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BEGIN:VEVENT
SUMMARY:Dongkwan Kim (University of Minnesota)
DTSTART:20201001T170000Z
DTEND:20201001T180000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/1
DESCRIPTION:Title: Robinson-Schensted correspondence for natural unit interval orders\nby Dongkwan Kim (University of Minnesota) as part of UCLA Combinatoric
s Seminar\n\n\nAbstract\nStanley-Stembridge conjecture\, currently one of
the most famous conjectures in algebraic combinatorics\, asks whether a ce
rtain generating function with respect to a natural unit interval order is
a nonnegative linear combination of complete homogeneous symmetric functi
ons. There are many partial progress on this conjecture\, including its co
nnection with the geometry of Hessenberg varieties. \n\nIn this talk we st
udy the Schur positivity\, which is originally proved by Haiman and Gashar
ov. We define an analogue of Knuth moves with respect to a natural unit in
terval order and study its equivalence classes in terms of D graphs introd
uced by Assaf. Then\, we show that if the given order avoids certain two s
uborders then an analogue of Robinson-Schensted correspondence is well-def
ined\, which proves that the generating function attached to each equivale
nce class is Schur positive. It is hoped that it proposes a new combinator
ial aspect to investigate the Stanley-Stembridge conjectures and cohomolog
y of Hessenberg varieties. This work is joint with Pavlo Pylyavskyy.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Pechenik (University of Waterloo)
DTSTART:20201008T170000Z
DTEND:20201008T180000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/2
DESCRIPTION:Title: Gröbner geometry of Schubert polynomials through ice\nby Oliver
Pechenik (University of Waterloo) as part of UCLA Combinatorics Seminar\n
\n\nAbstract\nKnutson and Miller (2005) showed that the equivariant cohomo
logy class of a matrix Schubert variety $X_w$ is the corresponding double
Schubert polynomial $S_w$. Moreover\, after Gröbner degeneration with res
pect to any antidiagonal term order\, the resulting irreducible components
are naturally labeled by the pipe dreams for w. In later work with Yong (
2009)\, they used diagonal term orders to obtain alternative combinatorics
for certain $X_w$. We present further results in this direction\, with co
nnections to a neglected Schubert polynomial formula of Lascoux (2002) in
terms of the 6-vertex ice model (recently rediscovered by Lam\, Lee\, and
Shimozono in the guise of “bumpless pipe dreams”).\n\nNote: the talk w
ill be accessible to the general audience.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Sherman-Bennett (Harvard University/UC Berkeley)
DTSTART:20201015T170000Z
DTEND:20201015T180000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/3
DESCRIPTION:Title: Plabic graphs and cluster structures on positroid varieties\nby
Melissa Sherman-Bennett (Harvard University/UC Berkeley) as part of UCLA C
ombinatorics Seminar\n\n\nAbstract\nOpen positroid varieties are smooth ir
reducible subvarieties of the Grassmannian\, which can be naturally define
d using "positively realizable" matroids (positroids\, for short). They w
ere first introduced by Knutson\, Lam\, and Speyer\, motivated by work of
Postnikov on the totally nonnegative (real) Grassmannian and positroid cel
ls. Open positroid varieties are indexed by a number of combinatorial obje
cts\, including families of plabic (i.e. planar bicolored) graphs. \n\nI w
ill discuss some algebraic information plabic graphs give us about open po
sitroid varieties. Together with Serhiyenko and Williams\, we showed that
plabic graphs for an open Schubert variety $V$ (a special case of open pos
itroid varieties) give seeds for a cluster algebra structure on the homoge
neous coordinate ring of $V$. Among other things\, this implies that plabi
c graphs give positivity tests for elements of $V$. \n\nOur work generali
zes a result of Scott on the Grassmannian\, and confirms a longstanding fo
lklore conjecture on Schubert varieties\; it was later generalized to arbi
trary positroid varieties by Galashin and Lam. I'll also discuss recent wo
rk with Fraser\, in which we show that relabeled plabic graphs also give s
eeds for a cluster algebra structure on coordinate rings of open positroid
varieties\, uncovering another source for positivity tests. \n\nNo knowle
dge of cluster algebras will be assumed in the talk.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swee Hong Chan (UCLA)
DTSTART:20201022T170000Z
DTEND:20201022T180000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/4
DESCRIPTION:Title: Sorting probability for Young diagrams\nby Swee Hong Chan (UCLA)
as part of UCLA Combinatorics Seminar\n\n\nAbstract\nCan you always find
two elements $x$\, $y$ of a partially ordered set\, such that\, the probab
ility that x is ordered before y when the poset is ordered randomly\, is b
etween $1/3$ and $2/3$?\nThis is the celebrated $1/3 - 2/3$ Conjecture\, w
hich has been called "one of the most intriguing problems in the combinato
rial theory of posets".\n\nWe will explore this conjecture for posets that
arise from (skew-shaped) Young diagrams\, where total orderings of these
posets correspond to standard Young tableaux. We will show that that these
probabilities are arbitrarily close to $1/2$\, by using random walk estim
ates and the state-of-the-art hook-length formulas of Naruse. \n\nThis is
a joint work with Igor Pak and Greta Panova. This talk is aimed at a gene
ral audience.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Escobar (Washington University in St. Louis)
DTSTART:20201029T170000Z
DTEND:20201029T180000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/5
DESCRIPTION:Title: Which Schubert varieties are Hessenberg varieties?\nby Laura Esc
obar (Washington University in St. Louis) as part of UCLA Combinatorics Se
minar\n\n\nAbstract\nSchubert varieties are subvarieties of the flag varie
ty parametrized by permutations\; they induce an important basis for the c
ohomology of the flag variety. Hessenberg varieties are also subvarieties
of the flag variety with connections to both algebraic combinatorics and r
epresentation theory. I will discuss joint work with Martha Precup and Joh
n Shareshian in which we investigate which Schubert varieties in the full
flag variety are Hessenberg varieties.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abdul Basit (Iowa State University)
DTSTART:20201112T180000Z
DTEND:20201112T190000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/7
DESCRIPTION:Title: Point-box incidences and logarithmic density of semilinear graphs\nby Abdul Basit (Iowa State University) as part of UCLA Combinatorics Se
minar\n\n\nAbstract\nZarankiewicz's problem in extremal graph theory asks
for the maximum number of edges in a bipartite graph on $n$ vertices which
does not contain a copy of $K_{k\,k}$\, the complete bipartite with $k$ v
ertices in both classes. We will consider this question for incidence grap
hs of geometric objects. Significantly better bounds are known in this set
ting\, in particular when the geometric objects are defined by systems of
algebraic inequalities. We show even stronger bounds under the additional
constraint that the defining inequalities are linear. We will also discuss
connections of these results to combinatorial geometry and model theory.
