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BEGIN:VEVENT
SUMMARY:Kasra Rafi (University of Toronto)
DTSTART:20200423T160000Z
DTEND:20200423T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/1
DESCRIPTION:Title: Absolutely continuous stationary measures for the mapping cl
ass group\nby Kasra Rafi (University of Toronto) as part of BISTRO - B
illiards and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstrac
t\nWe prove a version of a Theorem of Furstenberg in the setting of Mappin
g class groups. Thurston measure defines a smooth measure class on PML. Fo
r every measure \\nu in this measure class\, we produce a measure \\mu wit
h finite first moment on the mapping class group such that \\nu is the uni
que \\mu-stationary measure. In particular\, this gives an coding-free pro
of of the already known result that the Lyapunov spectrum of Kontsevich-Zo
rich cocycle on the principal stratum of quadratic differentials is simple
.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Costantini (Universität Bonn)
DTSTART:20200430T160000Z
DTEND:20200430T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/2
DESCRIPTION:Title: The Chern classes and the Euler characteristic of the moduli
spaces of abelian differentials\nby Matteo Costantini (Universität B
onn) as part of BISTRO - Billiards and Surfaces à la Teichmüller and Rie
mann\, Online\n\n\nAbstract\nRecently\, Bainbridge-Chen-Gendron-Grushevsky
-Möller defined the moduli space of multi scaled differentials\, which is
a compactification of the moduli spaces of abelian differentials with ver
y similar properties as the Deligne-Mumford compactification of the moduli
space of curves. During the talk I will explain how it is possible to dev
elop intersection 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 special case\, via Gauss-Bonnet\, we compute a formula for the Euler ch
aracteristic of the moduli spaces of abelian homolorphic and meromorphic d
ifferentials and obtain values in small genera. This is based on a joint w
ork with Martin Möller and Jonathan Zachhuber.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Curtis McMullen (Harvard)
DTSTART:20200521T170000Z
DTEND:20200521T180000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/3
DESCRIPTION:Title: Billiards\, heights and modular symbols\nby Curtis McMul
len (Harvard) as part of BISTRO - Billiards and Surfaces à la Teichmülle
r and Riemann\, Online\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Calderon (Yale University)
DTSTART:20200507T160000Z
DTEND:20200507T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/4
DESCRIPTION:Title: Shear-shape coordinates for Teichmüller space and applicati
ons to flat and hyperbolic geometry\nby Aaron Calderon (Yale Universit
y) as part of BISTRO - Billiards and Surfaces à la Teichmüller and Riema
nn\, Online\n\n\nAbstract\nThere is a deep yet mysterious connection betwe
en the hyperbolic and singular flat geometry of Riemann surfaces. Using Bo
nahon and Thurston’s “shear coordinates” for maximal laminations\, M
irzakhani related the earthquake and horocycle flows on Teichmüller space
\, two notions of unipotent flow coming from hyperbolic\, respectively fla
t\, geometry. In this talk\, I will describe joint work (in progress) with
James Farre in which we construct new “shear-shape coordinates” for T
eichmüller space adapted to any lamination. Using these coordinates\, we
extend Mirzakhani’s conjugacy to strata of quadratic differentials as we
ll as produce new examples of geodesics for the Lipschitz (asymmetric) met
ric with given stretch locus. These coordinates also yield information abo
ut the global structure of certain subloci in both Teichmüller space and
its cotangent bundle of quadratic differentials.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francisco Arana Herrera (Stanford)
DTSTART:20200514T160000Z
DTEND:20200514T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/5
DESCRIPTION:Title: Counting hyperbolic multi-geodesics with respect to the leng
ths of individual components\nby Francisco Arana Herrera (Stanford) as
part of BISTRO - Billiards and Surfaces à la Teichmüller and Riemann\,
Online\n\n\nAbstract\nIn her thesis\, Mirzakhani showed that on any closed
hyperbolic 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. Wolper
t conjectured that analogous results should hold for more general counting
s of multi-geodesics that keep track of the lengths of individual componen
ts. In this talk we will present a proof of this conjecture which combines
techniques and results of Mirzakhani with ideas introduced by Margulis in
his thesis.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jane Wang (Indiana University)
DTSTART:20200528T160000Z
DTEND:20200528T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/6
DESCRIPTION:Title: The realization problem for twisted quadratic differentials
(dilation surfaces)\nby Jane Wang (Indiana University) as part of BIST
RO - Billiards and Surfaces à la Teichmüller and Riemann\, Online\n\n\nA
bstract\nTwisted quadratic differentials\, also known as dilation surfaces
\, are geometric structures that are in a way a generalization of translat
ion surfaces. We can define a dilation surface either as a quadratic diffe
rential twisted by some real holonomy or as a collection of polygons with
sides identified by translations and dilations by nonzero real factors. Th
is small generalization is enough to introduce interesting new dynamical b
ehaviors on dilation surfaces that do not occur for translation surfaces.
