BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Wencin Poh (UC Davis)
DTSTART:20200928T190000Z
DTEND:20200928T200000Z
DTSTAMP:20260404T111103Z
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\nW
e construct a type A crystal\, which we call the *-crystal\, whose charact
er is the stable Grothendieck polynomials for fully-commutative permutatio
ns. This crystal is a K-theoretic generalization of Morse-Schilling cryst
al on decreasing factorizations. Using the residue map\, we showed that th
is crystal intertwines with the crystal on set-valued tableaux given by Mo
nical\, Pechenik and Scrimshaw. We also proved that this crystal is isomor
phic to that of pairs of semistandard Young tableaux using a newly defined
insertion called the *-insertion. The insertion offers a combinatorial in
terpretation to the Schur positivity of the stable Grothendieck polynomial
s for fully-commutative permutations. Furthermore\, the *-insertion has in
teresting properties in relation to row Hecke insertion and the uncrowding
algorithm. This is joint work with Jennifer Morse\, Jianping Pan and Anne
Schilling.\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yusra Naqvi (University of Sydney)
DTSTART:20201005T190000Z
DTEND:20201005T200000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/2
DESCRIPTION:Title: A gallery model for affine flag varieties\nby Yusra Naqvi (Univer
sity of Sydney) as part of York University Applied Algebra Seminar\n\n\nAb
stract\nGalleries\, which are special sequences of elements in a Coxeter g
roup\, provide a nice combinatorial way of studying flag varieties. In thi
s talk\, we will discuss what these objects are\, how they relate to each
other\, and how this relationship gives us a convenient recursion for comp
uting certain double coset intersections in affine flag varieties. This ta
lk is based on joint work with Elizabeth Milicģevicģ\, Petra Schwer and
Anne Thomas.\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yibo Gao (MIT)
DTSTART:20201019T190000Z
DTEND:20201019T200000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/3
DESCRIPTION:Title: The 1/3-2/3 Conjecture for Coxeter groups\nby Yibo Gao (MIT) as p
art of York University Applied Algebra Seminar\n\n\nAbstract\nThe 1/3-2/3
Conjecture\, originally formulated in 1968\, is one of the best-known open
problems in the theory of posets\, stating that the balance constant of a
ny 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 of balance constants to convex subsets C of any Coxeter group. Remar
kably\, we conjecture that the lower bound of 1/3 still applies in any fin
ite Coxeter group\, with new and interesting equality cases appearing. We
generalize several of the main results towards the 1/3-2/3 Conjecture to t
his new setting: we prove our conjecture when C is a weak order interval b
elow a fully commutative element in any acyclic Coxeter group (a generaliz
ation of the case of width-two posets)\, we give a uniform lower bound for
balance constants in all finite Weyl groups using a new generalization of
order polytopes to this context\, and we introduce generalized semiorders
for which we resolve the conjecture. We hope this new perspective may she
d light on the proper level of generality in which to consider the 1/3-2/3
Conjecture\, and therefore on which methods are likely to be successful i
n resolving it. This is joint work with Christian Gaetz.\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex McDonough (Brown University)
DTSTART:20201026T190000Z
DTEND:20201026T200000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/4
DESCRIPTION:Title: A Higher-Dimensional Sandpile Map\nby Alex McDonough (Brown Unive
rsity) as part of York University Applied Algebra Seminar\n\n\nAbstract\nT
raditionally\, the sandpile group is defined on a graph and the Matrix-Tre
e Theorem says that this group's size is equal to the number of spanning t
rees. An extension of the Matrix-Tree Theorem gives a relationship between
the sandpile group and bases of a class of orientable arithmetic matroids
. I provide a family of combinatorially meaningful maps between these two
sets. This generalizes a bijection given by Backman\, Baker\, and Yuen an
d extends work by Duval\, Klivans\, and Martin. I will not assume any back
ground beyond undergraduate linear algebra.\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Logan Crew (University of Waterloo)
DTSTART:20200921T190000Z
DTEND:20200921T200000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/11