\n\nNo background is assumed\, and the talk will be accessible to non-expe
rts. Joint work with Artёm Chernikov\, Sergei Starchenko\, Terence Tao\,
and Chieu-Minh Tran.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonah Blasiak (Drexel University)
DTSTART:20201119T180000Z
DTEND:20201119T190000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/8
DESCRIPTION:Title: Crystal graphs\, katabolism\, and Schur positivity\nby Jonah Bla
siak (Drexel University) as part of UCLA Combinatorics Seminar\n\n\nAbstra
ct\nKatabolism is a mysterious operation on tableaux which involves cuttin
g and reassembling the pieces\nusing Schensted insertion.\nIt is featured
in several Schur positivity conjectures related to\nk-Schur functions and
Hall-Littlewood polynomials.\nCrystal graphs are the combinatorial skeleto
ns of gl_n modules and are a powerful tool for connecting representation t
heory and combinatorics. \nFor instance\, they give a beautiful explanatio
n of the RSK correspondence.\nUsing crystal graphs\, we uncover the myster
y behind katabolism and resolve a Schur positivity conjecture of Shimozono
and Weyman.\nThis talk will include many pictures of crystals and tableau
x.\nThis is joint work with Jennifer Morse and Anna Pun.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Williams (UT Dallas)
DTSTART:20201203T180000Z
DTEND:20201203T190000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/10
DESCRIPTION:Title: Strange Expectations\nby Nathan Williams (UT Dallas) as part of
UCLA Combinatorics Seminar\n\n\nAbstract\nWe extend our previous work on
simultaneous cores for affine Weyl groups. In type A\, our uniform formula
recovers Drew Armstrong's conjecture for the average number of boxes in a
simultaneous core. This is joint work with Marko Thiel and Eric Stucky.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Bernardi (Brandeis University)
DTSTART:20201210T180000Z
DTEND:20201210T190000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/11
DESCRIPTION:Title: A Universal Tutte Polynomial\nby Olivier Bernardi (Brandeis Uni
versity) as part of UCLA Combinatorics Seminar\n\n\nAbstract\nWouldn't it
be nice to have a polynomial expression parametrizing at once the Tutte po
lynomial of every matroid of a given size?\nIn this talk\, I will explain
how to achieve this goal. The solution involves extending the definition o
f the Tutte polynomial from the setting of matroids to the setting of poly
matroids (this is akin to the generalization from graphs to hypergraphs)\,
and adopting a geometric point-counting perspective. On our way\, we will
connect several notions: the activity-counting invariants of Kalman and P
ostnikov\, the point-counting invariants of Cameron and Fink\, and the cla
ssical corank-nullity definition of the Tutte polynomial of matroids.\nThi
s is joint work with Tamas Kalman and Alex Postnikov.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swee Hong Chan (UCLA)
DTSTART:20210930T210000Z
DTEND:20210930T220000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/12
DESCRIPTION:Title: Log-concave inequalities for posets\nby Swee Hong Chan (UCLA) a
s part of UCLA Combinatorics Seminar\n\nLecture held in UCLA Math Sciences
building\, room MS 3915A.\n\nAbstract\nThe study of log-concave inequalit
ies for combinatorial objects have seen much progress in recent years. One
such progress is the solution to the strongest form of Mason's conjecture
(independently by Anari et. al. and Brándën-Huh) that the f-vectors of
matroid independence complex is ultra-log-concave. In this talk\, we discu
ss a new proof of this result through linear algebra and discuss generaliz
ations to greedoids and posets. This is a joint work with Igor Pak.\n\nThe
talk is aimed at a general audience.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Petrov (UVA and MSRI)
DTSTART:20211014T210000Z
DTEND:20211014T220000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/13
DESCRIPTION:Title: Schur rational functions\, vertex models\, and random domino tiling
s\nby Leonid Petrov (UVA and MSRI) as part of UCLA Combinatorics Semin
ar\n\nLecture held in UCLA Math Sciences Building\, room MS 3915A..\n\nAbs
tract\nIt is known that Schur symmetric polynomials admit a number of gene
ralizations (Macdonald's 1992 variations) which retain determinantal struc
ture - for example\, factorial and supersymmetric Schur functions. We desc
ribe an overarching family of Schur-like rational functions arising as par
tition functions of fully inhomogeneous free fermion six vertex model. The
se functions are indexed by partitions\, have as variables the pairs $(x_i
\,r_i)$\, $i=1\,...\,N$\, of horizontal rapidities and spin parameters\; a
nd\, moreover\, depend on vertical rapidities and spin parameters $(y_j\,s
_j)$\, $j>=1$. We establish determinantal formulas\, orthogonality\, Cauch
y identities\, and other properties of our functions. We also introduce ra
ndom domino tiling models based on the Schur rational functions (a la Schu
r processes of Okounkov-Reshetikhin 2001)\, and obtain bulk (lattice) asym
ptotics leading to a new deformation of the extended discrete sine kernel.
