BEGIN:VCALENDAR
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CALSCALE:GREGORIAN
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BEGIN:VEVENT
SUMMARY:Todd Kemp (UCSD)
DTSTART:20200508T190000Z
DTEND:20200508T200000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/1
DESCRIPTION:Title: Geometric matrix Brownian motion and the Lima Bean La
w\nby Todd Kemp (UCSD) as part of Integrable Probability\n\n\nAbstract
\nGeometric matrix Brownian motion is the solution (in $N\\times N$ matric
es) to the stochastic differential equation $dG_t = G_t dZ_t$\, $G_0 = I$\
, where $Z_t$ is a Ginibre Brownian motion (all independent complex Browni
an motion entries). It can also be described as the standard Brownian moti
on on the Lie group $\\mathrm{GL}(N\,\\mathbb{C})$. For $N>2$\, with proba
bility $1$ it is not a normal matrix for any $t>0$. Over the last 5 years\
, we have made progress in understanding its asymptotic moments and fluctu
ations\, but the non-normality (and lack of explicit symmetry) has made un
derstanding its large-$N$ limit empirical eigenvalue distribution quite ch
allenging.\n\nThe tools around the circular law are now rich and provide a
(log) potential course of action to understand the eigenvalues. There are
two sides to this problem in general\, both quite difficult: proving that
the empirical law of eigenvalues converges (which amounts to strong tight
ness conditions on singular values)\, and computing what it converges {\\e
m to}. In the case of the geometric matrix Brownian motion\, the question
of convergence is still a work in progress\; but in recent joint work with
Bruce Driver and Brian Hall\, we have explicitly calculated the limit emp
irical eigenvalue distribution. It has an analytic density with a nice pol
ar decomposition\, supported on a region that resembles a lima bean for sm
all $t>0$\, then folds over and becomes a topological annulus when $t>4$.\
n\nOur methods blend stochastic analysis\, complex analysis\, and PDE\, an
d approach the log potential in a new way that we hope will be useful in a
wider context.\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yun Li (University of Wisconsin\, Madison)
DTSTART:20200522T150000Z
DTEND:20200522T160000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/2
DESCRIPTION:Title: Pre-seminar for Benedek Valko's talk on the stochasti
c zeta function\nby Yun Li (University of Wisconsin\, Madison) as part
of Integrable Probability\n\n\nAbstract\nThis pre-seminar will provide re
levant background to Benedek Valko's seminar later in the day.\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benedek Valko (University of Wisconsin\, Madison)
DTSTART:20200522T180000Z
DTEND:20200522T190000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/3
DESCRIPTION:Title: The stochastic zeta function\nby Benedek Valko (U
niversity of Wisconsin\, Madison) as part of Integrable Probability\n\n\nA
bstract\nThe finite circular beta-ensembles and their point process scalin
g limit can be represented as the spectra of certain random differential o
perators. These operators can be realized on a single probability space so
that the point process scaling limit is a consequence of an operator leve
l limit. The construction allows the derivation of the scaling limit of th
e normalized characteristic polynomials of the finite models to a random a
nalytic function\, which we call the stochastic zeta function. I will revi
ew these representations and constructions\, and present a couple of appli
cations. Joint with B. Virág (Toronto).\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Bufetov (Bonn)
DTSTART:20200605T160000Z
DTEND:20200605T170000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/4
DESCRIPTION:Title: Interacting particle systems and random walks on Heck
e algebras\nby Alexey Bufetov (Bonn) as part of Integrable Probability
\n\n\nAbstract\nMulti-species versions of several interacting particle sys
tems\, including ASEP\, q-TAZRP\, and k-exclusion processes\, can be inter
preted as random walks on Hecke algebras. In the talk I will discuss this
connection and its probabilistic applications.\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Kuan (Texas A&M)
DTSTART:20200605T171500Z
DTEND:20200605T181500Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/5
DESCRIPTION:Title: Algebraic symmetries of multi--species models\nby
Jeff Kuan (Texas A&M) as part of Integrable Probability\n\n\nAbstract\nWe
review some recent results on multi--species interacting particle systems
and vertex models. In particular\, we show how the quantum group and Coxe