In this talk\, we will introduce dilation surfaces and discuss some of the
new and interesting dynamical behaviors that can occur on them. We will t
hen motivate and formulate the realization problem\, which asks which mapp
ing class group elements and subgroups can be realized as affine automorph
isms of a dilation surfaces\, and discuss challenges and progress toward r
esolving this problem.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barak Weiss (Tel Aviv University)
DTSTART:20200604T170000Z
DTEND:20200604T180000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/7
DESCRIPTION:Title: New bounds on the covering density of a lattice\nby Bara
k Weiss (Tel Aviv University) as part of BISTRO - Billiards and Surfaces
à la Teichmüller 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 natural Haar-Siegel measure on the space of lattices) that a randomly
chosen lattice L satisfies L+K=R^n. As a step in the proof\, we utilize an
d strengthen results on the discrete Kakeya problem. Joint work with Or Or
dentlich and Oded Regev.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Smith (Cambridge University)
DTSTART:20200611T160000Z
DTEND:20200611T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/8
DESCRIPTION:Title: Symplectic mapping class groups and flat surfaces\nby Iv
an Smith (Cambridge University) as part of BISTRO - Billiards and Surfaces
à la Teichmüller and Riemann\, Online\n\n\nAbstract\nI will try to expl
ain why one particular approach to studying the mapping class groups of hi
gher-dimensional symplectic manifolds leads to thinking about flat surface
s and their cousins\, and some of the open questions that arise in that co
ntext. The talk will try to be reasonably self-contained\, but will theref
ore necessarily be somewhat impressionistic.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amol Aggarwal (Harvard University)
DTSTART:20200618T160000Z
DTEND:20200618T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/9
DESCRIPTION:Title: Large Genus Asymptotics for Intersection Numbers and Strata
Volumes\nby Amol Aggarwal (Harvard University) as part of BISTRO - Bil
liards and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\
nCorrelators\, or intersection numbers between psi-classes on the moduli s
pace of stable curves\, are fundamental invariants ubiquitous in mathemati
cal physics\, algebraic geometry\, geometric topology\, and dynamical syst
ems. In this talk\, we analyze the large genus asymptotics for these corre
lators using a comparison between the recursive relations (Virasoro constr
aints) that uniquely determine them with the jump probabilities of a certa
in asymmetric simple random walk. By combining this result with a combinat
orial analysis of recently proven formulas of Delecroix-Goujard-Zograf-Zor
ich\, we further provide the large genus limits for Masur-Veech volumes an
d area Siegel-Veech constants associated with principal strata in the modu
li space of quadratic differentials.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Salter (Columbia University)
DTSTART:20200625T160000Z
DTEND:20200625T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/10
DESCRIPTION:Title: Framed mapping class groups and strata of abelian different
ials\nby Nick Salter (Columbia University) as part of BISTRO - Billiar
ds and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\nStr
ata of abelian differentials have long been of interest for their dynamica
l and algebro-geometric properties\, but relatively little is understood a
bout their topology. I will describe a project aimed at understanding the
(orbifold) fundamental groups of non-hyperelliptic stratum components. The
centerpiece of this is the monodromy representation valued in the mapping
class group of the surface relative to the zeroes of the differential. Fo
r g \\ge 5\, we give a complete description of this as the stabilizer of t
he framing of the (punctured) surface arising from the flat structure asso
ciated to the differential. This is joint work with Aaron Calderon.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanni Forni (University of Maryland)
DTSTART:20200702T160000Z
DTEND:20200702T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/11
DESCRIPTION:Title: On weak mixing for translation flows and billiards in polyg
ons\nby Giovanni Forni (University of Maryland) as part of BISTRO - Bi
lliards and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract
\nHow chaotic 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 dense (hence a dense G_delta). Along the way we will discuss results
and open questions on weak mixing and effective weak mixing of translation
flows and interval exchange transformations.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Kontsevich (IHES)
DTSTART:20200716T160000Z
DTEND:20200716T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/12
DESCRIPTION:Title: Integral PL actions from birational geometry\nby Maxim
Kontsevich (IHES) as part of BISTRO - Billiards and Surfaces à la Teichm
üller and Riemann\, Online\n\n\nAbstract\nTheory of flat surfaces provide
s a series of interesting actions of SL2(Z) on finite sets (isomorphism cl
asses of square-tiled surfaces with a given integer area). I will talk on
a different construction\, with the origin in mirror symmetry/tropical geo
metry\, producing somewhat similar actions. For example\, in the case of K
3-surfaces\, 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 describe a general construction\, and give numerous examples which
could be interesting from the dynamical point of view.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincent Delecroix and Elise Goujard (University of Bordeaux)
DTSTART:20200709T160000Z
DTEND:20200709T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/13
DESCRIPTION:Title: The number of components of a multicurve in large genus
\nby Vincent Delecroix and Elise Goujard (University of Bordeaux) as part
of BISTRO - Billiards and Surfaces à la Teichmüller and Riemann\, Online
\n\n\nAbstract\nA multicurve on a closed surface S of genus g >= 2 is a ho
motopy class of a disjoint collection of simple closed curves on S. A hype
rbolic metric on S allows to measure the length of a multicurve. We study
the number of components of a multicurve taken at random among all multicu
rves of length at most L on S. We then let L tend to infinity and talk abo
ut a random multicurve on S. M. Mirzakhani proved that the number of comp
onents of a random multicurve on S only depends on the topology of S and n
ot on the specific hyperbolic metric. It hence makes sense to talk about t
he number of components of a random multicurve of genus g. Furthermore M.
