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BEGIN:VEVENT
SUMMARY:Wencin Poh (UC Davis)
DTSTART:20200928T190000Z
DTEND:20200928T200000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/1
DESCRIPTION:Title: A
crystal for stable Grothendieck polynomials\nby Wencin Poh (UC Davis)
as part of York University Applied Algebra Seminar\n\n\nAbstract\nWe const
ruct a type A crystal\, which we call the *-crystal\, whose character is t
he stable Grothendieck polynomials for fully-commutative permutations. Th
is crystal is a K-theoretic generalization of Morse-Schilling crystal on d
ecreasing factorizations. Using the residue map\, we showed that this crys
tal intertwines with the crystal on set-valued tableaux given by Monical\,
Pechenik and Scrimshaw. We also proved that this crystal is isomorphic to
that of pairs of semistandard Young tableaux using a newly defined insert
ion called the *-insertion. The insertion offers a combinatorial interpret
ation to the Schur positivity of the stable Grothendieck polynomials for f
ully-commutative permutations. Furthermore\, the *-insertion has interesti
ng properties in relation to row Hecke insertion and the uncrowding algori
thm. This is joint work with Jennifer Morse\, Jianping Pan and Anne Schill
ing.\n
LOCATION:https://researchseminars.org/talk/YUAAS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yusra Naqvi (University of Sydney)
DTSTART:20201005T190000Z
DTEND:20201005T200000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/2
DESCRIPTION:Title: A
gallery model for affine flag varieties\nby Yusra Naqvi (University of
Sydney) as part of York University Applied Algebra Seminar\n\n\nAbstract\
nGalleries\, which are special sequences of elements in a Coxeter group\,
provide a nice combinatorial way of studying flag varieties. In this talk\
, we will discuss what these objects are\, how they relate to each other\,
and how this relationship gives us a convenient recursion for computing c
ertain double coset intersections in affine flag varieties. This talk is b
ased on joint work with Elizabeth Milicģevicģ\, Petra Schwer and Anne Th
omas.\n
LOCATION:https://researchseminars.org/talk/YUAAS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yibo Gao (MIT)
DTSTART:20201019T190000Z
DTEND:20201019T200000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/3
DESCRIPTION:Title: Th
e 1/3-2/3 Conjecture for Coxeter groups\nby Yibo Gao (MIT) as part of
York University Applied Algebra Seminar\n\n\nAbstract\nThe 1/3-2/3 Conject
ure\, originally formulated in 1968\, is one of the best-known open proble
ms in the theory of posets\, stating that the balance constant of any non-
total order is at least 1/3. By reinterpreting balance constants of posets
in terms of convex subsets of the symmetric group\, we extend the study o
f balance constants to convex subsets C of any Coxeter group. Remarkably\,
we conjecture that the lower bound of 1/3 still applies in any finite Cox
eter group\, with new and interesting equality cases appearing. We general
ize several of the main results towards the 1/3-2/3 Conjecture to this new
setting: we prove our conjecture when C is a weak order interval below a
fully commutative element in any acyclic Coxeter group (a generalization o
f the case of width-two posets)\, we give a uniform lower bound for balanc
e constants in all finite Weyl groups using a new generalization of order
polytopes to this context\, and we introduce generalized semiorders for wh
ich we resolve the conjecture. We hope this new perspective may shed light
on the proper level of generality in which to consider the 1/3-2/3 Conjec
ture\, and therefore on which methods are likely to be successful in resol
ving it. This is joint work with Christian Gaetz.\n
LOCATION:https://researchseminars.org/talk/YUAAS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex McDonough (Brown University)
DTSTART:20201026T190000Z
DTEND:20201026T200000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/4
DESCRIPTION:Title: A
Higher-Dimensional Sandpile Map\nby Alex McDonough (Brown University)
as part of York University Applied Algebra Seminar\n\n\nAbstract\nTraditio
nally\, the sandpile group is defined on a graph and the Matrix-Tree Theor
em says that this group's size is equal to the number of spanning trees. A
n extension of the Matrix-Tree Theorem gives a relationship between the sa
ndpile group and bases of a class of orientable arithmetic matroids. I pro
vide a family of combinatorially meaningful maps between these two sets.