ter group symmetries lead to duality\, color-position symmetry\, contour i
ntegral formulas\, and hydrodynamics.\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaetan Borot (Bonn)
DTSTART:20200619T150000Z
DTEND:20200619T160000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/6
DESCRIPTION:Title: Introduction to geometric recursion\nby Gaetan Bo
rot (Bonn) as part of Integrable Probability\n\n\nAbstract\nThe geometric
recursion is a general framework to make natural constructions attached to
surfaces S of any topology\, by using the idea of cutting the surface int
o elementary pieces -- I will explain what "natural" means. Examples of na
tural constructions are certain measures on the space Teich(S) of conforma
l classes of metrics on surfaces\, which can be used to talk about ensembl
es of random surfaces\, and statistical properties of simple geodesics on
them\, and can be approached by recursion on the topology generalizing Mir
zakhani's recursion. I will hint at other "natural constructions" that may
fit in this framework\, such as spectral statistics and measures from qua
ntum gravity.\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomohiro Sasamoto (Tokyo Institute of Technology)
DTSTART:20200703T130000Z
DTEND:20200703T140000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/7
DESCRIPTION:Title: Spin current statistics for the quantum 1D XX spin ch
ain and the Bessel kernel\nby Tomohiro Sasamoto (Tokyo Institute of Te
chnology) as part of Integrable Probability\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Quastel (University of Toronto)
DTSTART:20200703T170000Z
DTEND:20200703T190000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/8
DESCRIPTION:Title: From TASEP to the KPZ fixed point and KP\nby Jere
my Quastel (University of Toronto) as part of Integrable Probability\n\nAb
stract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alisa Knizel (Columbia University)
DTSTART:20200710T140000Z
DTEND:20200710T150000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/9
DESCRIPTION:Title: Invariant measure for the open KPZ equation\nby A
lisa Knizel (Columbia University) as part of Integrable Probability\n\n\nA
bstract\nI will talk about a construction of an invariant measure for the
open KPZ equation on a bounded interval with Neumann boundary conditions.
The approach relies on two main ingredients. The first is that open ASEP c
onverges to open KPZ under weakly asymmetric scaling around the triple poi
nt of the phase diagram. The second is that the invariant measure of open
ASEP can be computed exactly via Askey-Wilson processes\, a variant of the
matrix product ansatz. This construction is a joint work with Ivan Corwin
.\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeni Dimitrov (Columbia University)
DTSTART:20200710T150000Z
DTEND:20200710T160000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/10
DESCRIPTION:Title: Two-point convergence of the stochastic six-vertex m
odel to the Airy process\nby Evgeni Dimitrov (Columbia University) as
part of Integrable Probability\n\n\nAbstract\nWe consider the stochastic s
ix-vertex model in the quadrant started with step initial data. We will sh
ow that\, under suitable scaling\, the two-point distribution of the heigh
t function converges to the two-point distribution of the Airy process.\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/10
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Hammond (UC Berkeley)
DTSTART:20200717T170000Z
DTEND:20200717T180000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/11
DESCRIPTION:by Alan Hammond (UC Berkeley) as part of Integrable Probabilit
y\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/11
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yan Fyodorov (King's College London)
DTSTART:20200724T140000Z
DTEND:20200724T150000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/12
DESCRIPTION:Title: On eigenvector statistics in non-normal random matri
ces\nby Yan Fyodorov (King's College London) as part of Integrable Pro
bability\n\n\nAbstract\nI will discuss some results\, both old and more re
cent\, on 'non-orthogonality overlap matrix' between left and right eigenv
ectors of non-normal random matrices. Motivations range from understanding
eigenvalue dynamics under matrix perturbations to relevance for random ma
trix models describing chaotic wave scattering.\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/12
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinho Baik (University of Michigan)
DTSTART:20200724T170000Z