Mirzakhani provided explicit formulas for this distribution involving the
Kontsevich-Witten correlators. Thanks to the recent work of A. Aggarwal on
the asymptotics of these correlators we describe its behavior as the genu
s g tend to infinity. We show that it asymptotically behaves as the number
of cycles of a random permutation in Sym_{3g-3} taken with respect to a v
ery explicit probability distribution.\nThe number of components of a rand
om multicurve of genus g coincide with the number of cylinders of a random
square-tiled surface in genus g. Hence our work equivalently provides res
ults on the geometry of random square-tiled surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Apisa (Yale University)
DTSTART:20200914T160000Z
DTEND:20200914T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/14
DESCRIPTION:Title: Reconstructing an orbit closure from its boundary\, holomor
phic retracts of Teichmuller space\, and new Eierlegende-Wollmilchsau-like
orbit closures!\nby Paul Apisa (Yale University) as part of BISTRO -
Billiards and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstra
ct\nWork of McMullen in genus two and Eskin\, Mirzakhani\, Mohammadi\, and
Filip in general established that the GL(2\, R) orbit closure of any tran
slation surface is an affine invariant subvariety (AIS). Myriad questions
abound about AIS. We focus on the following - how does the boundary of an
AIS constrain the AIS? \n\nWe will begin by explaining how different bou
ndary components of an AIS can be accessed by cylinder degenerations. Whil
e considering one degeneration is often insufficient to completely determi
ne an AIS\, we will show that one can often identify the AIS from two dege
nerations that form what will be called a diamond. These results are key t
o 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 the rank is greater than g/2). To explain the connection\, we take a
seeming detour. \n\nThe Eierlegende-Wollmilchsau square-tiled surface has
the property that every cylinder is parallel to exactly one other cylinde
r\, which is isometric to it. In this talk\, we will generalize this prope
rty to AIS beyond those generated by square-tiled surfaces\, saying\, roug
hly\, that an AIS on which every cylinder on every surface has an isometri
c “twin” is called geminal. Loci of double covers are examples of gemi
nal AIS. Less trivially\, every sufficiently large AIS (with rel zero) is
geminal. Moreover\, work of Markovic and Gekhtman showed that if M is the
collection of points\, in a stratum of quadratic differentials\, whose cor
responding 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 descri
bed above\, we will show that geminal AIS are loci of covers. This result
has implications for the complex geometry of Teichmuller space and is a ke
y step in the aforementioned work showing that sufficiently large AIS are
loci of covers. Finally\, we will sketch the construction of new geminal A
IS. These examples negatively resolve two questions of Mirzakhani and Wri
ght and illustrate new behavior in the finite blocking problem. This work
is joint with Alex Wright.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bram Petri (IMG-PRG)
DTSTART:20200921T160000Z
DTEND:20200921T170000Z
DTSTAMP:20260404T111324Z
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 Teichmül
ler and Riemann\, Online\n\n\nAbstract\nThe main question in this talk is
what the "most connected" closed hyperbolic surface of a given genus is. T
here are multiple measures of the connectivity of a hyperbolic surface\, b
ut as the title suggests\, we will focus on their diameter. I will explain
how random constructions of hyperbolic surfaces help with this question.
This is joint work with Thomas Budzinski and Nicolas Curien.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaëtan Borot (Humboldt-Universität zu Berlin)
DTSTART:20200928T160000Z
DTEND:20200928T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/16
DESCRIPTION:Title: Geometry of combinatorial moduli spaces and multicurve coun
ts\nby Gaëtan Borot (Humboldt-Universität zu Berlin) as part of BIST
RO - Billiards and Surfaces à la Teichmüller and Riemann\, Online\n\n\nA
bstract\nThe Teichmuller space of bordered surfaces can be described via m
etric ribbon graphs\, leading to a natural geometry (the symplectic form i
ntroduced by Kontsevich in his proof of Witten's conjecture). I will show
that many tools of hyperbolic geometry can be adapted to this combinatoria
l geometry: there are Fenchel-Nielsen coordinates that are Darboux\, Mirza
khani-McShane type identity\, integration formulas\, recursions for volume
and statistics of multicurves\, etc. Besides\, combinatorial geometry is
hyperbolic geometry for large boundary lengths converges to combinatorial
geometry: we extend some results of Mondello in this direction\, but also
stress some non-uniformity than manifests itself in a different integrabil
ity behavior of the Thurston measure of unit balls wrt combinatorial lengt
h in the space of measured foliations than the one found in the hyperbolic
setting by Arana-Herrera and Athreya.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junho Peter Whang (MIT)
DTSTART:20201005T160000Z
DTEND:20201005T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/17
DESCRIPTION:Title: Integral points on moduli of local systems\nby Junho Pe
ter Whang (MIT) as part of BISTRO - Billiards and Surfaces à la Teichmül
ler and Riemann\, Online\n\n\nAbstract\nModuli spaces for special linear r
ank two local systems on topological surfaces are basic objects in geometr
y. 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-p
unctured torus. In the first part of the talk\, we describe a structure th
eorem for the integral points on these moduli spaces for general surfaces\
, proved using mapping class group dynamics and differential geometric too
ls. In the second part (based on joint work with Fan)\, we discuss excepti
onal isomorphisms between these varieties and moduli spaces of points on (
algebraic) 3-spheres. Using this connection and the previous structure the
orem for the twice-punctured torus\, we can deduce a Diophantine finitenes
s result for integral Stokes matrices of rank 4.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karl Winsor (Harvard)
DTSTART:20201012T160000Z
DTEND:20201012T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/18
DESCRIPTION:Title: Navigating absolute period leaves and the Arnoux-Yoccoz sur
face in genus 3\nby Karl Winsor (Harvard) as part of BISTRO - Billiard
s and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\nThe
moduli space of holomorphic 1-forms on genus g Riemann surfaces has a foli
ation whose leaves consist of 1-forms with locally constant absolute perio
ds. Individual leaves have a natural flat structure\, recording changes in
relative periods along paths between the zeros. In genus 2\, a typical le
af is topologically a disk\, after being completed. One can also restrict
this foliation to strata of 1-forms with given zero orders\, and we will m
ainly focus on strata in genus greater than 2. We will describe closed geo
desics on these leaves\, give an example of a leaf with infinite genus\, a
nd show how to upgrade this to a statement about a typical leaf in the amb
ient stratum component.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Monk (IRMA)
DTSTART:20201026T170000Z
DTEND:20201026T180000Z
DTSTAMP:20260404T111324Z
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 Teichm
üller and Riemann\, Online\n\n\nAbstract\nThe aim of this talk is to desc
ribe the geometry and spectrum of most random hyperbolic surfaces\, picked
with the Weil-Petersson probability measure.\n\nIn this model\, one can g
et a good understanding of the geometry of a typical surface: Cheeger cons
tant\, diameter (Mirzakhani)\, injectivity radius\, number of short closed
geodesics (Mirzakhani-Petri)\, length of the shortest non-simple closed g
eodesic\, improved collar theorem (joint work with Joe Thomas)\, Benjamini
-Schramm convergence.\n\nI will explain how these geometric properties\, t
ogether with the Selberg trace formula\, lead to precise estimates on the
distribution of the eigenvalues of the Laplacian on a typical surface.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yilin Wang (MIT)
DTSTART:20201102T170000Z
DTEND:20201102T180000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/20
DESCRIPTION:Title: SLE\, energy duality\, and foliations by Weil-Petersson qua
sicircles\nby Yilin Wang (MIT) as part of BISTRO - Billiards and Surfa
ces à la Teichmüller and Riemann\, Online\n\n\nAbstract\nSchramm-Loewner
evolution (SLE) is a one-parameter family of random simple planar curve.