Based on the joint project https://arxiv.org/abs/2109.06718 with A. Aggar
wal\, A. Borodin\, and M. Wheeler.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yibo Gao (MIT)
DTSTART:20211028T170000Z
DTEND:20211028T180000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/14
DESCRIPTION:Title: The canonical bijection between pipe dreams and bumpless pipe dream
s\nby Yibo Gao (MIT) as part of UCLA Combinatorics Seminar\n\nLecture
held in *Virtual only*.\n\nAbstract\nPipe dreams and bumpless pipe dreams
are two combinatorial objects that enumerate Schubert polynomials\, and it
has been an open problem to find a weight-preserving bijection between th
ese two objects since bumpless pipe dreams were introduced by Lam\, Lee an
d Shimozono. In this talk\, we present such a bijection and establish its
canonical nature by showing that it preserves Monk's rule. This is joint w
ork with Daoji Huang.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Terrence George (University of Michigan)
DTSTART:20211104T210000Z
DTEND:20211104T220000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/15
DESCRIPTION:Title: Electrical networks and Lagrangian Grassmannians\nby Terrence G
eorge (University of Michigan) as part of UCLA Combinatorics Seminar\n\n\n
Abstract\nCactus networks were introduced by Thomas Lam as a generalizatio
n of planar electrical networks.\nHe defined a map from these networks to
a Grassmannian and showed that the image of this map lies inside the total
ly nonnegative part of this Grassmannian. We show that the image of Lam's
map consists of exactly the elements that are both totally nonnegative and
isotropic for a particular skew-symmetric bilinear form. This is joint wo
rk with Sunita Chepuri and David Speyer.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Suho Oh (Texas State)
DTSTART:20211118T220000Z
DTEND:20211118T230000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/16
DESCRIPTION:Title: Extending Shellings\nby Suho Oh (Texas State) as part of UCLA C
ombinatorics Seminar\n\n\nAbstract\nShellable complexes are simplicial com
plexes with the shelling property: their facets can be ordered nicely\, wh
ich translates to interesting properties in algebra and combinatorics. Sim
on in 1994 conjectured that any shellable complex can be extended to the k
-skeleton of a simplex while maintaining the shelling property. We go over
various tools and results related to this problem. In particular\, we wil
l be going over a recent joint work with M. Coleman\, A. Dochtermann and N
. Geist on proving this conjecture for a smaller class.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Josh Swanson (USC)
DTSTART:20211007T210000Z
DTEND:20211007T220000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/17
DESCRIPTION:Title: Combinatorics of harmonic polynomial differential forms\nby Jos
h Swanson (USC) as part of UCLA Combinatorics Seminar\n\nLecture held in U
CLA Math Sciences Building\, room MS 3915A..\n\nAbstract\nA recent conject
ure of Zabrocki introduced super diagonal coinvariant algebras as a repres
entation-theoretic model for the Delta conjecture of Haglund--Remmel--Wils
on. Subsequent work with Wallach introduced a basis for the alternating co
mponent of the super coinvariant algebra consisting of explicit harmonic p
olynomials in commuting and anti-commuting variables. We will discuss two
families of relations involving these harmonics\, which are related to Tan
isaki ideals and which we call Tanisaki witness relations. This talk will
focus on the combinatorics of these objects rather than the underlying abs
tract motivation.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolle Gonzalez (UCLA)
DTSTART:20211021T210000Z
DTEND:20211021T220000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/18
DESCRIPTION:Title: From symmetric functions\, to knots\, and back again.\nby Nicol
le Gonzalez (UCLA) as part of UCLA Combinatorics Seminar\n\nLecture held i
n UCLA Math Sciences Building\, room MS 3915A.\n\nAbstract\nFor fourteen y
ears the shuffle conjecture remained open. In essence\, it gave a combinat
orial formula for the Frobenius character of the space of diagonal harmoni
cs in terms of word parking functions\, which are certain symmetric functi
ons that can be indexed by lattice paths. Concretely\, the conjecture stat
ed that this combinatorial sum was equal to the action of the ubiquitous n
abla operator on the nth elementary symmetric polynomial. In a startling p
aper\, Carlsson and Mellit proved this conjecture by introducing a new alg
ebra\, closely related to the double affine Hecke algebra\, called $A_{q\,
t}$ and defining an important polynomial action for it. This algebra allow
ed them to perform operations on symmetric functions by lifting the corres
ponding structures via raising and lowering operators to certain higher le
vel polynomial rings\, performing the computations there\, and then projec
ting them back. Shortly thereafter\, using parabolic flag Hilbert schemes\
, the algebra and its representation was also realized geometrically by Ca
rlsson\, Gorsky\, and Mellit\, reaffirming its connection to the work Haim
an on the space of diagonal harmonics. I will introduce a topological inte
rpretation of this algebra and its representation. Namely\, I will describ
e how we can realize symmetric functions and the $A_{q\,t}$ operators as b
raid diagrams on an annulus and how many of the complicated algebraic rela
tions using plethysms in the original formulation follow trivially from is
otopy of the diagrams. This paradigm not only eases many computations\, it
also informs us of new operators on symmetric functions that while natura
l from a topological perspective might be very difficult to see algebraica
lly\, thus yielding new light on an already rich structure. Of particular
interest is its ability to potentially explain the many conjectures relati
ng the homology of the toric links and q\,t combinatorics.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:GaYee Park (UMass Amherst)
DTSTART:20211012T170000Z
DTEND:20211012T180000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/19
DESCRIPTION:Title: Minimal semi-standard skew tableaux and the Hillman-Grassl correspo
ndence\nby GaYee Park (UMass Amherst) as part of UCLA Combinatorics Se
minar\n\nLecture held in *Virtual only*.\n\nAbstract\nStandard tableaux of
skew shape are fundamental objects in\nenumerative and algebraic combinat
orics and no product formula for the\nnumber is known. In 2014\, Naruse ga
ve a formula as a positive sum over\nexcited diagrams of products of hook-
lengths. In 2018\, Morales\, Pak\, and\nPanova gave a $q$-analogue of Naru
