BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Loïc Poulain d'Andecy (Laboratoire de Mathématiques de Reims)
DTSTART;VALUE=DATE-TIME:20200505T193000Z
DTEND;VALUE=DATE-TIME:20200505T203000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043748Z
UID:PhysiqueMathematique/1
DESCRIPTION:Title: Fused Hecke algebras and centralisers of tensor represe
ntations of quantum sl(N)\nby Loïc Poulain d'Andecy (Laboratoire de Math
ématiques de Reims) as part of CRM-Séminaire Physique Mathématique\n\n\
nAbstract\n(Joint work with Nicolas Crampé) The goal of the talk is to pr
esent diagrammatic algebras and their deformations generalising the symmet
ric group and the Hecke algebra. We call these algebras\, respectively\,
the algebra of fused permutations and the fused Hecke algebra. One motiva
tion for considering these algebras is to write explicit Baxterisation for
mulas providing\, on an abstract/algebraic level\, solutions of the Yang-B
axter equation. These formulas generalise the Baxterisation formula of th
e Hecke algebra related to the vector representation V of U_q(sl_N) (the s
pin 1/2 representation if N=2). The new Baxterisation formulas control th
e solutions of YB equation on any symmetric power of the vector representa
tion of U_q(sl_N) (the higher spin representations if N=2). Besides\, the
meaning of these algebras in the context of the Schur-Weyl duality will b
e explained: they provide a description of the centralisers of tensor prod
ucts of symmetric powers of V. The representation theory of these new alg
ebras will be explained and\, from this\, the centralisers can be construc
ted as quotients\, both with a representation-theoretic and an algebraic/d
iagrammatic description. These results can be seen as analogues for highe
r spins of a construction of the Temperley-Lieb algebras from the Hecke al
gebras.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hendrik de Bie (Universiteit Gent)
DTSTART;VALUE=DATE-TIME:20200512T193000Z
DTEND;VALUE=DATE-TIME:20200512T203000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043748Z
UID:PhysiqueMathematique/2
DESCRIPTION:Title: The Dunkl intertwining operator\nby Hendrik de Bie (Uni
versiteit Gent) as part of CRM-Séminaire Physique Mathématique\n\n\nAbst
ract\nThere are two crucial operators in the theory of Dunkl operators. Th
e first is the Dunkl transform\, which generalizes the Fourier transform.
The second is the intertwining operator\, which maps ordinary partial deri
vatives to Dunkl operators. Although some abstract statements are known ab
out the intertwining operator\, the explicit formula for classes of reflec
tion groups is generally not known. In recent work Yuan Xu proposed a form
ula in the case of dihedral groups and a restricted class of functions. We
extend his formula to all functions and give a general strategy on how to
obtain similar formulas for other reflections groups. This is based on jo
int work with Pan Lian\, available under arXiv:2002.09065.\n\nEn ligne/Web
- Svp remplir ce formulaire/Please fill in this form: https://forms.gle/S
1NcNQ8BxkzfAXcj9\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Maloney (McGill University)
DTSTART;VALUE=DATE-TIME:20200519T193000Z
DTEND;VALUE=DATE-TIME:20200519T203000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043748Z
UID:PhysiqueMathematique/3
DESCRIPTION:Title: Progress on Pure Gravity in Three Dimensions\nby Alex M
aloney (McGill University) as part of CRM-Séminaire Physique Mathématiqu
e\n\n\nAbstract\nI will describe the challenges and progress in constructi
ng a theory of "pure gravity" in three dimensions\, i.e. a theory which c
ontains only metric degrees of freedom and nothing else. Conformal bootst
rap techniques provide strong constraints on the theory\, and indicate tha
t the spectrum of the theory must contain new states in addition to gravit
ons and black holes. I will provide an interpretation for these new stat
es.\n\nEn ligne/Web - Svp remplir ce formulaire/Please fill in this form:
https://forms.gle/S1NcNQ8BxkzfAXcj9\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexis Morin-Duchesne (Université Catholique de Louvain-la-Neuve)