It first arises as interfaces in scaling limits of 2D statistical mechanic
s lattice models which exhibit conformal invariance. The small-parameter a
symptotic behaviors give rise to the Loewner energy for Jordan curves\, wh
ich is finite if and only if the curve is a Weil-Petersson quasicircle\, a
nd is moreover a Kahler potential on the Weil-Petersson Teichmuller space.
I will survey the link between SLE and Weil-Petersson quasicircles\, then
show the large-parameter asymptotic behaviors of SLE giving rise to Loewn
er-Kufarev energy\, provides a further duality via foliations of the Riema
nn sphere by Weil-Petersson quasicircles.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Serge Cantat (IRMAR)
DTSTART:20201207T170000Z
DTEND:20201207T180000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/21
DESCRIPTION:Title: Stationary measures on real projective surface\nby Serg
e Cantat (IRMAR) as part of BISTRO - Billiards and Surfaces à la Teichmü
ller and Riemann\, Online\n\n\nAbstract\nConsider a real projective surfac
e $X(\\R)$\, and a group $\\Gamma$ acting by algebraic diffeomorphisms on
$X(\\R)$. If $\\nu$ is a probability measure on $\\Gamma$\, one can random
ly and independently choose elements $f_j$ in $\\Gamma$ and look at the ra
ndom orbits $x$\, $f_1(x)$\, $f_2(f_1(x))$\, $\\ldots$ How do these orbits
distribute on the surface ? This is directly related to the classificatio
n of stationary measures on $X(\\R)$. I will describe recent results on th
is problem\, all obtained in collaboration with Romain Dujardin. The main
ingredients will be ergodic theory\, notably the work of Brown and Rodrigu
ez-Hertz\, algebraic geometry\, and complex analysis. Concrete geometric e
xamples will be given.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Chung (UChicago)
DTSTART:20201019T160000Z
DTEND:20201019T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/22
DESCRIPTION:Title: Stationary measure and orbit closure classification for ran
dom walks on surfaces\nby Brian Chung (UChicago) as part of BISTRO - B
illiards and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstrac
t\nWe study the problem of classifying stationary measures and orbit closu
res for non-abelian action on surfaces. Using a result of Brown and Rodrig
uez Hertz\, we show that under a certain average growth condition\, the or
bit closures are either finite or dense. Moreover\, every infinite orbit e
quidistributes on the surface. This is analogous to the results of Benoist
-Quint and Eskin-Lindenstrauss in the homogeneous setting\, and the result
of Eskin-Mirzakhani in the setting of moduli spaces of translation surfac
es.\n\nWe then consider the problem of verifying this growth condition in
concrete settings. In particular\, we apply the theorem to two settings\,
namely discrete perturbations of the standard map and the Out(F2)-action o
n a certain character variety. We verify the growth condition analytically
in the former setting\, and verify numerically in the latter setting.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frederik Benirschke (Stony Brook)
DTSTART:20201109T170000Z
DTEND:20201109T180000Z
DTSTAMP:20260404T111324Z
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 Teichmülle
r and Riemann\, Online\n\n\nAbstract\nModuli spaces of translation surface
s carry a natural GL(2\,R)-action by acting linearly on the periods of the
translation surface.\nRecent breakthroughs by Eskin\, Mirazakhani\, Moham
madi and Filip\, which extend results of McMullen in genus 2\, show that
orbit closures for the GL(2\,R)-action are surprisingly well behaved: Orb
it closures are algebraic varieties that are locally defined by linear equ
ations among periods. Orbit closures are never compact and it is natural t
o search for "nice" compactifications. One simple way of compactifying orb
it closures is by taking the closure inside the moduli space of multi-scal
e differentials\, which was constructed recently by Bainbridge-Chen-Gendro
n-Grushevsky-Möller. Our main result is a description of the boundary of
an orbit closure inside the moduli space of multi-scale differentials. In
particular the boundary is again given by linear equations among periods.
Time permitting\, we explain how our description of the boundary can be us
ed to extend Wrights cylinder deformation theorem to the case of meromorph
ic strata\, which is partially joint work with Benjamin Dozier and Samuel
Grushevsky.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Mullane (Frankfurt)
DTSTART:20201116T170000Z
DTEND:20201116T180000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/24
DESCRIPTION:Title: Strata of exact differentials and the birational geometry o
f Hurwitz spaces\nby Scott Mullane (Frankfurt) as part of BISTRO - Bil
liards and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\
nThe strata of exact differentials are obtained from Hurwitz spaces of cov
ers of the rational line with specified branching profiles and form linear
manifolds inside the strata of meromorphic differentials. Despite the uti
lity 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 pers
ist. I'll show how the perspective of the strata of exact differentials ca
n be used to prove\, that as conjectured\, the rational Picard group of th
e moduli 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 y
ields results on open questions on the irreducibility of non-simple Hurwit
z spaces and has applications to the birational geometry of moduli spaces
of pointed rational curves.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Marshall-Maldonado (Marseille)
DTSTART:20201123T170000Z
DTEND:20201123T180000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/25
DESCRIPTION:Title: Quantitative weakly mixing of flows over Salem type substit
utions\nby Juan Marshall-Maldonado (Marseille) as part of BISTRO - Bil
liards and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\
nSuspension flows over Vershik automorphisms provide a powerful symbolic f
rame for study linear flows over translation surfaces. The simplest case i
s the periodic one\, which leads us to substitutions. Spectral properties
depend strongly on the algebraic nature of the Perron eigenvalue of the ad
jacency matrix of the substitution\, as shown in the work of Bufetov and S
olomyak. In this talk I will consider the "border case" in which this eige
nvalue is a Salem number and I will show a modulus of continuity for spect
ral measures in a family of algebraic points.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chaya Norton (UMich)
DTSTART:20201130T170000Z
DTEND:20201130T180000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/26
DESCRIPTION:Title: Obtuse Veech Triangles\nby Chaya Norton (UMich) as part
of BISTRO - Billiards and Surfaces à la Teichmüller and Riemann\, Onlin
e\n\n\nAbstract\nThe question of which obtuse triangles ufold to Veech sur
faces has been open since Kenyon and Smillie's results on acute and right
triangles. There are two known infinite families of obtuse Veech triangles
due to Veech and Ward. More recently Hooper showed that the unfolding of
the sporadic example (pi/12\, pi/3\, 7*pi/12) generates a Teichmuller curv
