BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:Inviscid Limit and Prandtl System
DTSTART;VALUE=DATE-TIME:20190523T080000Z
DTEND;VALUE=DATE-TIME:20190523T100000Z
DTSTAMP;VALUE=DATE-TIME:20190618T145200Z
UID:indico-event-4688@indico.math.cnrs.fr
DESCRIPTION:Speakers: Nader Masmoudi (Université de New York)\nOne of the
main open problems in the mathematical analysis of fluid flows is the und
erstanding of the inviscid limit in the presence of boundaries. In the cas
e of a fixed bounded domain\, it is an open problem to know whether soluti
ons to the Navier-Stokes system with no slip boundary condition (zero Diri
chlet boundary condition) do converge to a solution to the Euler system wh
en the viscosity goes to zero. The main problem here comes from the fact t
hat we cannot impose a no slip boundary condition for the Euler system. To
recover a zero Dirichlet condition\, Prandtl proposed to introduce a boun
dary layer (a small neighborhood of the boundary) in which viscous effects
are still present. It turns out that the system that governs the flow in
this small neighborhood\, namely the Prandtl system has many mathematical
difficulties. The goal of this course is to discuss some of the recent dev
elopment in the inviscid limit as well as the study of the Prandtl system.
We will also discuss the singularity formation for both the stationary an
d non stationary Prandtl system.\nhttps://indico.math.cnrs.fr/event/4688/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/4688/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quantum Geometry of Moduli Spaces of Local Systems and Representat
ion Theory
DTSTART;VALUE=DATE-TIME:20190617T123000Z
DTEND;VALUE=DATE-TIME:20190617T143000Z
DTSTAMP;VALUE=DATE-TIME:20190618T145200Z
UID:indico-event-4375@indico.math.cnrs.fr
DESCRIPTION:Speakers: Alexander Goncharov (Yale University & IHES)\nLectur
es 1-3 are mostly based on our recent work with Linhui Shen.\n\nGiven a su
rface S with punctures and special points on the boundary considered modul
o isotopy\, and a split semi-simple adjoint group G\, we define and quanti
ze moduli spaces Loc(G\,S) G-local systems on S\, generalising character v
arieties.\n\nTo achieve this\, we introduce a new moduli space P(G\, S) cl
osely related to Loc(G\,S). We prove that it has a cluster Poisson variety
structure\, equivariant under the action of a discrete group\, containing
the mapping class group of S. This generalises results of V. Fock and the
author\, and I. Le.\n\nFor any cluster Poisson variety X\, we consider th
e quantum Langlands modular double of the algebra of regular functions on
X. If the Planck constant h is either real or unitary\, we equip it with a
structure of a *-algebra\, and construct its principal series of represen
tations.\n\nCombining this\, we get principal series representations of th
e quantum Langlands modular double of the algebras of regular functions on
moduli spaces P(G\, S) and Loc(G\,S).\n\nWe discuss applications to repre
sentations theory\, geometry\, and mathematical physics.\n\nIn particular\
, when S has no boundary\, we get a local system of infinite dimensional v
ector spaces over the punctured determinant line bundle on the moduli spac
e M(g\,n). Assigning to a complex structure on S the coinvariants of oscil
latory representations of W-algebras sitting at the punctures of S\, we ge
t another local system on the same spa. We conjecture there exists a natur
al non-degenerate pairing between these local systems\, providing conforma
l blocks for Liouville / Toda theories.\n\nIn Lecture 4 we discuss spectra
l description of non-commutative local systems on S\, providing a non-comm
utative cluster structure of the latter. It is based on our joint work wit
h Maxim Kontsevich.\nhttps://indico.math.cnrs.fr/event/4375/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/4375/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Inviscid Limit and Prandtl System
DTSTART;VALUE=DATE-TIME:20190701T080000Z
DTEND;VALUE=DATE-TIME:20190701T100000Z
DTSTAMP;VALUE=DATE-TIME:20190618T145200Z
UID:indico-event-4689@indico.math.cnrs.fr
DESCRIPTION:Speakers: Nader Masmoudi (Université de New York)\nOne of the
main open problems in the mathematical analysis of fluid flows is the und
erstanding of the inviscid limit in the presence of boundaries. In the cas
e of a fixed bounded domain\, it is an open problem to know whether soluti
ons to the Navier-Stokes system with no slip boundary condition (zero Diri
chlet boundary condition) do converge to a solution to the Euler system wh
en the viscosity goes to zero. The main problem here comes from the fact t
hat we cannot impose a no slip boundary condition for the Euler system. To
recover a zero Dirichlet condition\, Prandtl proposed to introduce a boun
dary layer (a small neighborhood of the boundary) in which viscous effects
are still present. It turns out that the system that governs the flow in
this small neighborhood\, namely the Prandtl system has many mathematical
difficulties. The goal of this course is to discuss some of the recent dev
elopment in the inviscid limit as well as the study of the Prandtl system.