se's formula for semi-standard tableaux\nof skew shapes. They also showed\
, partly algebraically\, that the\nHillman-Grassl map restricted to skew s
hapes gave their $q$-analogue. We\nstudy the problem of making this argume
nt completely bijective. For a skew\nshape\, we define a new set of semi-s
tandard Young tableaux\, called the\nminimal SSYT\, that are equinumerous
with excited diagrams via a new\ndescription of the Hillan-Grassl bijectio
n and have a version of excited\nmoves. Lastly\, we relate the minimal ske
w SSYT with the terms of the\nOkounkov-Olshanski formula for counting SYT
of skew shape. This is joint\nwork with Alejandro Morales and Greta Panova
.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Sherman-Bennett (University of Michigan)
DTSTART:20211116T220000Z
DTEND:20211116T230000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/20
DESCRIPTION:Title: The hypersimplex and the m=2 amplituhedron\nby Melissa Sherman-
Bennett (University of Michigan) as part of UCLA Combinatorics Seminar\n\n
Lecture held in MS 6627 (!).\n\nAbstract\nI'll discuss a curious correspon
dence between the $m=2$ amplituhedron\, a $2k$-dimensional subset of $\\ma
thrm{Gr}(k\, k+2)$\, and the hypersimplex\, an $(n-1)$-dimensional polytop
e in $\\mathbb R^n$. The amplituhedron and hypersimplex are both images of
the totally nonnegative Grassmannian under some map (the amplituhedron ma
p and the moment map\, respectively)\, but are different dimensions and li
ve in very different ambient spaces. I'll talk about joint work with Matte
o Parisi and Lauren Williams in which we give a bijection between decompos
itions of the amplituhedron and decompositions of the hypersimplex (origin
ally conjectured by Lukowski--Parisi--Williams). Along the way\, we prove
the sign-flip description of the $m=2$ amplituhedron conjectured by Arkani
-Hamed--Thomas--Trnka and give a new decomposition of the $m=2$ amplituhed
ron into Eulerian-number-many chambers\, inspired by an analogous hypersim
plex decomposition.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marianna Russkikh (MIT)
DTSTART:20211109T180000Z
DTEND:20211109T190000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/21
DESCRIPTION:Title: Dimers and circle patterns\nby Marianna Russkikh (MIT) as part
of UCLA Combinatorics Seminar\n\n\nAbstract\nThe dimer model is a model fr
om statistical mechanics corresponding to random perfect matchings on grap
hs. Circle patterns are a class of embeddings of planar graphs such that e
very face admits a circumcircle. We describe how to construct a 't-embeddi
ng' (or a circle pattern) of a dimer planar graph using its Kasteleyn weig
hts\, and discuss algebro-geometric properties of these embeddings.\nThis
new class of embeddings is the key for studying Miquel dynamics\, a discre
te integrable system on circle patterns: we identify Miquel dynamics on th
e space of square-grid circle patterns with the Goncharov-Kenyon dimer dyn
amics and deduce the integrability of the former one and show that the evo
lution is governed by cluster algebra mutations.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hunter Spink (Stanford)
DTSTART:20211202T220000Z
DTEND:20211202T230000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/22
DESCRIPTION:Title: Anti-concentration of random walks on model-theoretic definable set
s\nby Hunter Spink (Stanford) as part of UCLA Combinatorics Seminar\n\
n\nAbstract\nClassical anti-concentration results show that random walks i
n $\\mathbb{R}^d$ with BIG independent steps can’t concentrate in balls
much better than they can concentrate on individual points.\n\nModel-theor
etic *definable sets* include Boolean combinations of subsets of $\\mathbb
{R}^d$ defined using equalities and inequalities of arbitrary compositions
of polynomials\, $e^x$\, $\\ln(x)$ and analytic functions restricted to c
ompact boxes. For example\, the intersection of $e^{\\sin(1/(1+(xyz)^2))+x
^2y}+zy \\geq0$ and $xyz=5$ in $\\mathbb{R}^3$.\n\nIn this talk\, I will d
iscuss recent results which show that random walks in $\\mathbb{R}^d$ with
ARBITRARY independent steps can’t concentrate in definable sets not con
taining line segments much better than they can concentrate on individual
points. Time permitting\, I will discuss how these results extend to other
groups like $\\mathrm{GL}_d(\\mathbb{R})$.\n\nJoint work with Jacob Fox a
nd Matthew Kwan.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allen Knutson (Cornell)
DTSTART:20211204T000000Z
DTEND:20211204T010000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/23
DESCRIPTION:Title: The commuting scheme and generic pipe dreams\nby Allen Knutson
(Cornell) as part of UCLA Combinatorics Seminar\n\nLecture held in ! MS 52
25 !.\n\nAbstract\nThe space of pairs of commuting matrices is more myster
ious than you\nmight think -- in particular\, Hochster's 1984 conjecture t
hat it is\nreduced remains unresolved. I'll explain how to degenerate it t
o one\ncomponent of the "lower-upper scheme" {(X\,Y) : XY lower triangular
\,\nYX upper triangular}\, a reduced complete intersection\, and how to\nc
ompute the degree of any component as a sum over "generic pipe dreams".\nA
s a consequence\, this recovers both the "pipe dream" and\n"bumpless pipe
dream" formulae for double Schubert polynomials.\nSome of this work is joi
nt with Paul Zinn-Justin.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Karpenkov (University of Liverpool)
DTSTART:20220414T210000Z
DTEND:20220414T220000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/24
DESCRIPTION:Title: Combinatorics and Geometry of Markov numbers\nby Oleg Karpenkov
(University of Liverpool) as part of UCLA Combinatorics Seminar\n\nLectur
e held in MS 7608.\n\nAbstract\nMarkov numbers are positive solutions to t
he Markov Diophantine equation $x^2+y^2+z^2=3xyz$. The set of Markov numbe
rs can be very simple\, generated iteratively starting with the smallest s
olution $(1\,1\,1)$\, which defines a natural binary tree structure on the
set of all solutions. Markov numbers appear in the study of integer minim
a of quadratic forms\, cluster algebra\, etc.\n\nIn this talk we introduce
generalized Markov numbers and extend the classical Markov theory. We sho
w that the principles hidden in Markov's theory are much broader and can b
e substantively extended beyond the limits of Markov's theory.\n\nIn parti
cular we discuss recursive properties for these numbers and find correspon
ding values in the Markov spectrum. Further we give a counterexample to th
e generalized Markov uniqueness conjecture. The proposed generalization is
based on geometry of numbers\, it substantively uses lattice trigonometry