DESCRIPTION:Title: Edge Deletion-Contraction in the Chromatic and Tutte Symmetric Funct
ions\nby Logan Crew (University of Waterloo) as part of York Universit
y Applied Algebra Seminar\n\n\nAbstract\nWe consider symmetric function an
alogues of the chromatic and Tutte polynomials on graphs whose vertices ha
ve positive integer weights. We show that in this setting these functions
admit edge deletion-contraction relations akin to those of the correspondi
ng polynomials\, and we use these relations to give enumerative and/or ind
uctive proofs of properties of these functions. In particular we note that
the Tutte symmetric function in this form is related to a family of verte
x-weighted graph functions\, from which we derive a recipe theorem and a s
panning-tree expansion.\n\nThis is joint work with Sophie Spirkl.\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sophia Elia (Free University of Berlin)
DTSTART:20201102T200000Z
DTEND:20201102T210000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/12
DESCRIPTION:Title: Congruence Normality for Simplicial Hyperplane Arrangements\nby
Sophia Elia (Free University of Berlin) as part of York University Applied
Algebra Seminar\n\n\nAbstract\nSimplicial hyperplane arrangements still h
ave much to reveal. In rank 3\, it is not known whether the list of simpli
cial hyperplane arrangements is complete. We determine whether the associa
ted posets of regions possess the combinatorial property of "congruence no
rmality" for arrangements with up to 37 hyperplanes. We use methods from o
riented matroids\, which make the computations possible. This refines the
structure of the list\, breaking it into three separate combinatorial cate
gories. In particular\, we show that arrangements stemming from finite Wey
l groupoids have congruence normal posets of regions. This is joint work w
ith Jean-Philippe Labbé and Michael Cuntz.\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Galen Dorpalen-Barry (University of Minnesota)
DTSTART:20201109T200000Z
DTEND:20201109T210000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/13
DESCRIPTION:Title: Cones of Hyperplane Arrangements through the Varchenko-Gel’fand Ri
ng\nby Galen Dorpalen-Barry (University of Minnesota) as part of York
University Applied Algebra Seminar\n\n\nAbstract\nThe coefficients of the
characteristic polynomial of an arrangement in a real vector space have ma
ny interpretations. An interesting one is provided by the Varchenko-Gel’
fand ring\, which is the ring of functions from the chambers of the arrang
ement to the integers with pointwise multiplication. Varchenko and Gel’f
and gave a simple presentation for this ring\, along with a filtration who
se associated graded ring has its Hilbert function given by the coefficien
ts of the characteristic polynomial. We generalize these results to cones
defined by intersections of halfspaces of some of the hyperplanes. Time pe
rmitting\, we will discuss Varchenko–Gel’fand analogues of some well-k
nown results in the Orlik–Solomon algebra regarding Koszulity and supers
olvable arrangements.\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aida Maraj (Max Planck Institute)
DTSTART:20201116T200000Z
DTEND:20201116T210000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/14
DESCRIPTION:Title: Reciprocal ML-degree of Brownian Motion Tree Models\nby Aida Mar
aj (Max Planck Institute) as part of York University Applied Algebra Semin
ar\n\n\nAbstract\nBrownian Motion Tree Models (BMTM) are multivariate Gaus
sian models that arise in phylogenetics when studying the evolution of spe
cies through time. They are realized by rooted directed trees. BMTM are wo
nderful as the space of their covariance matrices is a linear space of sym
metric matrices\, and the space of their concentration matrices is a toric
variety. In applications\, one is interested in computing the point in a
model that is more probable for the observed data. The (reciprocal) Maxim
um Likelihood degree of the model gives an insight on the complexity of th
is problem. In BMTM the reciprocal ML-degree can be nicely computed from t
he structure of the tree. To prove this result we require help from toric
geometry. This is based on joint work with T. Boege\, J.I. Coons\, C. Eur\
, and F. Röttger.\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolle Gonzalez (UCLA)
DTSTART:20201123T200000Z
DTEND:20201123T210000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/15
DESCRIPTION:Title: Affine Demazure crystals for nonsymmetric Macdonald polynomials.