DTSTART;VALUE=DATE-TIME:20200526T193000Z
DTEND;VALUE=DATE-TIME:20200526T203000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043748Z
UID:PhysiqueMathematique/4
DESCRIPTION:Title: Boundary emptiness formation probabilities in the six-v
ertex model at $\\Delta=- 1/2$\nby Alexis Morin-Duchesne (Université Cath
olique de Louvain-la-Neuve) as part of CRM-Séminaire Physique Mathématiq
ue\n\n\nAbstract\nThe connection between statistical mechanics and the com
binatorics of alternating sign matrices is known since the work of Razumov
and Stroganov on the spin-1/2 XXZ chain. One important example of this co
mbinatorial relation occurs in the study of the emptiness formation probab
ility $EFP_{N\,m}$. This observable is defined as the sum of the squares o
f the ground state components for the chain of length $N$\, restricted to
components where $m$ consecutive spins are aligned. At the combinatorial p
oint $\\Delta = - 1/2$\, it takes the form of a simple product of integers
. This was proven in 2012 by L. Cantini\, who also found a combinatorial i
nterpretation for these probabilities in terms of plane partitions.\nIn jo
int work with C. Hagendorf and L. Cantini\, we define a new family of over
laps $C_{N\,m}$ for the spin-1/2 XXZ chain. It is equal to the linear sum
of the groundstate components that have $m$ consecutive aligned spins. For
reasons that will be discussed\, we refer to the ratio $C_{N\,m}/C_{N\,0}
$ as the {\\it boundary emptiness formation probability}. We compute $C_{N
\,m}$ at the combinatorial point as a simple product of integers.\n\nEn li
gne/Web - Svp remplir ce formulaire/Please fill in this form: https://form
s.gle/S1NcNQ8BxkzfAXcj9\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joris Van der Jeugt (Universiteit Gent)
DTSTART;VALUE=DATE-TIME:20200602T193000Z
DTEND;VALUE=DATE-TIME:20200602T203000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043748Z
UID:PhysiqueMathematique/5
DESCRIPTION:Title: Partition functions for paraboson and parafermion syste
ms\nby Joris Van der Jeugt (Universiteit Gent) as part of CRM-Séminaire P
hysique Mathématique\n\n\nAbstract\nParabosons and parafermions\, algebra
ically characterized by triple relations rather than just (anti)-commutati
on relations\, have been around for more than 60 years. Over the recent y
ears\, new mathematical results have been obtained for their representatio
ns\, in particular character formulae. In the present talk\, we give a sh
ort review of the algebraic structures behind parabosons and parafermions\
, and of their representations. We show how the new expressions for chara
cters lead to proper forms of grand partition functions for systems of par
abosons and parafermions. These forms of the partition function allow the
computation of statistical and thermodynamic functions for such systems.
We discuss some examples\, such as the average number of particles on an
orbital\, and the average number of particles in the system.\n\nEn ligne/W
eb - Svp remplir ce formulaire/Please fill in this form: https://forms.gle
/S1NcNQ8BxkzfAXcj9\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Brandenberger (McGill University)
DTSTART;VALUE=DATE-TIME:20200609T193000Z
DTEND;VALUE=DATE-TIME:20200609T203000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043748Z
UID:PhysiqueMathematique/6
DESCRIPTION:Title: S-brane cosmology\nby Robert Brandenberger (McGill Univ
ersity) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract\nTh
e Hawking-Penrose singularity theorems are usually used to argue that ther
e was a "Big Bang" singularity at the beginning of time. I will show that
by adding an "S-brane"\, a distributional source\, to the matter action\,
one can obtain a non-singular bouncing cosmology which obviates the need
for a period of cosmological inflation.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Théo Pinet (Université de Montréal)
DTSTART;VALUE=DATE-TIME:20200616T193000Z
DTEND;VALUE=DATE-TIME:20200616T203000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043748Z
UID:PhysiqueMathematique/7
DESCRIPTION:Title: The structure of the representations of the affine Temp