e\, and he conjectures that these are all the obtuse Veech triangles. We p
rove this conjecture when the largest angle is at least 135 degrees. Our m
ethod relies on a criterion of Mirzakhani and Wright which builds on work
of Moeller and McMullen studying the variation of the period matrix along
the GL(2\,R) action. This is joint work with Anne Larsen and Bradley Zykos
ki completed during the 2020 University of Michigan REU.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olga Paris-Romaskevich (CNRS)
DTSTART:20210201T170000Z
DTEND:20210201T180000Z
DTSTAMP:20260404T111324Z
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://stable.researchseminars.org/talk/BISTRO-Seminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Howard Masur (UChicago)
DTSTART:20210208T170000Z
DTEND:20210208T180000Z
DTSTAMP:20260404T111324Z
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 Teichmüller and Riemann\, Online\n\n\nAbstract\nLet S be a closed s
urface of genus g at least 2 and Mod(S) the mapping class group. Mod(S) ac
ts by isometries on the Teichmuller space of S with respect to the Teichmu
ller metric. The lattice counting problem was considered in a paper by Ath
reya\, Bufetov\, Eskin\, Mirzakhani. They showed that for any pair of poin
ts x and y\, the number of orbit points of y under the action of Mod(S) th
at 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 t
alk I will discuss estimates for the number of finite order elements in t
his lattice counting problem. This is joint work with Spencer Dowdall.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunhui Wu (Tsinghua University\, Beijing)
DTSTART:20210222T160000Z
DTEND:20210222T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/29
DESCRIPTION:Title: Random hyperbolic surfaces of large genus have first eigenv
alues greater than $\\frac{3}{16}-\\epsilon$\nby Yunhui Wu (Tsinghua U
niversity\, Beijing) as part of BISTRO - Billiards and Surfaces à la Teic
hmüller and Riemann\, Online\n\n\nAbstract\nLet M_g be the moduli space o
f hyperbolic surfaces of genus g endowed with the Weil-Petersson metric. I
n this paper\, we show that for any $\\epsilon>0$\, as genus g goes to inf
inity\, a generic surface $X\\in M_g$ satisfies that the first eigenvalue
$\\lambda_1(X)>\\frac{3}{16}-\\epsilon$. This is a joint work with Yuhao X
ue.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dawei Chen (Boston College)
DTSTART:20210301T170000Z
DTEND:20210301T180000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/30
DESCRIPTION:Title: Connected components of the strata of k-differentials\n
by Dawei Chen (Boston College) as part of BISTRO - Billiards and Surfaces
à la Teichmüller and Riemann\, Online\n\n\nAbstract\nk-differentials on
Riemann surfaces correspond to (1/k)-translation structures. The moduli sp
ace of k-differentials can be stratified according to the multiplicities o
f zeros and poles of k-differentials. While these strata are smooth\, some
of them can be disconnected. In this talk I will review known results and
open problems regarding the classification of their connected components\
, with a focus on geometric structures that can help distinguish different
components. This is joint work with Quentin Gendron. (https://arxiv.org/a
bs/2101.01650)\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Osama Khalil (University of Utah)
DTSTART:20210308T170000Z
DTEND:20210308T180000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/31
DESCRIPTION:Title: On the Mozes-Shah phenomenon for horocycle flows on moduli
spaces\nby Osama Khalil (University of Utah) as part of BISTRO - Billi
ards and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\nT
he Mozes-Shah phenomenon on homogeneous spaces of Lie groups asserts that
the space of ergodic measures under the action by subgroups generated by u
nipotents is closed. A key input to their work is Ratner's fundamental rig
idity theorems. Beyond its intrinsic interest\, this result has many appli
cations to counting problems in number theory. The problem of counting sad
dle connections on flat surfaces has motivated the search for analogous ph
enomena for horocycle flows on moduli spaces of flat structures. In this s
etting\, Eskin\, Mirzakhani\, and Mohammadi showed that this property is e
njoyed by the space of ergodic measures under the action of (the full uppe
r triangular subgroup of) SL(2\,R). We will discuss joint work with Jon Ch
aika and John Smillie showing that this phenomenon fails to hold for the h
orocycle flow on the stratum of genus two flat surfaces with one cone poin
t. As a corollary\, we show that a dense set of horocycle flow orbits are
not generic for any measure\; in contrast with Ratner's genericity theorem
.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viveka Erlandsson (University of Bristol)
DTSTART:20210215T170000Z
DTEND:20210215T180000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/32
DESCRIPTION:Title: Mirzakhani’s curve counting theorem\nby Viveka Erland
sson (University of Bristol) as part of BISTRO - Billiards and Surfaces à
la Teichmüller and Riemann\, Online\n\n\nAbstract\nIn her thesis\, Mirza
khani established the asymptotic behavior of the number of simple closed g
eodesics of a given type in a hyperbolic surface. Here we say that two geo
desics are of the same type if they differ by a homeomorphism. In this tal
k I will discuss this theorem\, the extension to geodesics which are not s
imple\, and some applications.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedram Safaee (Universität Zürich)
DTSTART:20210315T160000Z
DTEND:20210315T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/33
DESCRIPTION:Title: Quantitative Weak Mixing For Interval Exchange Transformati
ons\nby Pedram Safaee (Universität Zürich) as part of BISTRO - Billi
ards and Surfaces à la Teichmüller and Riemann\, Online\n\nAbstract: TBA
\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Umberto Zannier (Scuola Normale Superiore di Pisa)
DTSTART:20210412T160000Z
DTEND:20210412T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/34
DESCRIPTION:Title: Torsion values of sections\, elliptical billiards and dioph
antine problems in dynamics\nby Umberto Zannier (Scuola Normale Superi
ore di Pisa) as part of BISTRO - Billiards and Surfaces à la Teichmüller
and Riemann\, Online\n\n\nAbstract\nWe shall consider sections of (produc
ts 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 tor
sion on y^2=x(x-1)(x-b)? In particular\, we shall recall results of "Manin
-Mumford type" and illustrate some applications to elliptical billiards. F
inally\, we shall frame these issues as special cases of a general questio
n in arithmetic dynamics\, which can be treated with different methods\, d
epending on the context. (Most results refer to work with Pietro Corvaja a
nd David Masser.)\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Corinna Ulcigrai (Universität Zürich)
DTSTART:20210503T160000Z
DTEND:20210503T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/35
DESCRIPTION:Title: Rigidity of foliations in genus two and renormalization of
generalized IETs\nby Corinna Ulcigrai (Universität Zürich) as part o
f BISTRO - Billiards and Surfaces à la Teichmüller and Riemann\, Online\