This generalizes a bijection given by Backman\, Baker\, and Yuen and exten
ds work by Duval\, Klivans\, and Martin. I will not assume any background
beyond undergraduate linear algebra.\n
LOCATION:https://researchseminars.org/talk/YUAAS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Logan Crew (University of Waterloo)
DTSTART:20200921T190000Z
DTEND:20200921T200000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/11
DESCRIPTION:Title: E
dge Deletion-Contraction in the Chromatic and Tutte Symmetric Functions\nby Logan Crew (University of Waterloo) as part of York University Appli
ed Algebra Seminar\n\n\nAbstract\nWe consider symmetric function analogues
of the chromatic and Tutte polynomials on graphs whose vertices have posi
tive integer weights. We show that in this setting these functions admit e
dge deletion-contraction relations akin to those of the corresponding poly
nomials\, and we use these relations to give enumerative and/or inductive
proofs of properties of these functions. In particular we note that the Tu
tte symmetric function in this form is related to a family of vertex-weigh
ted graph functions\, from which we derive a recipe theorem and a spanning
-tree expansion.\n\nThis is joint work with Sophie Spirkl.\n
LOCATION:https://researchseminars.org/talk/YUAAS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sophia Elia (Free University of Berlin)
DTSTART:20201102T200000Z
DTEND:20201102T210000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/12
DESCRIPTION:Title: C
ongruence Normality for Simplicial Hyperplane Arrangements\nby Sophia
Elia (Free University of Berlin) as part of York University Applied Algebr
a Seminar\n\n\nAbstract\nSimplicial hyperplane arrangements still have muc
h to reveal. In rank 3\, it is not known whether the list of simplicial hy
perplane arrangements is complete. We determine whether the associated pos
ets of regions possess the combinatorial property of "congruence normality
" for arrangements with up to 37 hyperplanes. We use methods from oriented
matroids\, which make the computations possible. This refines the structu
re of the list\, breaking it into three separate combinatorial categories.
In particular\, we show that arrangements stemming from finite Weyl group
oids have congruence normal posets of regions. This is joint work with Jea
n-Philippe Labbé and Michael Cuntz.\n
LOCATION:https://researchseminars.org/talk/YUAAS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Galen Dorpalen-Barry (University of Minnesota)
DTSTART:20201109T200000Z
DTEND:20201109T210000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/13
DESCRIPTION:Title: C
ones of Hyperplane Arrangements through the Varchenko-Gel’fand Ring\
nby Galen Dorpalen-Barry (University of Minnesota) as part of York Univers
ity Applied Algebra Seminar\n\n\nAbstract\nThe coefficients of the charact
eristic polynomial of an arrangement in a real vector space have many inte
rpretations. An interesting one is provided by the Varchenko-Gel’fand ri
ng\, which is the ring of functions from the chambers of the arrangement t
o the integers with pointwise multiplication. Varchenko and Gel’fand gav
e a simple presentation for this ring\, along with a filtration whose asso
ciated graded ring has its Hilbert function given by the coefficients of t
he characteristic polynomial. We generalize these results to cones defined
by intersections of halfspaces of some of the hyperplanes. Time permittin
g\, we will discuss Varchenko–Gel’fand analogues of some well-known re
sults in the Orlik–Solomon algebra regarding Koszulity and supersolvable
arrangements.\n
LOCATION:https://researchseminars.org/talk/YUAAS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aida Maraj (Max Planck Institute)
DTSTART:20201116T200000Z
DTEND:20201116T210000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/14
DESCRIPTION:Title: R
eciprocal ML-degree of Brownian Motion Tree Models\nby Aida Maraj (Max
Planck Institute) as part of York University Applied Algebra Seminar\n\n\
nAbstract\nBrownian Motion Tree Models (BMTM) are multivariate Gaussian mo
dels that arise in phylogenetics when studying the evolution of species th
rough time. They are realized by rooted directed trees. BMTM are wonderful
as the space of their covariance matrices is a linear space of symmetric
matrices\, and the space of their concentration matrices is a toric variet