DTEND:20200724T180000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/13
DESCRIPTION:Title: Relaxation time limit of periodic TASEP\nby Jinh
o Baik (University of Michigan) as part of Integrable Probability\n\n\nAbs
tract\nThe marginals of a spatially periodic TASEP converge to non-trivial
limits when both the period and the time tend to infinity in a critical w
ay. To compare the periodic case and the infinite line KPZ fixed point\, w
e will focus primarily on the one-point distribution for the step initial
condition and show how the formula changes from the GUE Tracy-Widom distri
bution of the infinite line KPZ fixed point. We will discuss both the Fred
holm determinant formula and the differential equation formula. The later
formula will tell us connections to integrable differential equations.\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/13
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vadim Gorin (MIT and University of Wisconsin\, Madison)
DTSTART:20200807T170000Z
DTEND:20200807T190000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/14
DESCRIPTION:by Vadim Gorin (MIT and University of Wisconsin\, Madison) as
part of Integrable Probability\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/14
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Petrov (University of Virginia)
DTSTART:20200814T170000Z
DTEND:20200814T180000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/15
DESCRIPTION:by Leonid Petrov (University of Virginia) as part of Integrabl
e Probability\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/15
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Li-Cheng Tsai (Rutgers University)
DTSTART:20200821T170000Z
DTEND:20200821T180000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/16
DESCRIPTION:Title: Moments and tails of stochastic PDEs\nby Li-Chen
g Tsai (Rutgers University) as part of Integrable Probability\n\n\nAbstrac
t\nThis talk focuses on two aspects of stochastic PDEs: moments and large
deviations. For the Stochastic Heat Equation (with multiplicative noise) a
nd the Kardar--Parisi--Zhang equation\, I will explain how these two aspec
ts are interconnected\, and how to obtain precise descriptions of these tw
o aspects.\n\nThe talk will cover joint work with Sayan Das and joint work
with Yu Gu and Jeremy Quastel.\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/16
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amol Aggarwal (CMI and Columbia University)
DTSTART:20200821T180000Z
DTEND:20200821T190000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/17
DESCRIPTION:Title: Limit Shapes and Local Statistics for the Stochastic
Six-Vertex Model\nby Amol Aggarwal (CMI and Columbia University) as p
art of Integrable Probability\n\n\nAbstract\nIn this talk we outline how l
imit shapes for the stochastic six-vertex model under arbitrary initial da
ta can be proven using hydrodynamical limit methods from the context of in
teracting particle systems. This proceeds by first establishing the limit
shape result for specific (double-sided Bernoulli) initial data\, which is
often exactly solvable\, and then by extending it to general initial prof
iles. If time permits\, we will also discuss convergence of local statisti
cs to the translation-invariant\, extremal Gibbs measure of the appropriat
e slope.\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/17
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jon Warren (University of Warwick)
DTSTART:20200828T140000Z
DTEND:20200828T150000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/18
DESCRIPTION:Title: Reflecting Brownian motions and point-to-line last
passage percolation\nby Jon Warren (University of Warwick) as part of
Integrable Probability\n\n\nAbstract\nThe all-time supremum of a Brownian
motion with negative drift is exponentially distributed. A generalization
of this classical fact to random matrices is the statement that the supre
mum of the largest eigenvalue of a Hermitian Brownian motion with drift is
equal in distribution to a point-to-line last passage time through a fiel
d of exponentially distributed random variables. The same distribution a
rises as a marginal of the stationary distribution of a system of reflecti
ng Brownian motions with a wall. I will discuss these results and their
finite temperature analogues which link exponential functionals of Browni
an motion to the log gamma polymer.\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/18
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikos Zygouras (University of Warwick)
DTSTART:20200828T150000Z