\nby Nicolle Gonzalez (UCLA) as part of York University Applied Algebra Se
minar\n\n\nAbstract\nMacdonald polynomials have long been hailed as a brea
kthrough in algebraic combinatorics as they simultaneously generalize both
Hall-Littlewood and Jack symmetric polynomials. The nonsymmetric Macdonal
d polynomials $E_a(X\;q\,t)$ are a further generalization which contain th
e symmetric versions as special cases. When specialized at $t =0$ the nons
ymmetric Macdonald polynomials were shown by Bogdon and Sanderson to arise
as characters of affine Demazure modules\, which are certain truncations
of highest weight modules. In this talk\, I will describe a type A combina
torial crystal which realizes the affine Demazure module structure and rec
overs the results of Bogdon and Sanderson crystal-theoretically. The const
ruction yields a filtration of these affine crystals by finite Demazure cr
ystals via certain embedding operators that model those of Knop and Sahi f
or nonsymmetric Macdonald polynomials. Thus\, we obtain an explicit combin
atorial expansion of the specialized nonsymmetric Macdonald polynomials as
graded sums of key polynomials. As a consequence\, we derive a new combin
atorial formula for the Kostka-Foulkes polynomials. This is joint work wit
h Sami Assaf.\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Gaetz (MIT)
DTSTART:20201130T200000Z
DTEND:20201130T210000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/16
DESCRIPTION:Title: Stable characters from permutation patterns\nby Christian Gaetz
(MIT) as part of York University Applied Algebra Seminar\n\nAbstract: TBA\
n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Gunawan (Oklahoma University)
DTSTART:20201207T200000Z
DTEND:20201207T210000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/17
DESCRIPTION:Title: Cambrian combinatorics on quiver representations\nby Emily Gunaw
an (Oklahoma University) as part of York University Applied Algebra Semina
r\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Serrano (Zapata Computing)
DTSTART:20201214T200000Z
DTEND:20201214T210000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/18
DESCRIPTION:Title: Fundamentals and recent advances in machine learning and neural netw
orks\nby Luis Serrano (Zapata Computing) as part of York University Ap
plied Algebra Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sunita Chepuri (University of Michigan)
DTSTART:20210118T200000Z
DTEND:20210118T210000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/19
DESCRIPTION:Title: Kazhdan-Lusztig Immanants for $k$-positive Matrices\nby Sunita C
hepuri (University of Michigan) as part of York University Applied Algebra
Seminar\n\n\nAbstract\nImmanants are matrix functionals that generalize t
he determinant. One notable family of immanants are the Kazhdan-Lusztig im
manants. These immanants are indexed by permutations and are defined as su
ms involving Kazhdan-Lusztig polynomials specialized at $q=1$. Kazhdan-Lus
ztig immanants have several interesting combinatorial properties\, includi
ng that they are nonnegative on totally positive matrices. We give a condi
tion on permutations that allows us to extend this theorem to the setting
of $k$-positive matrices.\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olya Mandelshtam (Brown University)
DTSTART:20210125T200000Z
DTEND:20210125T210000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/20
DESCRIPTION:Title: The multispecies TAZRP and modified Macdonald polynomials\nby Ol
ya Mandelshtam (Brown University) as part of York University Applied Algeb
ra Seminar\n\n\nAbstract\nRecently\, a formula for the symmetric Macdonald
polynomials $P_{\\lambda}(X\;q\,t)$ was given in terms of objects called
multiline queues\, which also compute probabilities of a statistical mecha
nics model called the multispecies asymmetric simple exclusion process (AS
EP) on a ring. It is natural to ask whether the modified Macdonald polynom
ials $\\widetilde{H}_{\\lambda}(X\;q\,t)$ can be obtained using a combinat
orial gadget for some other statistical mechanics model. We answer this qu
estion in the affirmative. In this talk\, we will give a new formula for $
\\widetilde{H}_{\\lambda}(X\;q\,t)$ in terms of fillings of tableaux calle
d polyqueue tableaux. We define a multispecies totally asymmetric zero ran
ge process (TAZRP) on a ring with parameter $t$\, whose (unnormalized) sta
tionary probabilities are computed by polyqueue tableaux\, and whose parti
tion function is equal to $\\widetilde{H}_{\\lambda}(X\;1\,t)$. This talk
is based on joint work with Arvind Ayyer and James Martin.\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrés Vindas Meléndez (University of Kentucky)
DTSTART:20210201T200000Z
DTEND:20210201T210000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/21
DESCRIPTION:Title: Decompositions of Ehrhart h*-Polynomials for Rational Polytopes\
nby Andrés Vindas Meléndez (University of Kentucky) as part of York Univ
ersity Applied Algebra Seminar\n\n\nAbstract\nThe Ehrhart quasipolynomial
of a rational polytope P encodes the number of integer lattice points in d
ilates of P\, and the h* -polynomial of P is the numerator of the accompan
ying generating function. We provide two decomposition formulas for the h*
-polynomial of a rational polytope. The first decomposition generalizes a
theorem of Betke and McMullen for lattice polytopes. We use our rational B
etke--McMullen formula to provide a novel proof of Stanley's Monotonicity
Theorem for the h*-polynomial of a rational polytope. The second decomposi
tion generalizes a result of Stapledon\, which we use to provide rational
extensions of the Stanley and Hibi inequalities satisfied by the coefficie
nts of the h*-polynomial for lattice polytopes. Lastly\, we apply our resu
lts to rational polytopes containing the origin whose duals are lattice po
lytopes. This is joint work with Matthias Beck (San Francisco State Univ.