y. In applications\, one is interested in computing the point in a model
that is more probable for the observed data. The (reciprocal) Maximum Like
lihood degree of the model gives an insight on the complexity of this prob
lem. In BMTM the reciprocal ML-degree can be nicely computed from the stru
cture of the tree. To prove this result we require help from toric geometr
y. This is based on joint work with T. Boege\, J.I. Coons\, C. Eur\, and F
. Röttger.\n
LOCATION:https://researchseminars.org/talk/YUAAS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolle Gonzalez (UCLA)
DTSTART:20201123T200000Z
DTEND:20201123T210000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/15
DESCRIPTION:Title: A
ffine Demazure crystals for nonsymmetric Macdonald polynomials.\nby Ni
colle Gonzalez (UCLA) as part of York University Applied Algebra Seminar\n
\n\nAbstract\nMacdonald polynomials have long been hailed as a breakthroug
h in algebraic combinatorics as they simultaneously generalize both Hall-L
ittlewood and Jack symmetric polynomials. The nonsymmetric Macdonald polyn
omials $E_a(X\;q\,t)$ are a further generalization which contain the symme
tric versions as special cases. When specialized at $t =0$ the nonsymmetri
c Macdonald polynomials were shown by Bogdon and Sanderson to arise as cha
racters of affine Demazure modules\, which are certain truncations of high
est weight modules. In this talk\, I will describe a type A combinatorial
crystal which realizes the affine Demazure module structure and recovers t
he results of Bogdon and Sanderson crystal-theoretically. The construction
yields a filtration of these affine crystals by finite Demazure crystals
via certain embedding operators that model those of Knop and Sahi for nons
ymmetric Macdonald polynomials. Thus\, we obtain an explicit combinatorial
expansion of the specialized nonsymmetric Macdonald polynomials as graded
sums of key polynomials. As a consequence\, we derive a new combinatorial
formula for the Kostka-Foulkes polynomials. This is joint work with Sami
Assaf.\n
LOCATION:https://researchseminars.org/talk/YUAAS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Gaetz (MIT)
DTSTART:20201130T200000Z
DTEND:20201130T210000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/16
DESCRIPTION:Title: S
table characters from permutation patterns\nby Christian Gaetz (MIT) a
s part of York University Applied Algebra Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/YUAAS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Gunawan (Oklahoma University)
DTSTART:20201207T200000Z
DTEND:20201207T210000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/17
DESCRIPTION:Title: C
ambrian combinatorics on quiver representations\nby Emily Gunawan (Okl
ahoma University) as part of York University Applied Algebra Seminar\n\nAb
stract: TBA\n
LOCATION:https://researchseminars.org/talk/YUAAS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Serrano (Zapata Computing)
DTSTART:20201214T200000Z
DTEND:20201214T210000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/18
DESCRIPTION:Title: F
undamentals and recent advances in machine learning and neural networks\nby Luis Serrano (Zapata Computing) as part of York University Applied A
lgebra Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/YUAAS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sunita Chepuri (University of Michigan)
DTSTART:20210118T200000Z
DTEND:20210118T210000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/19
DESCRIPTION:Title: K
azhdan-Lusztig Immanants for $k$-positive Matrices\nby Sunita Chepuri
(University of Michigan) as part of York University Applied Algebra Semina
r\n\n\nAbstract\nImmanants are matrix functionals that generalize the dete
rminant. One notable family of immanants are the Kazhdan-Lusztig immanants
. These immanants are indexed by permutations and are defined as sums invo
lving Kazhdan-Lusztig polynomials specialized at $q=1$. Kazhdan-Lusztig im
manants have several interesting combinatorial properties\, including that
they are nonnegative on totally positive matrices. We give a condition on
permutations that allows us to extend this theorem to the setting of $k$-
positive matrices.\n
LOCATION:https://researchseminars.org/talk/YUAAS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olya Mandelshtam (Brown University)
DTSTART:20210125T200000Z