n\n\nAbstract\nIt follows from a celebrated result by Michel Herman on cir
cle diffeomorphisms (later improved by Yoccoz) that minimal smooth orienta
ble foliations on surfaces of genus one\, under a full measure arithmetic
condition on\, are geometrically rigid\, namely: if they are topologically
conjugated to a linear flow\, then they are actually differentiably conju
gated to it.\n\nIn very recent joint work with Selim Ghazouani\, we prove
a generalization of this result to genus two\, in particular by showing th
at smooth\, orientable foliations with non-degenerate (Morse) singularitie
s on surfaces of genus two\, under a full measure arithmetic condition\, a
re geometrically rigid.\n\nAt the level of Poincare maps\, this can be tra
nslated in a statement about generalized interval exchange transformations
(or GIETs\, for short) and answers a conjecture by Marmi\, Moussa and Yoc
coz in genus two.\n\nThe result is based on the study of the dynamics of a
renormalization operator on the space of GIETs (which is a suitable accel
eration of Rauzy-Veech induction). We prove in particular a dynamical dich
otomy for orbits under renormalization which is valid in any genus.\n\nIn
the talk we will motivate and explain the result\, by giving a brief surve
y of some of the key results in the theory of circle diffeos and in the st
udy of GIETs and then an brief overview the main steps of the proof.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Payne (University of Texas)
DTSTART:20210524T160000Z
DTEND:20210524T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/36
DESCRIPTION:Title: The moduli space of tropical curves and top weight cohomolo
gy of M_g\nby Sam Payne (University of Texas) as part of BISTRO - Bill
iards and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\n
I will discuss a natural proper and surjective map from the moduli space o
f Riemann surfaces of genus g to the moduli space of tropical curves of ge
nus g and its applications. In joint work with Chan and Galatius\, we sho
w that the pullback on compactly supported cohomology is an injection and
that the compactly supported cohomology of the tropical moduli space is is
omorphic to the cohomology of Kontsevich’s commutative graph complex. Co
mbining this with deep results of Brown and Willwacher from Grothendieck-T
eichmüller theory\, we deduce that the dimension of H^{4g-6}(M_g\, Q) gro
ws exponentially with g. This growth was unexpected and disproves conjectu
res of Church-Farb-Putman and Kontsevich.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nalini Anantharaman (IRMA)
DTSTART:20210607T160000Z
DTEND:20210607T170000Z
DTSTAMP:20260404T111324Z
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://stable.researchseminars.org/talk/BISTRO-Seminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Fougeron (Université de Paris)
DTSTART:20210419T160000Z
DTEND:20210419T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/38
DESCRIPTION:Title: A cyclotomic family of thin groups\nby Charles Fougeron
(Université de Paris) as part of BISTRO - Billiards and Surfaces à la T
eichmüller and Riemann\, Online\n\n\nAbstract\nThin matrix groups are a d
elicate 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 r
emains to be understood about these groups and explicit examples are still
rare.\n\nIn this talk\, we will focus on matrix monodromy groups associat
ed to hypergeometric differential equations. It was noticed a few years ag
o by Eskin-Kontsevich-Möller-Zorich that in a family of 14 of these matri
x groups (associated to moduli spaces of Calabi-Yau varieties) the 7 cases
that were known to be thin coincide with cases that numerically satisfied
an equality between their Lyapunov exponents and some algebraic invariant
.\n\nBy exploring numerically the Lyapunov exponents of these differential
equations\, 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://stable.researchseminars.org/talk/BISTRO-Seminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriele Mondello (Università di Roma)
DTSTART:20210426T160000Z
DTEND:20210426T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/39
DESCRIPTION:Title: On spherical surfaces of genus 1 with 1 conical point\n
by Gabriele Mondello (Università di Roma) as part of BISTRO - Billiards a
nd Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\nA spher
ical metric on a surface is a metric of constant curvature 1\, which thus
makes the surface locally isometric to S^2. Such a metric has a conical po
int x of angle 2\\pi\\theta if its area element vanishes of order 2(\\thet
a-1) at x. If the conformal class is prescribed\, a spherical metric can b
e viewed as a solution of a suitable singular Liouville equation. If the c
onformal class is not prescribed\, isotopy classes of spherical metrics ca
n be considered as flat (SO(3\,R)\,S^2)-structure\, and so their deformati
on space has a natural finite-dimensional real-analytic structure. Additio
nally\, the moduli space of spherical surfaces of genus g with n conical p
oints comes endowed with a natural forgetful map to the moduli space of Ri
emann surfaces of genus g with n marked points.\nI will begin by giving an
overview of what is known about the topology of the moduli space of spher
ical surfaces and the above mentioned forgetful map.\nI will then focus on
the case of genus 1 with 1 conical point (joint work with Eremenko-Panov)
.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Grushevsky (Stony Brook University)
DTSTART:20210531T160000Z
DTEND:20210531T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/40
DESCRIPTION:Title: Equations for affine invariant manifolds\, via degeneration
\nby Samuel Grushevsky (Stony Brook University) as part of BISTRO - Bi
lliards and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract
\nStudying the closures of the orbits of the $SL(2\,\\RR)$ action on the s
trata of holomorphic differentials is a central question in Teichmueller d
ynamics. By the results of Eskin-Mirzakhani-Mohammadi\, locally in period
coordinates these orbit closures are given by linear equations. We use the
compactification of the strata given by the moduli space of multi-scale d
ifferentials to restrict the kinds of linear equations that can thus appea
r\, by using a mix of algebraic and dynamic techniques\, and in particular
obtaining a new proof of Wright's cylinder deformation theorem as a bypro
duct of our study. Based on joint work with F. Benirschke and B. Dozier.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Umberto Zannier (Scuola Normale Superiore di Pisa)
DTSTART:20210510T160000Z
DTEND:20210510T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/41
DESCRIPTION:Title: Torsion values of sections\, elliptical billiards and dioph
antine problems in dynamics.\nby Umberto Zannier (Scuola Normale Super
iore di Pisa) as part of BISTRO - Billiards and Surfaces à la Teichmülle
r and Riemann\, Online\n\n\nAbstract\nWe shall consider sections of (produ
cts 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 to
rsion on y^2=x(x-1)(x-b)? In particular\, we shall recall results of "Mani
n-Mumford type" and illustrate some applications to elliptical billiards.