& FU Berlin) and Ben Braun (Univ. of Kentucky).\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Mucciconi (Tokyo Institute of Technology)
DTSTART:20210208T200000Z
DTEND:20210208T210000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/22
DESCRIPTION:Title: Symmetric polynomials in Integrable Probability\nby Matteo Mucci
coni (Tokyo Institute of Technology) as part of York University Applied Al
gebra Seminar\n\n\nAbstract\n"A number of solvable stochastic processes ca
n be described in terms of notable families of symmetric functions. Classi
cal models as the last passage percolation (LPP) or the totally asymmetric
simple exclusion process (TASEP) sample measures built on Schur polynomia
ls. Analogously\, Whittaker functions are related to solvable models of ra
ndom polymers as the O’Connell-Yor Polymer (OYP). \n\nIn 2015 Corwin and
Petrov introduced the higher spin vertex model\, a family of stochastic p
rocesses sitting on top of a hierarchy of models including TASEP\, LPP\, O
YP and of many other interesting systems including random walkers in rando
m environment. \n\nWe find that the higher spin vertex model and all of it
s degenerations can be solved using a unifying family of symmetric functio
ns\, the spin q-Whittaker (sqW) polynomials\, a version of which was defin
ed first by Borodin and Wheeler in 2017. Probabilistic intepretation of sq
W allows us to establish a number of interesting combinatorial properties
along with surprising conjectural relations. Studying scaling limits of sq
W we recover classical objects as Schur and Grothendieck polynomials along
with new families of symmetric functions.\n\nBased on a joint work with L
eonid Petrov."\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Weigandt (Univeristy of Michigan)
DTSTART:20210222T200000Z
DTEND:20210222T210000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/23
DESCRIPTION:Title: The Castelnuovo-Mumford Regularity of Matrix Schubert Varieties\
nby Anna Weigandt (Univeristy of Michigan) as part of York University Appl
ied Algebra Seminar\n\n\nAbstract\nThe Castelnuovo-Mumford regularity of a
graded module provides a measure of how complicated its minimal free reso
lution is. In work with Rajchogt\, Ren\, Robichaux\, and St. Dizier\, we
noted that the CM-regularity of matrix Schubert varieties can be easily ob
tained by knowing the degree of the corresponding Grothendieck polynomial.
Furthermore\, we gave explicit\, combinatorial formulas for these degree
s for symmetric Grothendieck polynomials. In this talk\, I will present a
general degree formula for Grothendieck polynomials. This is joint work
with Oliver Pechenik and David Speyer.\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Foster Tom (University of California\, Berkeley)
DTSTART:20210301T200000Z
DTEND:20210301T210000Z
DTSTAMP:20260404T111103Z
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://stable.researchseminars.org/talk/YUAAS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Tamayo (Université Paris-Saclay)
DTSTART:20210308T200000Z
DTEND:20210308T210000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/25
DESCRIPTION:Title: Permutree Sorting\, Lattice Quotients\, and Automata\nby Daniel
Tamayo (Université Paris-Saclay) as part of York University Applied Algeb
ra Seminar\n\n\nAbstract\nWe define permutree sorting which generalizes Kn
uth's stack sorting and Reading's Coxeter sorting algorithms. (U\,D)-permu
tree sorting consists of an algorithm that succeeds or fails for a permuta
tion depending 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 reduced words and show that the accepted reduced words form a search
-tree structure related to lattice quotients of the weak order. This is jo
int work with Vincent Pilaud and Viviane Pons.\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rosa Orellana (Dartmouth College)
DTSTART:20210315T190000Z
DTEND:20210315T200000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/26
DESCRIPTION:Title: Restricting Howe Duality\nby Rosa Orellana (Dartmouth College) a
s part of York University Applied Algebra Seminar\n\n\nAbstract\nClassical
Howe duality provides a representation theoretic framework for classical
invariant 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 polynomial 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 partiti
on algebra\, MP_k(n)\, as the Howe dual to the action of the symmetric gro