DTEND:20210125T210000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/20
DESCRIPTION:Title: T
he multispecies TAZRP and modified Macdonald polynomials\nby Olya Mand
elshtam (Brown University) as part of York University Applied Algebra Semi
nar\n\n\nAbstract\nRecently\, a formula for the symmetric Macdonald polyno
mials $P_{\\lambda}(X\;q\,t)$ was given in terms of objects called multili
ne queues\, which also compute probabilities of a statistical mechanics mo
del called the multispecies asymmetric simple exclusion process (ASEP) on
a ring. It is natural to ask whether the modified Macdonald polynomials $\
\widetilde{H}_{\\lambda}(X\;q\,t)$ can be obtained using a combinatorial g
adget for some other statistical mechanics model. We answer this question
in the affirmative. In this talk\, we will give a new formula for $\\widet
ilde{H}_{\\lambda}(X\;q\,t)$ in terms of fillings of tableaux called polyq
ueue tableaux. We define a multispecies totally asymmetric zero range proc
ess (TAZRP) on a ring with parameter $t$\, whose (unnormalized) stationary
probabilities are computed by polyqueue tableaux\, and whose partition fu
nction is equal to $\\widetilde{H}_{\\lambda}(X\;1\,t)$. This talk is base
d on joint work with Arvind Ayyer and James Martin.\n
LOCATION:https://researchseminars.org/talk/YUAAS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrés Vindas Meléndez (University of Kentucky)
DTSTART:20210201T200000Z
DTEND:20210201T210000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/21
DESCRIPTION:Title: D
ecompositions of Ehrhart h*-Polynomials for Rational Polytopes\nby And
rés Vindas Meléndez (University of Kentucky) as part of York University
Applied Algebra Seminar\n\n\nAbstract\nThe Ehrhart quasipolynomial of a ra
tional polytope P encodes the number of integer lattice points in dilates
of P\, and the h* -polynomial of P is the numerator of the accompanying ge
nerating function. We provide two decomposition formulas for the h*-polyno
mial of a rational polytope. The first decomposition generalizes a theorem
of Betke and McMullen for lattice polytopes. We use our rational Betke--M
cMullen formula to provide a novel proof of Stanley's Monotonicity Theorem
for the h*-polynomial of a rational polytope. The second decomposition ge
neralizes a result of Stapledon\, which we use to provide rational extensi
ons of the Stanley and Hibi inequalities satisfied by the coefficients of
the h*-polynomial for lattice polytopes. Lastly\, we apply our results to
rational polytopes containing the origin whose duals are lattice polytopes
. This is joint work with Matthias Beck (San Francisco State Univ. & FU Be
rlin) and Ben Braun (Univ. of Kentucky).\n
LOCATION:https://researchseminars.org/talk/YUAAS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Mucciconi (Tokyo Institute of Technology)
DTSTART:20210208T200000Z
DTEND:20210208T210000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/22
DESCRIPTION:Title: S
ymmetric polynomials in Integrable Probability\nby Matteo Mucciconi (T
okyo Institute of Technology) as part of York University Applied Algebra S
eminar\n\n\nAbstract\n"A number of solvable stochastic processes can be de
scribed in terms of notable families of symmetric functions. Classical mod
els as the last passage percolation (LPP) or the totally asymmetric simple
exclusion process (TASEP) sample measures built on Schur polynomials. Ana
logously\, Whittaker functions are related to solvable models of random po
lymers as the O’Connell-Yor Polymer (OYP). \n\nIn 2015 Corwin and Petrov
introduced the higher spin vertex model\, a family of stochastic processe
s sitting on top of a hierarchy of models including TASEP\, LPP\, OYP and
of many other interesting systems including random walkers in random envir
onment. \n\nWe find that the higher spin vertex model and all of its degen
erations can be solved using a unifying family of symmetric functions\, th
e spin q-Whittaker (sqW) polynomials\, a version of which was defined firs
t by Borodin and Wheeler in 2017. Probabilistic intepretation of sqW allow
s us to establish a number of interesting combinatorial properties along w
ith surprising conjectural relations. Studying scaling limits of sqW we re
cover classical objects as Schur and Grothendieck polynomials along with n
ew families of symmetric functions.\n\nBased on a joint work with Leonid P
etrov."\n