erley-Lieb algebras on the periodic XXZ chain\nby Théo Pinet (Université
de Montréal) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstr
act\nThe affine Temperley-Lieb algebras aTLN(β) are a family of infinite
dimensional algebras generalizing the well-known Temperley-Lieb algebras T
LN(β). They play\, for the periodic XXZ chain\, the role played by the or
iginal Temperley-Lieb algebra for the open XXZ chain. Their representation
theory is much richer than that of the original TL family and admits a lo
t of similiraties with the representation theory of the Virasoro algebra V
ir. In particular\, we will show in this talk that there exists aTLN(β)-m
odules (called critical) whose structure is akin that of the so-called Fei
gin-Fuchs Vir-modules. To do this\, we will highlight the link between the
se critical modules and other canonical representations of aTLN(β) (the s
tandard modules) while building up on the well-known quantum Schur-Weyl du
ality between TLN(β) and Uqsl2.\n\nL'exposé sera donné en français ave
c des diapositives en anglais - The talk be given in French with slides wr
itten in English\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincent Chalifour (Université de Montréal)
DTSTART;VALUE=DATE-TIME:20200908T193000Z
DTEND;VALUE=DATE-TIME:20200908T203000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043748Z
UID:PhysiqueMathematique/8
DESCRIPTION:Title: General solution of the exceptional Hermite differentia
l equation and its minimal surface representation\nby Vincent Chalifour (U
niversité de Montréal) as part of CRM-Séminaire Physique Mathématique\
n\n\nAbstract\nThe main aim of this presentation is the study of the gener
al solution of the exceptional Hermite differential equation with fixed pa
rtition and the construction of minimal surfaces associated with this solu
tion. We derive a linear second-order ordinary differential equation assoc
iated with a specific family of exceptional polynomials of codimension two
. We show that these polynomials can be expressed in terms of classical He
rmite polynomials. We find the general analytic solution of the exceptiona
l Hermite differential equation which has no gap in its spectrum. We show
that the spectrum is complemented by non-polynomial solutions. We present
an implementation of the obtained results for the surfaces expressed in te
rms of the general solution making use of the classical Enneper-Weierstras
s formula for the immersion in the Euclidean space $\\mathbb{E}^3$\, leadi
ng to minimal surfaces. Three-dimensional displays of these surfaces are p
resented.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Éric Dupuis (Université de Montréal)
DTSTART;VALUE=DATE-TIME:20200915T193000Z
DTEND;VALUE=DATE-TIME:20200915T203000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043748Z
UID:PhysiqueMathematique/9
DESCRIPTION:Title: Monopole operators in gauged Gross-Neveu models\nby Ér
ic Dupuis (Université de Montréal) as part of CRM-Séminaire Physique Ma
thématique\n\n\nAbstract\nCompact quantum electrodynamics in 2+1 dimensio
ns with massless fermions (QED3) describes the quantum spin liquid phase i
n certain quantum magnets. This model includes monopoles whose proliferat
ion may be prevented by the massless fermions. This screening effect is h
owever lost if a fermion mass is generated\, which leads to confinement.
Such confinement-deconfinement transitions are found in QED3-Gross-Neveu (
QED3-GN) models where the GN interaction induces the mass. Monopole opera
tors are studied at the critical point of these theories. Using the state
-operator correspondence\, we obtain the scaling dimension of monopole ope
rators at leading order in 1/N where 2N is the number of fermion flavors.
Two universality classes with distinct flavor symmetries are considered.
For a SU(2) x SU(N) symmetry\, a hierarchy is shown by constraining the m
agnetic spin of monopoles and comparing the scaling dimensions in the vari
ous spin sectors. The representation of monopoles reflects this hierarchy
and a degeneracy lifting relative to the QED3 case. For a SU(2N) symmetr
y\, the monopole scaling dimension is used to test a field theory duality.