We will also discuss the singularity formation for both the stationary an
d non stationary Prandtl system.\nhttps://indico.math.cnrs.fr/event/4689/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/4689/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quantum Geometry of Moduli Spaces of Local Systems and Representat
ion Theory
DTSTART;VALUE=DATE-TIME:20190701T123000Z
DTEND;VALUE=DATE-TIME:20190701T143000Z
DTSTAMP;VALUE=DATE-TIME:20190618T145200Z
UID:indico-event-4377@indico.math.cnrs.fr
DESCRIPTION:Speakers: Alexander Goncharov (Yale University & IHES)\nLectur
es 1-3 are mostly based on our recent work with Linhui Shen.\n\nGiven a su
rface S with punctures and special points on the boundary considered modul
o isotopy\, and a split semi-simple adjoint group G\, we define and quanti
ze moduli spaces Loc(G\,S) G-local systems on S\, generalising character v
arieties.\n\nTo achieve this\, we introduce a new moduli space P(G\, S) cl
osely related to Loc(G\,S). We prove that it has a cluster Poisson variety
structure\, equivariant under the action of a discrete group\, containing
the mapping class group of S. This generalises results of V. Fock and the
author\, and I. Le.\n\nFor any cluster Poisson variety X\, we consider th
e quantum Langlands modular double of the algebra of regular functions on
X. If the Planck constant h is either real or unitary\, we equip it with a
structure of a *-algebra\, and construct its principal series of represen
tations.\n\nCombining this\, we get principal series representations of th
e quantum Langlands modular double of the algebras of regular functions on
moduli spaces P(G\, S) and Loc(G\,S).\n\nWe discuss applications to repre
sentations theory\, geometry\, and mathematical physics.\n\nIn particular\
, when S has no boundary\, we get a local system of infinite dimensional v
ector spaces over the punctured determinant line bundle on the moduli spac
e M(g\,n). Assigning to a complex structure on S the coinvariants of oscil
latory representations of W-algebras sitting at the punctures of S\, we ge
t another local system on the same spa. We conjecture there exists a natur
al non-degenerate pairing between these local systems\, providing conforma
l blocks for Liouville / Toda theories.\n\nIn Lecture 4 we discuss spectra
l description of non-commutative local systems on S\, providing a non-comm
utative cluster structure of the latter. It is based on our joint work wit
h Maxim Kontsevich.\nhttps://indico.math.cnrs.fr/event/4377/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/4377/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Inviscid Limit and Prandtl System
DTSTART;VALUE=DATE-TIME:20190703T080000Z
DTEND;VALUE=DATE-TIME:20190703T100000Z
DTSTAMP;VALUE=DATE-TIME:20190618T145200Z
UID:indico-event-4690@indico.math.cnrs.fr
DESCRIPTION:Speakers: Nader Masmoudi (Université de New York)\nOne of the
main open problems in the mathematical analysis of fluid flows is the und
erstanding of the inviscid limit in the presence of boundaries. In the cas
e of a fixed bounded domain\, it is an open problem to know whether soluti
ons to the Navier-Stokes system with no slip boundary condition (zero Diri
chlet boundary condition) do converge to a solution to the Euler system wh
en the viscosity goes to zero. The main problem here comes from the fact t
hat we cannot impose a no slip boundary condition for the Euler system. To
recover a zero Dirichlet condition\, Prandtl proposed to introduce a boun
dary layer (a small neighborhood of the boundary) in which viscous effects
are still present. It turns out that the system that governs the flow in
this small neighborhood\, namely the Prandtl system has many mathematical
difficulties. The goal of this course is to discuss some of the recent dev
elopment in the inviscid limit as well as the study of the Prandtl system.