and geometric theory of continued numbers.\n\nThe talk is accessible to t
he general audience.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugene Gorsky (UC Davis)
DTSTART:20221006T210000Z
DTEND:20221006T220000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/25
DESCRIPTION:Title: Cluster structures on braid varieties\nby Eugene Gorsky (UC Dav
is) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 7608.\n\nA
bstract\nGiven a positive braid\, one can define a smooth affine algebraic
variety called the braid variety. Braid varieties generalize several impo
rtant varieties in Lie theory such as open Richardson and positroid variet
ies. I will construct a cluster structure on a braid variety of arbitrary
type using combinatorial objects called weaves. This is a joint work with
Roger Casals\, Mikhail Gorsky\, Ian Le\, Linhui Shen and Jose Simental.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Be'eri Greenfeld (UCSD)
DTSTART:20221027T233000Z
DTEND:20221028T001000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/26
DESCRIPTION:Title: Growth of unbounded subsets in nilpotent groups and random mapping
statistics\nby Be'eri Greenfeld (UCSD) as part of UCLA Combinatorics S
eminar\n\nLecture held in MS 6627.\n\nAbstract\nLet $G$ be an infinite gro
up. Let $g(k\,n)$ be the maximum number of length-$n$ words over an arbitr
ary $k$-letter subset of $G$. How does $g(k\,n)$ behave? Obviously\, $g(k\
,n)$ is at most $k^n$\, and Semple-Shalev proved that if $G$ is finitely g
enerated and residually finite then $g(k\,n)< k^n$ if and only if $G$ is v
irtually nilpotent. It is then natural to ask how far $g(k\,n)$ can get fr
om $k^n$\; for $k$ fixed and $n$ tending to infinity\, $g(k\,n)$ is polyno
mially bounded.\n\nWe quantify the Semple-Shalev Theorem at the other extr
eme\, where $k=\\Theta(n)$. Specifically\, for a finitely generated residu
ally finite group $G$\, the ratio $g(k\,n)/k^n$ either tends to zero (if a
nd only if $G$ is virtually abelian)\, or is greater than or equal to an e
xplicitly calculated optimal threshold. For higher- step free nilpotent gr
oups\, this ratio tends to 1.\n\nAlong the way\, we find the probability t
hat a random function $f:[n]\\to [n]$ can be recovered from a suitable "in
version set"\, and geometrically interpret our results via random paths in
$\\mathbb{Z}^n$ and the areas of their projected polygons. Finally\, we p
rovide a model-theoretic characterization of suboptimality of $g(k\,n)$ by
means of free sub-models and polynomial identities\, which enables to gen
eralize the discussion to various other classes of algebraic structures.\n
\nThis is a joint work with Hagai Lavner.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Colleen Robichaux (UCLA)
DTSTART:20221028T002000Z
DTEND:20221028T010000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/27
DESCRIPTION:Title: Degrees of Grothendieck polynomials and Castelnuovo-Mumford regular
ity\nby Colleen Robichaux (UCLA) as part of UCLA Combinatorics Seminar
\n\nLecture held in MS 6627.\n\nAbstract\nWe give an explicit formula for
the degree of a vexillary Grothendieck polynomial. This generalizes a prev
ious result of Rajchgot-Ren-Robichaux-St.Dizier-Weigandt for degrees of sy
mmetric Grothendieck polynomials. We apply these formulas to compute the C
astelnuovo-Mumford regularity of certain Kazhdan-Lusztig varieties coming
from open patches of Grassmannians as well as the regularity of mixed one-
sided ladder determinantal ideals. This is joint work with Jenna Rajchgot
and Anna Weigandt.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (UC Davis)
DTSTART:20221028T011000Z
DTEND:20221028T015000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/28
DESCRIPTION:Title: Grid plabic graphs\, Legendrian weaves\, and (quasi-)cluster struct
ures\nby Daping Weng (UC Davis) as part of UCLA Combinatorics Seminar\
n\nLecture held in MS 6627.\n\nAbstract\nGiven a "grid" plabic graph on $\
\mathbb{R}^2$\, we can construct a Legendrian link\, which is a link in $\
\mathbb{R}^3$ satisfying certain tangential conditions. We study a moduli
space problem associated with the Legendrian link\, and construct a natura
l (quasi-)cluster structure on this moduli space using Legendrian weaves.
In particular\, we prove that any braid variety associated with $\\beta \\
Delta$ for a 3-strand braid $\\beta$ admits cluster structures with an exp
licit construction of initial seeds. We also construct Donaldson-Thomas tr
ansformations for these moduli spaces.\n\nIn this talk\, I will introduce
the theoretical background and describe the basic combinatorics for constr
ucting Legendrian weaves and the (quasi-)cluster structures from a grid pl
abic graph. This is based on a joint work with Roger Casals (arXiv:2204.13
244).\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Korotkikh (MIT)
DTSTART:20221111T003000Z
DTEND:20221111T011000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/29
DESCRIPTION:Title: Spin $q$-Whittaker symmetric functions and vertex models.\nby S
ergei Korotkikh (MIT) as part of UCLA Combinatorics Seminar\n\nLecture hel
d in MS 6627.\n\nAbstract\nWe introduce a new family of symmetric function
s called spin $q$-Whittaker functions. We have found these functions using
solvable vertex model from mathematical physics and they basically are de
fined by taking a specific sum over path ensembles on a square grid. I wil
l describe this construction from scratch and will explain how it leads to
the following two properties. First property is the generalization of Cau
chy summation identity: an important identity from algebraic combinatorics
which encapsulates orthogonality relations for symmetric functions. Secon
d property is a unique structure of the vanishing points of our functions
which leads to a characterization in terms of an interpolation problem whi
ch is similar to the work of Okounkov from 1997 about interpolation proper
ties of symmetric functions. All necessary background on vertex models and
symmetric functions will be explained and\, time permitting\, I will also
cover connections to probability and quantum groups.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Greta Panova (USC)
DTSTART:20221111T012000Z
DTEND:20221111T020000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/31
DESCRIPTION:Title: The world of poset inequalities\nby Greta Panova (USC) as part
of UCLA Combinatorics Seminar\n\nLecture held in MS 6627.\n\nAbstract\nPar
tially ordered sets are ubiquitous\, yet poorly understood structures in c
ombinatorics. Counting their linear extensions and order preserving maps d
o not have nice closed formulas and thus we can only hope to understand th