LOCATION:https://researchseminars.org/talk/YUAAS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Weigandt (Univeristy of Michigan)
DTSTART:20210222T200000Z
DTEND:20210222T210000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/23
DESCRIPTION:Title: T
he Castelnuovo-Mumford Regularity of Matrix Schubert Varieties\nby Ann
a Weigandt (Univeristy of Michigan) as part of York University Applied Alg
ebra Seminar\n\n\nAbstract\nThe Castelnuovo-Mumford regularity of a graded
module provides a measure of how complicated its minimal free resolution
is. In work with Rajchogt\, Ren\, Robichaux\, and St. Dizier\, we noted t
hat the CM-regularity of matrix Schubert varieties can be easily obtained
by knowing the degree of the corresponding Grothendieck polynomial. Furth
ermore\, we gave explicit\, combinatorial formulas for these degrees for s
ymmetric Grothendieck polynomials. In this talk\, I will present a genera
l degree formula for Grothendieck polynomials. This is joint work with Ol
iver Pechenik and David Speyer.\n
LOCATION:https://researchseminars.org/talk/YUAAS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Foster Tom (University of California\, Berkeley)
DTSTART:20210301T200000Z
DTEND:20210301T210000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/24
DESCRIPTION:by Foster Tom (University of California\, Berkeley) as part of
York University Applied Algebra Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/YUAAS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Tamayo (Université Paris-Saclay)
DTSTART:20210308T200000Z
DTEND:20210308T210000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/25
DESCRIPTION:Title: P
ermutree Sorting\, Lattice Quotients\, and Automata\nby Daniel Tamayo
(Université Paris-Saclay) as part of York University Applied Algebra Semi
nar\n\n\nAbstract\nWe define permutree sorting which generalizes Knuth's s
tack sorting and Reading's Coxeter sorting algorithms. (U\,D)-permutree so
rting consists of an algorithm that succeeds or fails for a permutation de
pending if it contains or avoids certain patterns determined by the sets U
and D. We present this algorithm through a family of automata that read r
educed words and show that the accepted reduced words form a search-tree s
tructure related to lattice quotients of the weak order. This is joint wor
k with Vincent Pilaud and Viviane Pons.\n
LOCATION:https://researchseminars.org/talk/YUAAS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rosa Orellana (Dartmouth College)
DTSTART:20210315T190000Z
DTEND:20210315T200000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/26
DESCRIPTION:Title: R
estricting Howe Duality\nby Rosa Orellana (Dartmouth College) as part
of York University Applied Algebra Seminar\n\n\nAbstract\nClassical Howe d
uality provides a representation theoretic framework for classical invaria
nt theory. In the classical Howe duality\, the general linear group\, $GL_
n(\\mathbb{C})$\, is the dual to $GL_n(\\mathbb{C})$ when acting on the po
lynomial ring of the variables $x_{i\,j}$ where $1\\leq i \\leq n$ and $1\
\leq j \\leq k$. In this talk\, I will introduce a multiset partition alge
bra\, MP_k(n)\, as the Howe dual to the action of the symmetric group\, $S
_n$\, on the polynomial ring.\\\n
LOCATION:https://researchseminars.org/talk/YUAAS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hugo Mlodecki (Université Paris-Saclay)
DTSTART:20210322T190000Z
DTEND:20210322T200000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/27
DESCRIPTION:Title: A
bidendriform automorphism of WQSym\nby Hugo Mlodecki (Université Par
is-Saclay) as part of York University Applied Algebra Seminar\n\n\nAbstrac
t\nBy Foissy's work\, the bidendriform structure of the Word Quasisymmetri
c Functions Hopf algebra (WQSym) implies that it is isomorphic to its dual
. In this talk\, we present the construction of an explicit combinatorial
bidendriform isomorphism. We represent two recursive decompositions of pac
ked words by two new combinatorial families called red and blue biplan for
ests. We then obtain two bases of WQSym and its dual. The advantage of the
se bases is that by taking explicit subsets\, we obtain bases of primitive
elements and totally primitive elements. We then carefully combine red an
d blue forests to get bicolors forests. A simple re-coloring of the edges
allows us to obtain the first explicit bidendriform automorphism of WQSym.