We will also discuss the singularity formation for both the stationary an
d non stationary Prandtl system.\nhttps://indico.math.cnrs.fr/event/4690/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/4690/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quantum Geometry of Moduli Spaces of Local Systems and Representat
ion Theory
DTSTART;VALUE=DATE-TIME:20190708T123000Z
DTEND;VALUE=DATE-TIME:20190708T143000Z
DTSTAMP;VALUE=DATE-TIME:20190618T145200Z
UID:indico-event-4376@indico.math.cnrs.fr
DESCRIPTION:Speakers: Alexander Goncharov (Yale University & IHES)\nLectur
es 1-3 are mostly based on our recent work with Linhui Shen.\n\nGiven a su
rface S with punctures and special points on the boundary considered modul
o isotopy\, and a split semi-simple adjoint group G\, we define and quanti
ze moduli spaces Loc(G\,S) G-local systems on S\, generalising character v
arieties.\n\nTo achieve this\, we introduce a new moduli space P(G\, S) cl
osely related to Loc(G\,S). We prove that it has a cluster Poisson variety
structure\, equivariant under the action of a discrete group\, containing
the mapping class group of S. This generalises results of V. Fock and the
author\, and I. Le.\n\nFor any cluster Poisson variety X\, we consider th
e quantum Langlands modular double of the algebra of regular functions on
X. If the Planck constant h is either real or unitary\, we equip it with a
structure of a *-algebra\, and construct its principal series of represen
tations.\n\nCombining this\, we get principal series representations of th
e quantum Langlands modular double of the algebras of regular functions on
moduli spaces P(G\, S) and Loc(G\,S).\n\nWe discuss applications to repre
sentations theory\, geometry\, and mathematical physics.\n\nIn particular\
, when S has no boundary\, we get a local system of infinite dimensional v
ector spaces over the punctured determinant line bundle on the moduli spac
e M(g\,n). Assigning to a complex structure on S the coinvariants of oscil
latory representations of W-algebras sitting at the punctures of S\, we ge
t another local system on the same spa. We conjecture there exists a natur
al non-degenerate pairing between these local systems\, providing conforma
l blocks for Liouville / Toda theories.\n\nIn Lecture 4 we discuss spectra
l description of non-commutative local systems on S\, providing a non-comm
utative cluster structure of the latter. It is based on our joint work wit
h Maxim Kontsevich.\nhttps://indico.math.cnrs.fr/event/4376/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/4376/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quantum Geometry of Moduli Spaces of Local Systems and Representat
ion Theory
DTSTART;VALUE=DATE-TIME:20190710T123000Z
DTEND;VALUE=DATE-TIME:20190710T143000Z
DTSTAMP;VALUE=DATE-TIME:20190618T145200Z
UID:indico-event-4378@indico.math.cnrs.fr
DESCRIPTION:Speakers: Alexander Goncharov (Yale University & IHES)\nLectur
es 1-3 are mostly based on our recent work with Linhui Shen.\n\nGiven a su
rface S with punctures and special points on the boundary considered modul
o isotopy\, and a split semi-simple adjoint group G\, we define and quanti
ze moduli spaces Loc(G\,S) G-local systems on S\, generalising character v
arieties.\n\nTo achieve this\, we introduce a new moduli space P(G\, S) cl
osely related to Loc(G\,S). We prove that it has a cluster Poisson variety