Finally\, we shall frame these issues as special cases of a general questi
on in arithmetic dynamics\, which can be treated with different methods\,
depending on the context. (Most results refer to work with Pietro Corvaja
and David Masser.)\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bertrand Deroin (CNRS)
DTSTART:20210517T160000Z
DTEND:20210517T170000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/42
DESCRIPTION:Title: Irreducible lattices in semi-simple Lie groups of rank at l
east 2 are not left-orderable\nby Bertrand Deroin (CNRS) as part of BI
STRO - Billiards and Surfaces à la Teichmüller and Riemann\, Online\n\n\
nAbstract\nI'll report on the problem of the left orderability of lattices
in semi-simple Lie groups\, and give some insight of our joint proof with
Sebastian Hurtado that in rank at least two an irreducible lattice is not
left-orderable.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Kontsevich (IHÉS)
DTSTART:20210614T180000Z
DTEND:20210614T190000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/43
DESCRIPTION:Title: Wall-crossing for abelian differentials\nby Maxim Konts
evich (IHÉS) as part of BISTRO - Billiards and Surfaces à la Teichmülle
r and Riemann\, Online\n\n\nAbstract\nFor an abelian differential on a com
plex curve one can count saddle connections in all possible relative homol
ogy classes. These numbers jump when one crosses a wall in the moduli spac
e of abelian differentials. I will show that the jumping formula is a part
icular case of the general wall-crossing formalism of Y.Soibelman and myse
lf. The corresponding graded Lie algebra is the algebra of matrices over t
he ring of Laurent polynomials in several variables. The wall-crossing str
ucture is explicitly calculable\, and is determined by a finite collection
of invertible matrices over the field of rational functions. The whole st
ory generalizes from curves to higher-dimensional complex algebraic variet
ies.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Skripchenko (HSE University)
DTSTART:20220126T170000Z
DTEND:20220126T174500Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/44
DESCRIPTION:Title: Real-normalized differentials with a single order 2 pole: t
he first steps\nby Alexandra Skripchenko (HSE University) as part of B
ISTRO - Billiards and Surfaces à la Teichmüller and Riemann\, Online\n\n
\nAbstract\nA meromorphic differential on a Riemann surface is said to be
real-normalized if all its periods are real. This notion was introduced by
I. Krichever in connection with the study of geometry of moduli spaces.\n
\nReal-normalized differentials on Riemann surfaces of given genus with pr
escribed orders of their poles form real orbifolds whose topology is close
ly related to that of moduli spaces of Riemann surfaces with marked points
. In our joint work with Sergei Lando and Igor Krichever we propose a comb
inatorial model for the real normalized differentials with a single order
2 pole and use it to analyze the corresponding absolute period foliation.\
n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrien Sauvaget (CNRS)
DTSTART:20220126T174500Z
DTEND:20220126T183000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/45
DESCRIPTION:Title: Moduli of large pluricanonical divisors\nby Adrien Sauv
aget (CNRS) as part of BISTRO - Billiards and Surfaces à la Teichmüller
and Riemann\, Online\n\n\nAbstract\nWe will study moduli spaces of k-canon
ical divisors. A standard invariant of these spaces is their (Masur-Veech)
volume which can be computed by means of intersection theory. Considering
the large k behavior of these volumes one may compute volumes of moduli s
paces of flat surfaces (by "approximation" of these spaces). I’ll also e
xplain how different choices of limit should allow to compute the Weil-Pet
ersson volumes of moduli spaces of hyperbolic surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedram Safaee (Universität Zürich)
DTSTART:20220126T183000Z
DTEND:20220126T191500Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/46
DESCRIPTION:Title: Quantitative Weak Mixing For Interval Exchange Transformati
ons\nby Pedram Safaee (Universität Zürich) as part of BISTRO - Billi
ards and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\nA
n interval exchange transformation (IET) is an orientation preserving piec
ewise isometry of the unit interval. These transformations are low complex
ity systems that exhibit interesting spectral properties\; They are never
mixing\, typically uniquely ergodic\, typically rigid\, and typically weak
ly mixing. Weak mixing is equivalent to having the Cesaro averages of corr
elations tend to zero. In this talk\, we will focus on the rate of decay o
f the Cesaro averages of correlations for sufficiently regular observables
for typical IETs. We show that a (rather unexpected) dichotomy holds for
this decay depending on whether the IET is of rotation class or not. In th
e former case\, we provide logarithmic lower and upper bounds for the deca
y of Cesaro averages whereas we provide polynomial upper bounds in the lat
ter case. This is joint work with Artur Avila and Giovanni Forni.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samantha Fairchild (MPI MiS)
DTSTART:20220330T160000Z
DTEND:20220330T164500Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/47
DESCRIPTION:Title: Counting pairs of saddle connections\nby Samantha Fairc
hild (MPI MiS) as part of BISTRO - Billiards and Surfaces à la Teichmüll
er and Riemann\, Online\n\n\nAbstract\nWe will discuss recent work showing
that for almost every translation surface the number of pairs of saddle c
onnections with bounded virtual area has asymptotic growth like $c R^2$ wh
ere the constant $c$ depends only on the area and the connected component
of the stratum. The proof techniques combine classical results for countin