up\, $S_n$\, on the polynomial ring.\\\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hugo Mlodecki (Université Paris-Saclay)
DTSTART:20210322T190000Z
DTEND:20210322T200000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/27
DESCRIPTION:Title: A bidendriform automorphism of WQSym\nby Hugo Mlodecki (Universi
té Paris-Saclay) as part of York University Applied Algebra Seminar\n\n\n
Abstract\nBy Foissy's work\, the bidendriform structure of the Word Quasis
ymmetric Functions Hopf algebra (WQSym) implies that it is isomorphic to i
ts dual. In this talk\, we present the construction of an explicit combina
torial bidendriform isomorphism. We represent two recursive decompositions
of packed words by two new combinatorial families called red and blue bip
lan forests. We then obtain two bases of WQSym and its dual. The advantage
of these bases is that by taking explicit subsets\, we obtain bases of pr
imitive elements and totally primitive elements. We then carefully combine
red and 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://stable.researchseminars.org/talk/YUAAS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxime Bergeron (Riskfuel)
DTSTART:20210329T190000Z
DTEND:20210329T200000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/28
DESCRIPTION:Title: Hilbert\, Deep Neural Nets and Empirical Moduli Spaces\nby Maxim
e Bergeron (Riskfuel) as part of York University Applied Algebra Seminar\n
\n\nAbstract\nThe motivation behind Hilbert's 13th problem is often overlo
oked. In his original statement\, he opens with: "nomography deals with th
e problem of solving equations by means of drawing families of curves depe
nding on an arbitrary parameter". The question he posed sought to identify
a family of functions amenable to such graphical solvers that were essent
ial tools of his time. More formally\, he asked if it was possible to solv
e algebraic equations in terms of towers of algebraic functions of a singl
e parameter. While the question in its original form remains open to this
day\, in 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 into the modern deep learning framework\, forming a bridge between alg
ebra and analysis.\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Colmenarejo (UMass Amherst)
DTSTART:20210412T190000Z
DTEND:20210412T200000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/29
DESCRIPTION:Title: Chromatic symmetric functions for Dyck paths and $q$-rook theory
\nby Laura Colmenarejo (UMass Amherst) as part of York University Applied
Algebra Seminar\n\n\nAbstract\n"Given a graph and a set of colors\, a colo
ring is a function that associates each vertex in the graph with a color.
In 1995\, Stanley generalized this definition to symmetric functions by lo
oking at the number of times each color is used and extending the set of c
olors to $\\mathbb{Z}^+$. In 2012\, Shareshian and Wachs introduced a refi
nement of the chromatic functions for ordered graphs as $q$-analogues.\n\n
In the particular case of Dyck paths\, Stanley and Stembridge described th
e connection between chromatic symmetric functions of abelian Dyck paths a
nd square hit numbers\, and Guay-Paquet described their relation to rectan
gular hit numbers. Recently\, Abreu-Nigro generalized the former connectio
n for the Shareshian-Wachs $q$-analogue\, and in unpublished work\, Guay-P
aquet generalized the latter. \n\nIn this talk\, I want to give an overvi
ew of the framework and present another proof of Guay-Paquet's identity us
ing $q$-rook theory. Along the way\, we will also discuss $q$-hit numbers\
, two variants of their statistic\, and some deletion-contraction relation
s. This is recent work with Alejandro H. Morales and Greta Panova. "\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ezgi Kantarcı Oğuz (Royal Institute of Technology\, Stockholm)
DTSTART:20210405T190000Z
DTEND:20210405T200000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/30
DESCRIPTION:Title: Promotion and cyclic sieving on families of SSYT\nby Ezgi Kantar
cı Oğuz (Royal Institute of Technology\, Stockholm) as part of York Univ
ersity Applied Algebra Seminar\n\n\nAbstract\nCyclic sieving phenomenon is
a connection between cyclic actions on a set with a polynomial evaluated
at roots of unity that is surprisingly ubiquitous in the context of algebr
aic combinatorics. In this talk\, we will consider some new instances of t
his phenomenon on families of tableaux under the promotion action. Based o