structure\, equivariant under the action of a discrete group\, containing
the mapping class group of S. This generalises results of V. Fock and the
author\, and I. Le.\n\nFor any cluster Poisson variety X\, we consider th
e quantum Langlands modular double of the algebra of regular functions on
X. If the Planck constant h is either real or unitary\, we equip it with a
structure of a *-algebra\, and construct its principal series of represen
tations.\n\nCombining this\, we get principal series representations of th
e quantum Langlands modular double of the algebras of regular functions on
moduli spaces P(G\, S) and Loc(G\,S).\n\nWe discuss applications to repre
sentations theory\, geometry\, and mathematical physics.\n\nIn particular\
, when S has no boundary\, we get a local system of infinite dimensional v
ector spaces over the punctured determinant line bundle on the moduli spac
e M(g\,n). Assigning to a complex structure on S the coinvariants of oscil
latory representations of W-algebras sitting at the punctures of S\, we ge
t another local system on the same spa. We conjecture there exists a natur
al non-degenerate pairing between these local systems\, providing conforma
l blocks for Liouville / Toda theories.\n\nIn Lecture 4 we discuss spectra
l description of non-commutative local systems on S\, providing a non-comm
utative cluster structure of the latter. It is based on our joint work wit
h Maxim Kontsevich.\nhttps://indico.math.cnrs.fr/event/4378/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/4378/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorentzian Methods in Conformal Field Theory (1/4)
DTSTART;VALUE=DATE-TIME:20191004T080000Z
DTEND;VALUE=DATE-TIME:20191004T100000Z
DTSTAMP;VALUE=DATE-TIME:20190618T145200Z
UID:indico-event-4310@indico.math.cnrs.fr
DESCRIPTION:Speakers: Slava Rychkov (IHES\, ENS)\n\n\nTBA\n\n\nhttps://ind
ico.math.cnrs.fr/event/4310/
LOCATION:Salle Claude Itzykson (IPhT)
URL:https://indico.math.cnrs.fr/event/4310/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorentzian Methods in Conformal Field Theory (2/4)
DTSTART;VALUE=DATE-TIME:20191011T080000Z
DTEND;VALUE=DATE-TIME:20191011T100000Z
DTSTAMP;VALUE=DATE-TIME:20190618T145200Z
UID:indico-event-4311@indico.math.cnrs.fr
DESCRIPTION:Speakers: Slava Rychkov (IHES\, ENS)\n\n\nTBA\n\n\nhttps://ind
ico.math.cnrs.fr/event/4311/
LOCATION:Salle Claude Itzykson (IPhT)
URL:https://indico.math.cnrs.fr/event/4311/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorentzian Methods in Conformal Field Theory (3/4)
DTSTART;VALUE=DATE-TIME:20191018T080000Z
DTEND;VALUE=DATE-TIME:20191018T100000Z
DTSTAMP;VALUE=DATE-TIME:20190618T145200Z
UID:indico-event-4312@indico.math.cnrs.fr
DESCRIPTION:Speakers: Slava Rychkov (IHES\, ENS)\n\n\nTBA\n\n\nhttps://ind
ico.math.cnrs.fr/event/4312/
LOCATION:Salle Claude Itzykson (IPhT)
URL:https://indico.math.cnrs.fr/event/4312/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorentzian Methods in Conformal Field Theory (4/4)
DTSTART;VALUE=DATE-TIME:20191025T080000Z
DTEND;VALUE=DATE-TIME:20191025T100000Z
DTSTAMP;VALUE=DATE-TIME:20190618T145200Z
UID:indico-event-4313@indico.math.cnrs.fr
DESCRIPTION:Speakers: Slava Rychkov (IHES\, ENS)\n\n\nTBA\n\n\nhttps://ind
ico.math.cnrs.fr/event/4313/
LOCATION:Salle Claude Itzykson (IPhT)
URL:https://indico.math.cnrs.fr/event/4313/
END:VEVENT
END:VCALENDAR