\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Zelaya (Université de Montréal)
DTSTART;VALUE=DATE-TIME:20200922T193000Z
DTEND;VALUE=DATE-TIME:20200922T203000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043748Z
UID:PhysiqueMathematique/10
DESCRIPTION:Title: Fourth Painlevé and Ermakov equations: quantum invaria
nts and new exactly-solvable time-dependent Hamiltonians\nby Kevin Zelaya
(Université de Montréal) as part of CRM-Séminaire Physique Mathématiqu
e\n\n\nAbstract\nIn this talk\, we discuss a new realization of exactly-so
lvable time-dependent Hamiltonians based on the solutions of the fourth Pa
inlevé and the Ermakov equations. The latter is achieved by introducing a
shape-invariant condition between an unknown quantum invariant and a set
of third-order intertwining operators with time-dependent coefficients. Th
e new quantum invariant is constructed by adding a deformation term to the
well-known parametric oscillator invariant. Such a deformation depends ex
plicitly on time through the solutions of the Ermakov equation\, which ens
ures the regularity of the new time-dependent potential of the Hamiltonian
at each time. On the other hand\, with the aid of the proper reparametriz
ation\, the fourth Painlevé equation appears\, the parameters of which di
ctate the spectral behavior of the quantum invariant. In particular\, the
eigenfunctions of the third-order ladder operators lead to several sequenc
es of solutions to the Schroedinger equation\, determined in terms of the
solutions of a Riccati equation\, Okamoto polynomials\, or nonlinear bound
states of the derivative nonlinear Schroedinger equation. Remarkably\, it
is noticed that the solutions in terms of the nonlinear bound states lead
to a quantum invariant with equidistant eigenvalues\, which contains both
an (N+1)-dimensional and an infinite sequence of eigenfunctions. The resu
lting family of time-dependent Hamiltonians is such that\, to the authors'
knowledge\, have been unnoticed in the literature of nonstationary system
s.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steven Rayan (University of Saskatchevan)
DTSTART;VALUE=DATE-TIME:20200929T193000Z
DTEND;VALUE=DATE-TIME:20200929T203000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043748Z
UID:PhysiqueMathematique/11
DESCRIPTION:Title: The geometry and physics of Hitchin systems\nby Steven
Rayan (University of Saskatchevan) as part of CRM-Séminaire Physique Math
ématique\n\n\nAbstract\nThe moduli space of stable Higgs bundles on a Rie
mann surface\, known as the Hitchin system\, arises as a space of gauge-eq
uivalent solutions to dimensionally-reduced self-dual Yang-Mills equations
. This moduli space turns out to be the phase space for a non-trivial com
pletely integrable Hamiltonian system\, is a noncompact Calabi-Yau manifol
d\, and has a mirror symmetry that is intertwined with Langlands duality.
In this talk\, I will review a number of geometric features of the Hitchi
n system that have been discovered over the past 30 years. I will conclud
e by speculating on connections between Higgs bundles and condensed-matter
physics.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuela Girotti (Mila\, Université de Montréal)
DTSTART;VALUE=DATE-TIME:20201006T193000Z
DTEND;VALUE=DATE-TIME:20201006T203000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043748Z
UID:PhysiqueMathematique/12
DESCRIPTION:Title: Fredholm Determinant Solutions of the Painlevé II Hier
archy and Gap Probabilities of Determinantal Point Processes\nby Manuela G
irotti (Mila\, Université de Montréal) as part of CRM-Séminaire Physiqu
e Mathématique\n\n\nAbstract\nWe study Fredholm determinants of a class o
f integral operators\, whose kernels can be expressed as double contour in
tegrals of a special type. Such Fredholm determinants appear in various ra
ndom matrix and statistical physics models. We show that the logarithmic d
erivatives of the Fredholm determinants are directly related to solutions
of the Painlevé II hierarchy. This confirms and generalizes a recent conj
ecture by Le Doussal\, Majumdar\, and Schehr (2018). In addition\, we obta
in asymptotics at infinity for the Painlevé transcendents and large gap a
symptotics for the corresponding point processes. This is a joint work wit
h Mattia Cafasso (Univ. Angers) and Tom Claeys (UC Louvain).\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Harnad (Concordia University and Centre des recherches mathé
matiques)
DTSTART;VALUE=DATE-TIME:20201013T193000Z
DTEND;VALUE=DATE-TIME:20201013T203000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043748Z