em qualitatively or asymptotically in greater generality. In this talk I w
ill show some inequalities relating linear extensions and order preserving
maps for general posets. We will discuss various proofs\, problems and co
njectures. Based on a series of joint papers with Swee Hong Chan and Igor
Pak.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tianyi Yu (UCSD)
DTSTART:20221130T003000Z
DTEND:20221130T011000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/32
DESCRIPTION:Title: Top degree components of Grothendieck and Lascoux polynomials\n
by Tianyi Yu (UCSD) as part of UCLA Combinatorics Seminar\n\nLecture held
in MS 6627.\n\nAbstract\nThe Schubert polynomials of the Symmetric group o
f n form a basis of the space they span. This vector space is well-studied
and has dimension $n!$. Its Hilbert series is the $q$-analogue of $n!$. A
nother basis of this space is given by key polynomials\, which are charact
ers of the Demazure modules. Schubert and key polynomials are the ``bottom
layers'' of Grothendieck and Lascoux polynomials\, two inhomogeneous poly
nomials. In this talk\, we look at the space spanned by their ``top layers
''. We construct two bases involving the top layer of Grothendieck and the
top layer of Lascoux polynomials. We then develop a diagrammatic way to c
ompute the degrees of these polynomials. Finally\, we describe the Hilbert
series of this space involving a classical q-analogue of the Bell numbers
. \nThe talk does not assume knowledge of Grothendieck or Lascoux polynomi
als. This is a joint work with Jianping Pan.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cosmin Pohoata (IAS)
DTSTART:20221130T012000Z
DTEND:20221130T020000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/33
DESCRIPTION:Title: Convex polytopes from fewer points\nby Cosmin Pohoata (IAS) as
part of UCLA Combinatorics Seminar\n\nLecture held in MS 6627.\n\nAbstract
\nFinding the smallest integer N=ES_d(n) such that in every configuration
of N points in R^d in general position there exist n points in convex posi
tion is one of the most classical problems in extremal combinatorics\, kno
wn as the Erdos-Szekeres problem. In 1935\, Erdos and Szekeres famously co
njectured that ES_2(n)=2^{n−2}+1 holds\, which was nearly settled by Suk
in 2016\, who showed that ES_2(n)≤2^{n+o(n)}. We discuss a recent proof
that ES_d(n)=2^{o(n)} holds for all d≥3. Joint work with Dmitrii Zakhar
ov.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Gaetz (Cornell)
DTSTART:20230314T233000Z
DTEND:20230315T001000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/34
DESCRIPTION:Title: An SL(4) web basis from hourglass plabic graphs\nby Christian G
aetz (Cornell) as part of UCLA Combinatorics Seminar\n\nLecture held in MS
6221.\n\nAbstract\nThe SL(3) web basis is a special basis of certain spac
es of tensor invariants developed in the late 90's by Khovanov and Kuperbe
rg as a tool for computing quantum link invariants. Since then this basis
has found connections and applications to cluster algebras\, canonical bas
es\, dimer models\, and tableau combinatorics. The main open problem has r
emained: how to find a basis replicating the desirable properties of this
basis for SL(4) and beyond? I will describe joint work with Oliver Pecheni
k\, Stephan Pfannerer\, Jessica Striker\, and Josh Swanson in which we con
struct such a basis for SL(4). Modified versions of plabic graphs and the
six-vertex model and new tableau combinatorics will appear along the way\,
but knowledge of these topics won't be assumed in the talk.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Mazin (KSU)
DTSTART:20230315T002000Z
DTEND:20230315T010000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/35
DESCRIPTION:Title: Springer Fibers and Rational Dyck Paths\nby Mikhail Mazin (KSU)
as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6221.\n\nAbst
ract\nAffine Grassmanian can be thought of as the space of linear subspace
s V in the space of Laurent power series C((t))\, invariant under multipli
cation by t^n. It admits a cell decomposition with cells enumerated by cof
inite subsets in the set of non-negative integers\, invariant under additi
on of n. An Affine Springer Fiber is a subvariety in the Affine Grassmania
n\, consisting of subspaces that are also invariant under the multiplicati
on by a fixed function f(t). If f(t)=t^m\, where n and m are relatively pr
ime\, then the corresponding Affine Springer Fiber is particularly well be
haved: its intersection with a cell of the Affine Grassmanian is non-empty
if and only if the corresponding subset of integers is also invariant und
er addition of m\, in which case the intersection itself is an affine cell
of a possibly smaller dimension. One can further see that the (m\,n)-inva
riant subsets of integers are in bijection with the (m\,n)-Dyck paths\, an
d the dimensions of cells are computed using the so-called dinv statistic.
\n\nIn this talk I will present a recent generalization of the above const
ruction to the case when m and n are not relatively prime and f(t)=t^m+t^{
m+1}. Turns out that the Springer Fiber in this case is again well-behaved
\, with the non-empty intersections enumerated by the (m\,n)-invariant sub
sets satisfying an additional admissibility condition. Furthermore\, such
subsets turn out to be in bijection with the (m\,n)-Dyck paths\, and the d
imensions of cells are again computed using the dinv statistic. The talk i
s based on a joint work with Eugene Gorsky and Alexei Oblomkov (arXiv:2210
.12569).\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Black (UC Davis)
DTSTART:20231005T233000Z
DTEND:20231006T020000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/36
DESCRIPTION:Title: Monotone Paths on Polytopes in Combinatorics and Optimization\n
by Alexander Black (UC Davis) as part of UCLA Combinatorics Seminar\n\nLec
ture held in MS 6621.\n\nAbstract\nLinear programming is a core problem in
optimization\, and geometrically\, it is the problem of finding the highe
st point in some direction on a polytope. The standard combinatorial algor
ithm for solving linear programs is the simplex method\, which works by wa
lking from vertex to vertex of the polytope along edges moving higher at e
ach step. We call such a walk a monotone path. There are many ways for the
simplex method to choose monotone paths called pivot rules\, and the main
open problem in the area is to find a pivot rule that guarantees the path
followed is always of polynomial length. In this talk\, I will discuss an
approach to this problem grounded in understanding the space of monotone
paths on a polytope and pivot rules on a fixed linear program. The key too