DTEND:20200828T160000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/19
DESCRIPTION:Title: Variants of geometric RSK and polymers\nby Nikos
Zygouras (University of Warwick) as part of Integrable Probability\n\n\nA
bstract\nWe will review the use of geometric Robinson-Schensted-Knuth corr
espondence and how this can be applied to obtain laws of polymer models. W
e will focus\, in particular\, on more recent work with E. Bisi and N. O'C
onnell where we constructed the geometric Burge correspondence and applied
it to obtain the law of replicas of partition functions.\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/19
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Petrov (University of Virginia)
DTSTART:20201009T183000Z
DTEND:20201009T200000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/20
DESCRIPTION:Title: Random polymers and symmetric functions\nby Leon
id Petrov (University of Virginia) as part of Integrable Probability\n\n\n
Abstract\nI will survey integrable random polymers (based on gamma / inver
se gamma or beta distributed weights)\, and explain their connection to sy
mmetric functions (respectively\, gl_n Whittaker and new spin Whittaker fu
nctions). The work on spin Whittaker functions is joint with Matteo Muccic
oni.\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/20
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maurice Duits (KTH)
DTSTART:20201023T183000Z
DTEND:20201023T200000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/21
DESCRIPTION:Title: CLTs for biorthogonal ensembles: Beyond the Strong S
zegö Limit Theorem\nby Maurice Duits (KTH) as part of Integrable Prob
ability\n\n\nAbstract\nThe Strong Szegö Limit Theorem for Toeplitz determ
inants implies a CLT for linear statistics for eigenvalues of a CUE matrix
. The first part of the talk will be an overview of results on various ext
ensions of the Strong Szegö Limit theorem to determinants of truncated ex
ponentials of banded matrices\, providing CLTs for more general classes of
determinantal point processes including orthogonal polynomial ensembles o
n the real line and unit circle. A time-dependent analogue can be used tot
establish Gaussian Free Field fluctuations in certain non-colliding proce
ss and random tilings of planar domains. The second part of the talk will
focus on discussing a recent joint work with Fahs and Kozhan on Multiple O
rthogonal Polynomials Ensembles. Such models include Gaussian Unitary Ense
mbles with external source\, complex Wishart matrices\, two matrix models
and certain specialization of the Schur process. A new feature in those mo
dels is that there is no canonical choice for the recurrence matrix.\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/21
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kurt Johansson (KTH)
DTSTART:20201112T193000Z
DTEND:20201112T210000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/22
DESCRIPTION:Title: Multivariate normal approximation for traces of rand
om unitary matrices\nby Kurt Johansson (KTH) as part of Integrable Pro
bability\n\n\nAbstract\nConsider an n x n random unitary matrix U taken wi
th respect to normalized Haar measure. It is a well known consequence of t
he strong Szego limit theorem that the traces of powers of U converge to i
ndependent complex normal random variables as n grows. I will discuss a re
cent result where we obtain a super-exponential rate of convergence in tot
al variation distance between the traces of the first m powers of an n ×
n random unitary matrices and a 2m-dimensional Gaussian random vector. Thi
s generalizes previous results in the scalar case\, which answered a conje
cture by Diaconis\, to the multivariate setting. We are especially interes
ted in the regime where m grows with n. The problem on how the rate of con
vergence changes as m grows with n was raised recently by Sarnak. The resu
lt we obtain gives the dependence on the dimensions m and n in the estimat
e with explicit constants for m almost up to the square root of n. This is
joint work with Gaultier Lambert.\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/22
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiaoyang Huang (NYU)
DTSTART:20201211T193000Z
DTEND:20201211T210000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/23
DESCRIPTION:Title: Height Fluctuations of Random Lozenge Tilings Throug
h Nonintersecting Random Walks\nby Jiaoyang Huang (NYU) as part of Int
egrable Probability\n\n\nAbstract\nIn this talk\, we will discuss global f
luctuations of random lozenge tilings of polygonal domains. We study their