n work with Per Alexandersson and Svante Linusson.\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonah Blasiak (Drexel University)
DTSTART:20210419T190000Z
DTEND:20210419T200000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/31
DESCRIPTION:Title: A raising operator formula for $\\nabla$ on an LLT polynomial\nb
y Jonah Blasiak (Drexel University) as part of York University Applied Alg
ebra Seminar\n\n\nAbstract\nThe symmetric function operator $\\nabla$ aros
e in the theory of Macdonald polynomials and its action on various bases h
as been the subject of numerous conjectures over the last two decades. It
developed that $\\nabla$ is but a shadow of a more complete picture involv
ing the elliptic Hall algebra of Burban and Schiffmann. This algebra is ge
nerated by subalgebras $\\Lambda(X^{m\,n})$ isomorphic to the ring of symm
etric functions\, one for each coprime pair of integers $(m\,n)$. We ident
ify certain combinatorially defined rational functions which correspond to
LLT polynomials in any of the subalgebras $\\Lambda(X^{m\,n})$. As a coro
llary\, we deduce an explicit raising operator formula for $\\nabla$ on an
y LLT polynomial.\nThis is joint work with Mark Haiman\, Jennifer Morse\,
Anna Pun\, and George Seelinger.\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nancy Wallace (Université du Québec à Montréal)
DTSTART:20210426T190000Z
DTEND:20210426T200000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/32
DESCRIPTION:Title: Unexpected relations between parking function formulas\, pattern avo
iding permutations and the Robinson-Schensted algorithm.\nby Nancy Wal
lace (Université du Québec à Montréal) as part of York University Appl
ied Algebra Seminar\n\n\nAbstract\nThe Shuffle theorem of Carlsson and Mel
lit\, states that $\\nabla(e_n)$ is given by parking function formulas. Th
ese formulas 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 put forth a partial expansion in terms of the irreducible bicharacte
rs of these modules. Namely we will expand a subset of the parking functio
n formulas 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 f
ormulas 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 You
ng tableaux $(P\,Q)$ to a given permutation. We will end by showing how th
e previous bijection is linked to the $Q$-tableau of some pattern avoiding
permutations that is unrelated to the word of the parking function.\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:McCabe Olsen (Rose-Hulman Institute of Technology)
DTSTART:20210503T190000Z
DTEND:20210503T200000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/33
DESCRIPTION:Title: Unconditional Reflexive Polytopes\nby McCabe Olsen (Rose-Hulman
Institute of Technology) as part of York University Applied Algebra Semina
r\n\n\nAbstract\nA convex body is unconditional if it is symmetric with re
spect to reflections in all coordinate hyperplanes. We investigate uncondi
tional lattice polytopes with respect to geometric\, combinatorial\, and a
lgebraic properties. In particular\, we characterize unconditional reflexi
ve polytopes in terms of perfect graphs. As a prime example\, we study the
signed Birkhoff polytope. Moreover\, we derive constructions for Gale-dua
l pairs of polytopes and we explicitly describe Gröbner bases for uncondi
tional reflexive polytopes coming from partially ordered sets. This is joi
nt work with Florian Kohl (Aalto University) and Raman Sanyal (Goethe Univ
ersität Frankfurt).\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Vanden Wyngaerd (Université Libre de Bruxelles)
DTSTART:20210510T190000Z
DTEND:20210510T200000Z
DTSTAMP:20260404T111103Z
UID:YUAAS/34
DESCRIPTION:Title: Two Delta conjecture implications\nby Anna Vanden Wyngaerd (Univ
ersité Libre de Bruxelles) as part of York University Applied Algebra Sem
inar\n\n\nAbstract\nThe famous shuffle theorem is a combinatorial formula
for a Schur positive symmetric function\, nabla(e_n). Since its formulatio
n\, a number of variations and generalisations of the shuffle formula have
been proposed\, many of which remain open problems today. In this talk we
present some of these conjectures and discuss two logical implications be
tween them we recently established (joined work with Alessandro Iraci). Th
e relevant combinatorial objects are decorated labelled lattice paths.\n
LOCATION:https://stable.researchseminars.org/talk/YUAAS/34/
END:VEVENT
END:VCALENDAR