ls will be the fiber polytope construction of Billera and Sturmfels and an
analogous construction called the pivot rule polytope introduced by mysel
f in joint work with De Loera\, Lütjeharms\, and Sanyal. My focus will be
on the many examples that arise from these constructions such as the perm
utahedron and associahedron.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yelena Mandelshtam (UC Berkeley)
DTSTART:20231005T233000Z
DTEND:20231006T020000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/37
DESCRIPTION:Title: Combinatorics of m=1 Grasstopes\nby Yelena Mandelshtam (UC Berk
eley) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6621.\n\
nAbstract\nThe amplituhedron is an object introduced by physicists in 2013
arising from their study of scattering amplitudes which has garnered much
recent attention from physicists and mathematicians alike. Mathematically
\, it is a linear projection of a nonnegative Grassmannian to a smaller Gr
assmannian\, via a map induced by a totally positive matrix. A Grassmann p
olytope\, or Grasstope\, is a generalization of the amplituhedron\, define
d to be such a projection by any matrix\, removing one of the positivity c
onditions. In this talk\, I will discuss joint work with Dmitrii Pavlov an
d Lizzie Pratt in which we study these objects\, with hope that we may gai
n new insights by broadening our horizons and studying all Grasstopes.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Terrence George (UCLA)
DTSTART:20231005T233000Z
DTEND:20231006T020000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/38
DESCRIPTION:Title: Inverse problem for electrical networks\nby Terrence George (UC
LA) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6621.\n\nA
bstract\nAn electrical network is a graph embedded in a disk with some ver
tices on the boundary of the disk\, and with positive real numbers\, calle
d conductances\, associated to its edges. Associated to such an electrical
network is its response matrix which encodes all information that can be
deduced by making electrical measurements on the boundary. I will discuss
how the inverse problem of recovering the conductances from the response m
atrix can be solved using an electrical-network version of the twist map o
n the positive Grassmannian.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chenchen Zhao (USC)
DTSTART:20231026T233000Z
DTEND:20231027T020000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/39
DESCRIPTION:Title: Kronecker product of Schur functions of square shapes\nby Chenc
hen Zhao (USC) as part of UCLA Combinatorics Seminar\n\nLecture held in MS
6627.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lenny Fukshansky (Claremont McKenna College)
DTSTART:20231026T233000Z
DTEND:20231027T020000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/40
DESCRIPTION:Title: A geometric construction for integer sparse recovery\nby Lenny
Fukshansky (Claremont McKenna College) as part of UCLA Combinatorics Semin
ar\n\nLecture held in MS 6627.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Soukup (UCLA)
DTSTART:20231026T233000Z
DTEND:20231027T020000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/41
DESCRIPTION:Title: Complexity of sign imbalance and parity of linear extensions\nb
y David Soukup (UCLA) as part of UCLA Combinatorics Seminar\n\nLecture hel
d in MS 6621.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiliang Gao (UIUC)
DTSTART:20231117T003000Z
DTEND:20231117T030000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/42
DESCRIPTION:Title: Combinatorics of the Plucker map?\nby Shiliang Gao (UIUC) as pa
rt of UCLA Combinatorics Seminar\n\nLecture held in MS 6621.\n\nAbstract\n
I will discuss how Young tableaux arise from the Plucker map. Influential
work of Hodge from the 1940s led the way in using Grobner bases to combina
torially study the Grassmannian. In the past decade\, the work of Knutson-
Lam-Speyer\, and more recently Galashin-Lam\, has brought to the fore the
significance of positroid subvarieties in the Grassmannian. I will explain
how to use Young tableaux to understand these subvarieties and thereby ho
w to connect promotion on Young tableaux with the cyclic symmetry of posit
roid varieties. This is based on joint work with Ayah Almousa and Daoji Hu
ang\, see arxiv.org/abs/2309.15384.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theo Douvropoulos (Brandeis University)
DTSTART:20231117T003000Z
DTEND:20231117T030000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/43
DESCRIPTION:Title: Families of Shi-like and Catalan-like deformations of braid and ref
lection arrangements\nby Theo Douvropoulos (Brandeis University) as pa
rt of UCLA Combinatorics Seminar\n\nLecture held in MS 6621.\n\nAbstract\n
The Shi arrangement $Shi_n$ is a deformation of the braid arrangement $Br_
n$ and was introduced by Shi to study Kazhdan-Lusztig cells (that turn out
to be unions of the regions of $Shi_n$). It has remarkable numerological
and structural properties: it has $(n+1)^{n-1}$-many regions that can be n
aturally labeled by parking functions or trees\; it has analogs for all We
yl groups\; its characteristic polynomial factors with positive integer ro
ots.\n\nWe will present recent work\, joint with Olivier Bernardi\, where
we give an $n$-parameter family of deformations of the braid arrangement $
Br_n$ that generalize the Shi arrangement $Shi_n$. They share many of the
remarkable properties of $Shi_n$\, in particular they come with product fo
rmulas for their characteristic polynomials\, and their regions are natura
lly labeled by Cayley trees. We will present a parallel story for Catalan-
like deformations\, generalizations to other Weyl groups\, and application
s on the theory of parking spaces.\n\nWe will finish with the original mot
ivation for this construction\, which was the study of coxeter theoretic i
nvariants on restrictions of reflection arrangements and associated multi-
arrangements.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Grebík (UCLA)
DTSTART:20231117T003000Z
DTEND:20231117T030000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/44
DESCRIPTION:Title: Edge colorings and distributed computing\nby Jan Grebík (UCLA)
as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6621.\n\nAbst
ract\nOne of fundamental notions of graph theory is the chromatic index $\
\chi'(G)$ of a graph $G$ which is the smallest number of colors needed to
color all edges of $G$ so that every two edges that intersect have differe
nt colors. The famous upper bound of Vizing states that $\\Delta+1$ colors
is enough\, where $\\Delta$ is the maximum degree of $G$. In fact\, there
is a polynomial time sequential algorithm that produces such a coloring.