g saddle connections with the crucial result that the Siegel-Veech transfo
rm is in $L^2$. This is joint work with Jayadev Athreya and Howard Masur.\
n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erwan Lanneau (Institut Fourier)
DTSTART:20220330T164500Z
DTEND:20220330T173000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/48
DESCRIPTION:Title: Pseudo-Anosov stretch factors\nby Erwan Lanneau (Instit
ut Fourier) as part of BISTRO - Billiards and Surfaces à la Teichmüller
and Riemann\, Online\n\n\nAbstract\nPseudo-Anosov mapping classes first ap
peared in Thurston's work in connection to classification of surface homeo
morphisms. Nowadays\, their study is a theory by itself combining Teichmü
ller theory\, dynamics\, flat geometry and number theory. An important asp
ect of this theory emerged with Fried's work and concerns the study of the
stretch factors. They reflect the geometry of the moduli spaces (e.g. by
the lengths spectrum for the Teichmüller metric) and the fine properties
of the dynamics of the map (e.g. by the Ruelle spectrum). I will review se
veral old and new results on pseudo-Anosov stretch factors.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jenya Sapir (Binghamton University)
DTSTART:20220330T173000Z
DTEND:20220330T181500Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/49
DESCRIPTION:Title: A projection from geodesic currents to Teichmuller space\nby Jenya Sapir (Binghamton University) as part of BISTRO - Billiards an
d Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\nGiven a
genus g surface S\, we consider the space of projective geodesic currents
on S. This space contains many objects of interest in low dimensional topo
logy\, such as the set of all closed curves on S up to homotopy\, the set
of all marked\, negatively curved metrics on S\, as well as some higher Te
ichmuller spaces. We show that there is a mapping class group invariant\,
length minimizing projection from the space of filling projective currents
onto Teichmuller space\, and that this projection is continuous and prope
r. This is joint work with Sebastian Hensel.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonardo Lerer (Weizmann Institute)
DTSTART:20220525T160000Z
DTEND:20220525T163000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/50
DESCRIPTION:Title: Bi-algebraic geometry of strata of abelian differentials\nby Leonardo Lerer (Weizmann Institute) as part of BISTRO - Billiards an
d Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\nA stratu
m of abelian differentials is endowed with an atlas of charts\, with linea
r transition functions\, given by mapping a differential to its relative p
eriods. In this talk\, we consider the transcendence properties (both arit
hmetic and functional) of these period coordinates. More precisely\, we wi
ll discuss the transcendence over \\bar{\\mathbb{Q}} of the relative perio
ds of abelian differentials\, together with a characterization of the "lea
st" transcendental ones and their distribution inside a stratum. On the ge
ometric side\, we will discuss the algebraic relations satisfied by the pe
riods of an abelian differential when it varies inside an algebraic subvar
iety of a stratum. This is joint work with B. Klingler.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anja Randecker (Heidelberg University)
DTSTART:20220525T164500Z
DTEND:20220525T171500Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/51
DESCRIPTION:Title: Topological behaviour of conjugacy classes of big mapping c
lass group\nby Anja Randecker (Heidelberg University) as part of BISTR
O - Billiards and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAb
stract\nClassical mapping class groups\, i.e. for surfaces of finite type\
, are well-studied objects: they are discrete groups expressing the symmet
ries of the surface.\n\nWhen we turn our attention to surfaces of infinite
type\, the situation changes drastically: In particular\, the mapping cla
ss groups are now uncountable and we can define an interesting topology on
them. This lets us ask many new questions: When considering the conjugacy
action of a big mapping class group on itself\, can there be comeager orb
its? Or at least dense orbits? Or at least somewhere dense orbits?\n\nIn t
his talk\, I will give a very short introduction to big mapping class grou
ps\, answer the questions above\, and give an idea of the tools from model
theory that we use in the proofs. This is based on joint work with Jesús
Hernández Hernández\, Michael Hrušák\, Israel Morales\, Manuel Sedano
\, and Ferrán Valdez.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seung uk Jang (University of Chicago)
DTSTART:20220525T173000Z
DTEND:20220525T180000Z
DTSTAMP:20260404T111324Z
UID:BISTRO-Seminar/52
DESCRIPTION:Title: Kummer Rigidity for Hyperbolic Hyperkähler Automorphisms\nby Seung uk Jang (University of Chicago) as part of BISTRO - Billiards
and Surfaces à la Teichmüller and Riemann\, Online\n\n\nAbstract\nDynam
ical systems that have volume-class measures of maximal entropy typically
have locally homogeneous structures. In complex dynamics\, this usually me
ans that the automorphism comes from a torus\, as established by Zdunik\,
Berteloot--Dupont\, Cantat--Dupont\, Filip--Tosatti\, and others. As a suc
cessor to this series\, we present another result that applies to projecti
ve hyperkahler manifolds\, a higher-dimensional analogue of K3 surfaces.\n
\nWe discuss how such a system has a surprisingly simple dynamical structu
re\, and how we can make use of this structure to identify the given auto
morphism as a "Kummer example" with a (Ricci-flat) flat metric. All the ne
cessary background will be provided.\n
LOCATION:https://stable.researchseminars.org/talk/BISTRO-Seminar/52/
END:VEVENT
END:VCALENDAR