UID:PhysiqueMathematique/13
DESCRIPTION:Title: Fermionic approach to bilinear expansions of KP correla
tors in terms of BKP correlators\nby John Harnad (Concordia University and
Centre des recherches mathématiques) as part of CRM-Séminaire Physique
Mathématique\n\n\nAbstract\nThis talk will present a synthesis and genera
lization of two results relating determinants and Pfaffians of minors of a
skew symmetric matrix\, with applications to solutions of the KP and DKP
integrable hierarchies. The first is an algebraic identity expressing the
determinant of any minor of a skew matrix as a sum over products of Pfaff
ians of its principal minors\; the second an expression for Schur function
s as bilinear sums over Schur $Q$-functions. A general bilinear identity\
, of which these two results are special cases\, expresses determinantal d
erivative correlators of $\\tau$-functions of the KP hierarchy as sums ove
r products of pairs of Pfaffian derivative correlators for the BKP $\\tau$
function.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrian Escobar (Universidad Autonoma Metropolitana-Iztapalapa)
DTSTART;VALUE=DATE-TIME:20201117T203000Z
DTEND;VALUE=DATE-TIME:20201117T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043748Z
UID:PhysiqueMathematique/14
DESCRIPTION:Title: New infinite families of Nth-order superintegrable syst
ems\nby Adrian Escobar (Universidad Autonoma Metropolitana-Iztapalapa) as
part of CRM-Séminaire Physique Mathématique\n\n\nAbstract\nIn this talk\
, a general description of quantum superintegrable systems in a two-dimens
ional Euclidean space is presented. We consider Hamiltonian systems allowi
ng separation of variables in cartesian coordinates for which one polynomi
al integral (symmetry) of second order in momentum variables and one more
of Nth-order occur. The main properties of doubly exotic superintegrable p
otentials\, i.e. potentials $V(x\, y) = V_1(x) + V_2(y)$ where neither $V_
1(x)$ nor $V_2(y)$ satisfy any linear ordinary differential equation\, are
discussed. In particular\, we present two new infinite families of $N$th
order superintegrable systems with the property that $V_1(x)$ and $V_2(y)$
are given by the solution of a nonlinear ODE that passes the Painlev\\'e
test. We conjecture that these potentials will always actually have the Pa
inlev\\'e property. In the classical case the latter property disappears.\
n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Marquette (University of Queensland)
DTSTART;VALUE=DATE-TIME:20201103T203000Z
DTEND;VALUE=DATE-TIME:20201103T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043748Z
UID:PhysiqueMathematique/15
DESCRIPTION:Title: Embedding of Racah algebra and superintegrable systems\
nby Ian Marquette (University of Queensland) as part of CRM-Séminaire Phy
sique Mathématique\n\n\nAbstract\nThe rank-$1$ Racah algebra $R(3)$ plays
a pivotal role in the theory of superintegrable systems. It appears as t
he symmetry algebra of the $3$-parameter system on the $2$-sphere from whi
ch all second-order conformally flat superintegrable models in $2$D can be
obtained by means of suitable limits and contractions. A higher rank gene
ralization of $R(3)$\, the so-called rank $n-2$ Racah algebra $R(n)$\, has
been considered recently and showed to be the symmetry algebra of the gen
eral superintegrable model on the $(n-1)$-sphere. I will discuss how such
an algebraic structure naturally arises as embedded inside a larger quadra
tic algebra characterizing $n$D superintegrable models with non-central te
rms. This is shown both in classical and quantum mechanics through suitabl
e (symplectic or differential) realisations of the Racah and additional ge
nerators. I will also present an explicit construction of the complete sym
metry algebras for two families of $n$-dimensional maximally superintegrab
le models\, the Smorodinsky-Winternitz system and the generalized Kepler-C
oulomb system. For both families\, the underlying symmetry algebras are h
igher-rank quadratic algebras containing the Racah algebra $R(n)$ as subal
gebra. High-order algebraic relations among the generators of the full qua
dratic algebras are also obtained both in the classical and quantum framew
orks. However\, these approaches rely on explicit realizations as differen
tial operators. I will also briefly discuss how an algebraic construction
of the symmetry algebra of the generic superintegrable systems on the 2-sp
here can be generated from an underlying Lie algebra connected with intert
wining operators.\n
END:VEVENT
END:VCALENDAR