicit examples are still rare.\
n\nIn this talk\, we will focus on matrix monodromy groups associated to h
ypergeometric differential equations. It was noticed a few years ago by Es
kin-Kontsevich-Möller-Zorich that in a family of 14 of these matrix group
s (associated to moduli spaces of Calabi-Yau varieties) the 7 cases that w
ere known to be thin coincide with cases that numerically satisfied an equ
ality between their Lyapunov exponents and some algebraic invariant.\n\nBy
exploring numerically the Lyapunov exponents of these differential equati
ons\, we found candidates for an infinite family of thin groups in Sp4(R)
. After explaining the path to these numerical observations\, I will
explain how we proved their thinness. (j.w. Simion Filip)\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriele Mondello (Università di Roma)
DTSTART;VALUE=DATE-TIME:20210426T160000Z
DTEND;VALUE=DATE-TIME:20210426T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/39
DESCRIPTION:Title: On spherical surfaces of genus 1 with 1 conical point\nby Gabr
iele Mondello (Università di Roma) as part of BISTRO - Billiards and Surf
aces à la Teichmüller and Riemann\, Online\n\n\nAbstract\nA spherical me
tric on a surface is a metric of constant curvature 1\, which thus makes t
he surface locally isometric to S^2. Such a metric has a conical point x o
f angle 2\\pi\\theta if its area element vanishes of order 2(\\theta-1) at
x. If the conformal class is prescribed\, a spherical metric can be viewe
d as a solution of a suitable singular Liouville equation. If the conforma
l class is not prescribed\, isotopy classes of spherical metrics can be co
nsidered as flat (SO(3\,R)\,S^2)-structure\, and so their deformation spac
e has a natural finite-dimensional real-analytic structure. Additionally\,
the moduli space of spherical surfaces of genus g with n conical points c
omes endowed with a natural forgetful map to the moduli space of Riemann s
urfaces of genus g with n marked points.\nI will begin by giving an overvi
ew of what is known about the topology of the moduli space of spherical su
rfaces and the above mentioned forgetful map.\nI will then focus on the ca
se of genus 1 with 1 conical point (joint work with Eremenko-Panov).\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Grushevsky (Stony Brook University)
DTSTART;VALUE=DATE-TIME:20210531T160000Z
DTEND;VALUE=DATE-TIME:20210531T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/40
DESCRIPTION:Title: Equations for affine invariant manifolds\, via degeneration\nb
y Samuel Grushevsky (Stony Brook University) as part of BISTRO - Billiards
and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\nStudy
ing the closures of the orbits of the $SL(2\,\\RR)$ action on the strata o
f holomorphic differentials is a central question in Teichmueller dynamics
. By the results of Eskin-Mirzakhani-Mohammadi\, locally in period coordin
ates these orbit closures are given by linear equations. We use the compac
tification of the strata given by the moduli space of multi-scale differen
tials to restrict the kinds of linear equations that can thus appear\, by
using a mix of algebraic and dynamic techniques\, and in particular obtain
ing a new proof of Wright's cylinder deformation theorem as a byproduct of
our study. Based on joint work with F. Benirschke and B. Dozier.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Umberto Zannier (Scuola Normale Superiore di Pisa)
DTSTART;VALUE=DATE-TIME:20210510T160000Z
DTEND;VALUE=DATE-TIME:20210510T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/41
DESCRIPTION:Title: Torsion values of sections\, elliptical billiards and diophantine
problems in dynamics.\nby Umberto Zannier (Scuola Normale Superiore di
Pisa) as part of BISTRO - Billiards and Surfaces à la Teichmüller and R
iemann\, Online\n\n\nAbstract\nWe shall consider sections of (products of)
elliptic schemes\, and their "torsion values". For instance\, what can be
said of the complex numbers b for which (2\, \\sqrt{2(2-b)}) is torsion o
n y^2=x(x-1)(x-b)? In particular\, we shall recall results of "Manin-Mumfo
rd type" and illustrate some applications to elliptical billiards. Finally
\, we shall frame these issues as special cases of a general question in a
rithmetic dynamics\, which can be treated with different methods\, dependi
ng on the context. (Most results refer to work with Pietro Corvaja and Dav
id Masser.)\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bertrand Deroin (CNRS)
DTSTART;VALUE=DATE-TIME:20210517T160000Z
DTEND;VALUE=DATE-TIME:20210517T170000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/42
DESCRIPTION:Title: Irreducible lattices in semi-simple Lie groups of rank at least 2
are not left-orderable\nby Bertrand Deroin (CNRS) as part of BISTRO -
Billiards and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstra
ct\nI'll report on the problem of the left orderability of lattices in sem
i-simple Lie groups\, and give some insight of our joint proof with Sebast
ian Hurtado that in rank at least two an irreducible lattice is not left-o
rderable.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Kontsevich (IHÉS)
DTSTART;VALUE=DATE-TIME:20210614T180000Z
DTEND;VALUE=DATE-TIME:20210614T190000Z
DTSTAMP;VALUE=DATE-TIME:20210612T230934Z
UID:BISTRO-Seminar/43
DESCRIPTION:Title: Wall-crossing for abelian differentials\nby Maxim Kontsevich (
IHÉS) as part of BISTRO - Billiards and Surfaces à la Teichmüller and R
iemann\, Online\n\n\nAbstract\nFor an abelian differential on a complex cu
rve one can count saddle connections in all possible relative homology cla
sses. These numbers jump when one crosses a wall in the moduli space of ab
elian differentials. I will show that the jumping formula is a particular
case of the general wall-crossing formalism of Y.Soibelman and myself. The
corresponding graded Lie algebra is the algebra of matrices over the ring
of Laurent polynomials in several variables. The wall-crossing structure
is explicitly calculable\, and is determined by a finite collection of inv
ertible matrices over the field of rational functions. The whole story gen
eralizes from curves to higher-dimensional complex algebraic varieties.\n
LOCATION:https://researchseminars.org/talk/BISTRO-Seminar/43/
END:VEVENT
END:VCALENDAR