\n
LOCATION:https://researchseminars.org/talk/YUAAS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxime Bergeron (Riskfuel)
DTSTART:20210329T190000Z
DTEND:20210329T200000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/28
DESCRIPTION:Title: H
ilbert\, Deep Neural Nets and Empirical Moduli Spaces\nby Maxime Berge
ron (Riskfuel) as part of York University Applied Algebra Seminar\n\n\nAbs
tract\nThe motivation behind Hilbert's 13th problem is often overlooked. I
n his original statement\, he opens with: "nomography deals with the probl
em of solving equations by means of drawing families of curves depending o
n an arbitrary parameter". The question he posed sought to identify a fami
ly of functions amenable to such graphical solvers that were essential too
ls of his time. More formally\, he asked if it was possible to solve algeb
raic equations in terms of towers of algebraic functions of a single param
eter. While the question in its original form remains open to this day\, i
n the continuous realm it turns out that there is no such thing as a truly
multivariate function. In this talk\, we will see how these ideas fit int
o the modern deep learning framework\, forming a bridge between algebra an
d analysis.\n
LOCATION:https://researchseminars.org/talk/YUAAS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Colmenarejo (UMass Amherst)
DTSTART:20210412T190000Z
DTEND:20210412T200000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/29
DESCRIPTION:Title: C
hromatic symmetric functions for Dyck paths and $q$-rook theory\nby La
ura Colmenarejo (UMass Amherst) as part of York University Applied Algebra
Seminar\n\n\nAbstract\n"Given a graph and a set of colors\, a coloring is
a function that associates each vertex in the graph with a color. In 1995
\, Stanley generalized this definition to symmetric functions by looking a
t the number of times each color is used and extending the set of colors t
o $\\mathbb{Z}^+$. In 2012\, Shareshian and Wachs introduced a refinement
of the chromatic functions for ordered graphs as $q$-analogues.\n\nIn the
particular case of Dyck paths\, Stanley and Stembridge described the conne
ction between chromatic symmetric functions of abelian Dyck paths and squa
re hit numbers\, and Guay-Paquet described their relation to rectangular h
it numbers. Recently\, Abreu-Nigro generalized the former connection for t
he Shareshian-Wachs $q$-analogue\, and in unpublished work\, Guay-Paquet g
eneralized the latter. \n\nIn this talk\, I want to give an overview of t
he framework and present another proof of Guay-Paquet's identity using $q$
-rook theory. Along the way\, we will also discuss $q$-hit numbers\, two v
ariants of their statistic\, and some deletion-contraction relations. This
is recent work with Alejandro H. Morales and Greta Panova. "\n
LOCATION:https://researchseminars.org/talk/YUAAS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ezgi Kantarcı Oğuz (Royal Institute of Technology\, Stockholm)
DTSTART:20210405T190000Z
DTEND:20210405T200000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/30
DESCRIPTION:Title: P
romotion and cyclic sieving on families of SSYT\nby Ezgi Kantarcı Oğ
uz (Royal Institute of Technology\, Stockholm) as part of York University
Applied Algebra Seminar\n\n\nAbstract\nCyclic sieving phenomenon is a conn
ection between cyclic actions on a set with a polynomial evaluated at root
s of unity that is surprisingly ubiquitous in the context of algebraic com
binatorics. In this talk\, we will consider some new instances of this phe
nomenon on families of tableaux under the promotion action. Based on work
with Per Alexandersson and Svante Linusson.\n
LOCATION:https://researchseminars.org/talk/YUAAS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonah Blasiak (Drexel University)
DTSTART:20210419T190000Z
DTEND:20210419T200000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/31
DESCRIPTION:Title: A
raising operator formula for $\\nabla$ on an LLT polynomial\nby Jonah
Blasiak (Drexel University) as part of York University Applied Algebra Se
minar\n\n\nAbstract\nThe symmetric function operator $\\nabla$ arose in th
e theory of Macdonald polynomials and its action on various bases has been
the subject of numerous conjectures over the last two decades. It develop