height functions from a dynamical pointview\, by identifying lozenge tili
ngs with nonintersecting Bernoulli random walks. For a large class of poly
gons which have exactly one horizontal upper boundary edge\, we show that
these random height functions converge to a Gaussian Free Field as predict
ed by Kenyon and Okounkov.\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/23
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sasha Sodin (QMUL)
DTSTART:20201130T200000Z
DTEND:20201130T213000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/24
DESCRIPTION:Title: A random operator constructed from the representatio
ns of the symmetric group\nby Sasha Sodin (QMUL) as part of Integrable
Probability\n\n\nAbstract\nWe shall discuss the construction of an amusin
g random operator acting on certain representations of the infinite symmet
ric group and sharing some features with the Anderson model. Particularly\
, we show that the spectrum of the operator exhibits so-called quantum Lif
shitz tails\, characteristic of d-dimensional random operators. The operat
or is also closely related to a randomised version of the fifteen puzzle o
n an infinite board\; this connection plays a central role in the proof of
the main result. Based on joint work with Ohad N. Feldheim.\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/24
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shirshendu Ganguly (Berkeley)
DTSTART:20201123T193000Z
DTEND:20201123T210000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/25
DESCRIPTION:Title: Stability and chaos in dynamical last passage percol
ation\nby Shirshendu Ganguly (Berkeley) as part of Integrable Probabil
ity\n\n\nAbstract\nMany complex disordered systems in statistical mechanic
s are characterized by intricate energy landscapes. The ground state\, the
configuration with lowest energy\, lies at the base of the deepest valley
. In important examples\, such as Gaussian polymers and spin glass models\
, the landscape has many valleys and the abundance of near-ground states (
at the base of valleys) indicates the phenomenon of chaos\, under which th
e ground state alters profoundly when the disorder of the model is slightl
y perturbed.\n\nIn this talk\, we will discuss a recent work computing the
critical exponent that governs the onset of chaos in a dynamic manifestat
ion of a canonical model in the Kardar-Parisi-Zhang [KPZ] universality cla
ss\, Brownian last passage percolation [LPP]. In this model in its static
form\, semi-discrete polymers advance through Brownian noise\, their energ
y given by the integral of the white noise encountered along their journey
. A ground state is a geodesic\, of extremal energy given its endpoints.\n
\nWe will show that when Brownian LPP is perturbed by evolving the disorde
r under an Ornstein-Uhlenbeck flow\, for polymers of length n\, a sharp ph
ase transition marking the onset of chaos is witnessed at the critical tim
e $n^{-1/3}$\, by showing that the overlap between the geodesics at times
zero and $t > 0$ that travel a given distance of order is of order $n$ whe
n $t \\ll n^{-1/3}$\; and of a smaller order when $t \\gg n^{-1/3}$. We ex
pect this exponent to be universal across a wide range of interface models
. The proof relies on Chatterjee's harmonic analytic theory of equivalence
of superconcentration and chaos in Gaussian spaces and a refined understa
nding of the static landscape geometry of Brownian LPP.\n\nThe talk is bas
ed on joint work with Alan Hammond (https://arxiv.org/abs/2010.05837 and t
he companion paper https://arxiv.org/abs/2010.05836).\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/25
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sayan Das (Columbia)
DTSTART:20210226T190000Z
DTEND:20210226T200000Z
DTSTAMP:20260404T094319Z
UID:IntegrableProbability/26
DESCRIPTION:Title: Fractal Properties of the KPZ temporal Process\n
by Sayan Das (Columbia) as part of Integrable Probability\n\n\nAbstract\nI
n this talk\, we study the macroscopic fractal properties of the Cole-Hopf
solution of the Kardar-Parisi-Zhang (KPZ) equation. We show that under th
e exponential transformation of the time variable\, the peaks of the KPZ h
eight function mutate from being monofractal to multifractal. Our proof re
lies on three main ingredients: i) multipoint composition law of the KPZ e
quation ii) Gibbsian line ensemble techniques iii) short time tail probabi
lities of KPZ height function. Joint work with Promit Ghosal.\n
LOCATION:https://stable.researchseminars.org/talk/IntegrableProbability/26
/
END:VEVENT
END:VCALENDAR