ed that $\\nabla$ is but a shadow of a more complete picture involving the
elliptic Hall algebra of Burban and Schiffmann. This algebra is generated
by subalgebras $\\Lambda(X^{m\,n})$ isomorphic to the ring of symmetric f
unctions\, one for each coprime pair of integers $(m\,n)$. We identify cer
tain combinatorially defined rational functions which correspond to LLT po
lynomials in any of the subalgebras $\\Lambda(X^{m\,n})$. As a corollary\,
we deduce an explicit raising operator formula for $\\nabla$ on any LLT p
olynomial.\nThis is joint work with Mark Haiman\, Jennifer Morse\, Anna P
un\, and George Seelinger.\n
LOCATION:https://researchseminars.org/talk/YUAAS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nancy Wallace (Université du Québec à Montréal)
DTSTART:20210426T190000Z
DTEND:20210426T200000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/32
DESCRIPTION:Title: U
nexpected relations between parking function formulas\, pattern avoiding p
ermutations and the Robinson-Schensted algorithm.\nby Nancy Wallace (U
niversité du Québec à Montréal) as part of York University Applied Alg
ebra Seminar\n\n\nAbstract\nThe Shuffle theorem of Carlsson and Mellit\, s
tates that $\\nabla(e_n)$ is given by parking function formulas. These for
mulas are symmetric in the variables q and t. More preciously\, for all n\
, $\\nabla(e_n)$ can be seen as a $GL2×Sn-module$. In this talk we will p
ut forth a partial expansion in terms of the irreducible bicharacters of t
hese modules. Namely we will expand a subset of the parking function formu
las as products of Schur functions in the variables q and t and the usual
Schur functions in the variables $X={x1\,x2\,…}$. Part of these formulas
are uncovered using a bijection between a subset of paths of area $0$ and
standard Young tableaux that sends the dinv statistic to the major index.
The Robinson-Schensted algorithm associates a pair of standard Young tabl
eaux $(P\,Q)$ to a given permutation. We will end by showing how the previ
ous bijection is linked to the $Q$-tableau of some pattern avoiding permut
ations that is unrelated to the word of the parking function.\n
LOCATION:https://researchseminars.org/talk/YUAAS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:McCabe Olsen (Rose-Hulman Institute of Technology)
DTSTART:20210503T190000Z
DTEND:20210503T200000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/33
DESCRIPTION:Title: U
nconditional Reflexive Polytopes\nby McCabe Olsen (Rose-Hulman Institu
te of Technology) as part of York University Applied Algebra Seminar\n\n\n
Abstract\nA convex body is unconditional if it is symmetric with respect t
o reflections in all coordinate hyperplanes. We investigate unconditional
lattice polytopes with respect to geometric\, combinatorial\, and algebrai
c properties. In particular\, we characterize unconditional reflexive poly
topes in terms of perfect graphs. As a prime example\, we study the signed
Birkhoff polytope. Moreover\, we derive constructions for Gale-dual pairs
of polytopes and we explicitly describe Gröbner bases for unconditional
reflexive polytopes coming from partially ordered sets. This is joint work
with Florian Kohl (Aalto University) and Raman Sanyal (Goethe Universitä
t Frankfurt).\n
LOCATION:https://researchseminars.org/talk/YUAAS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Vanden Wyngaerd (Université Libre de Bruxelles)
DTSTART:20210510T190000Z
DTEND:20210510T200000Z
DTSTAMP:20260422T212724Z
UID:YUAAS/34
DESCRIPTION:Title: T
wo Delta conjecture implications\nby Anna Vanden Wyngaerd (Université
Libre de Bruxelles) as part of York University Applied Algebra Seminar\n\
n\nAbstract\nThe famous shuffle theorem is a combinatorial formula for a S
chur positive symmetric function\, nabla(e_n). Since its formulation\, a n
umber of variations and generalisations of the shuffle formula have been p
roposed\, many of which remain open problems today. In this talk we presen
t some of these conjectures and discuss two logical implications between t
hem we recently established (joined work with Alessandro Iraci). The relev
ant combinatorial objects are decorated labelled lattice paths.\n
LOCATION:https://researchseminars.org/talk/YUAAS/34/
END:VEVENT
END:VCALENDAR