In this talk I will discuss edge colorings from the perspective of the LOC
AL model of distributed computing. In particular\, I will talk about what
happens when we try to replace the sequential algorithm by a distributed o
ne.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daoji Huang (UMN)
DTSTART:20240202T003000Z
DTEND:20240202T030000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/45
DESCRIPTION:Title: Tableaux theory inspired methods for Schubert calculus\nby Daoj
i Huang (UMN) as part of UCLA Combinatorics Seminar\n\nLecture held in MS
6621.\n\nAbstract\nThe classical Littlewood-Richardson (LR) coefficients a
re special cases of Schubert structure constants\, for which many combinat
orial interpretations are known. The theory of symmetric functions and com
binatorics of Young tableaux provide a combinatorial toolbox for many diff
erent but related rules for the LR coefficients. In this talk\, I will exp
lain the basic ideas to lift many components of the classical theory to th
e context of Schubert structure constants\, as well as the obstructions an
d challenges to solving the full problems using these methods.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasu Tewari (U of Toronto)
DTSTART:20240202T003000Z
DTEND:20240202T030000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/46
DESCRIPTION:Title: The ideal of quasisymmetric polynomials\nby Vasu Tewari (U of T
oronto) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6621.\
n\nAbstract\nWith an eye toward mimicking the combinatorial theory of Schu
bert polynomials\, I will describe a new perspective on the quotient of th
e polynomial ring modulo the ideal $QSym_n^+$ of quasisymmetric polynomial
s. This involves two simple operators-- trimming and blossoming-- acting o
n the polynomial ring. The trimming operators are degree-lowering operator
s that are a mild modification of divided difference operators (central to
Lascoux-Schützenberger's construction of Schubert polynomials). We ident
ify a basis that may be considered an appropriate analogue to Schubert pol
ynomials with regard to these operators. The blossoming operators are deg
ree-increasing operators that grow volume polynomials of certain cubes dec
omposing the permutahedron.\n\nJoint work with Philippe Nadeau (Lyon/CNRS)
and Hunter Spink (UofT).\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karim Adiprasito (IMJ-PRG)
DTSTART:20240223T003000Z
DTEND:20240223T030000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/47
DESCRIPTION:Title: Efficiently encoding configuration spaces\nby Karim Adiprasito
(IMJ-PRG) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6621
.\n\nAbstract\nWe discuss how difficult it is to encode the complement of
a configuration space\, naturally a neat algebraic variety\, by a smaller
than naïve number of algebraic constraints\, in an attempt to deepen our
understanding of the work of Haiman. We also translate this to varieties
that merely resemble configuration spaces. Joint work with Itaï Ben Yacoo
v and Ehud Hrushovski.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brendan Pawlowski
DTSTART:20240223T003000Z
DTEND:20240223T030000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/49
DESCRIPTION:Title: The fraction of an $S_n$-orbit on a hyperplane\nby Brendan Pawl
owski as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6621.\n\
nAbstract\nFix a point in $\\mathbb{R}^n$ with distinct coordinates and co
nsider the $S_n$-orbit obtained by permuting its coordinates. Huang\, McKi
nnon\, and Satriano conjectured that a hyperplane other than $x_1 + ... +
x_n = 0$ can contain at most $2⌊n/2⌋(n-2)!$ points of this orbit. We e
xplain\nhow to prove their conjecture using the Sperner property for Bruha
t\norder and bounds on q-binomial coefficients.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amanda Schwartz (UMich)
DTSTART:20241018T000000Z
DTEND:20241018T021500Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/50
DESCRIPTION:Title: The HOMFLY Polynomial of a Forest Quiver\nby Amanda Schwartz (U
Mich) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6221.\n\
nAbstract\nThe HOMFLY polynomial of a link is a two-variable link invarian
t which was introduced in the 1980s. It can be defined recursively using a
skein relation and specializes to other link invariants such as the Alexa
nder polynomial and Jones polynomial. In this talk\, we will begin by defi
ning the HOMFLY polynomial of a forest quiver via a recursive definition o
n the underlying graph of the quiver. Then\, we will discuss how the HOMFL
Y polynomial of a forest quiver is related to the HOMFLY polynomial of cer
tain plabic links. In particular\, given any connected plabic graph $G$ wh
ose quiver $Q_G$ is a forest quiver\, the HOMFLY polynomial of the associa
ted plabic link is in fact equal to the HOMFLY polynomial of the quiver $Q
_G$. We will sketch a proof of this result and also discuss a closed-form
expression for the Alexander polynomial of a forest quiver.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steven Karp (Notre Dame)
DTSTART:20241018T000000Z
DTEND:20241018T021500Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/51
DESCRIPTION:Title: Positivity in real Schubert calculus\nby Steven Karp (Notre Dam
e) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6221.\n\nAb
stract\nSchubert calculus involves studying intersection problems among li
near subspaces of C^n. A classical example of a Schubert problem is to fin
d all 2-dimensional subspaces of C^4 which intersect 4 given 2-dimensional
subspaces nontrivially (it turns out there are 2 of them). In the 1990's\
, B. and M. Shapiro conjectured that a certain family of Schubert problems
has the remarkable property that all of its complex solutions are real. T
his conjecture inspired a lot of work in the area\, including its proof by
Mukhin-Tarasov-Varchenko in 2009. I will present a strengthening of this
result which resolves some conjectures of Sottile\, Eremenko\, Mukhin-Tara
sov\, and myself\, based on surprising connections with total positivity\,
the representation theory of symmetric groups\, symmetric functions\, and
the KP hierarchy. This is joint work with Kevin Purbhoo\, and with Evgeny
Mukhin and Vitaly Tarasov.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catherine Babecki (CalTech)
DTSTART:20241018T000000Z
DTEND:20241018T021500Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/52
DESCRIPTION:Title: Spectrahedral Geometry of Graph Sparsifiers\nby Catherine Babec
ki (CalTech) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6
221.\n\nAbstract\nWe propose an approach to graph sparsification based on
the idea of preserving the smallest k eigenvalues and eigenvectors of the
graph Laplacian. This is motivated by the fact that small eigenvalues and
their associated eigenvectors tend to be more informative of the global st
ructure and geometry of the graph than larger eigenvalues and their eigenv
ectors. The set of all weighted subgraphs of a graph G that have the same
first k eigenvalues (and eigenvectors) as G is the intersection of a polyh
edron with a cone of positive semidefinite matrices. We discuss the geomet
ry of these sets and deduce the natural scale of k. Various families of gr
aphs illustrate our construction.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Swanson (USC)
DTSTART:20241108T000000Z
DTEND:20241108T004000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/53
DESCRIPTION:Title: Webs\, pockets\, and buildings\nby Joshua Swanson (USC) as part
of UCLA Combinatorics Seminar\n\nLecture held in UCLA Boelter hall\, room
5436.\n\nAbstract\nWebs are certain diagrams which are part of a powerful
graphical calculus arising from quantum groups and knot invariants. Gaetz
\, Pechenik\, Pfannerer\, Striker\, and I recently introduced a web basis
for $U_q(\\mathfrak{sl}_4)$ using the new framework of hourglass plabic gr
aphs. In this talk\, I will explain how our basis naturally models the geo
metry of the affine building $\\Delta(\\SL(4)^\\vee)$. Specifically\, dual
s of move-equivalence classes of basis webs assemble to form remarkable 3D
simplicial complexes we call pockets\, which in turn generically extend t
he irreducible components of Satake fibers. Special cases correspond to pl
ane partitions\, alternating sign matrices\, tilings of the Aztec diamond\
, and more. Joint with Christian Gaetz\, Jessica Striker\, and Haihan Wu.\
n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wonwoo Kang (UIUC)
DTSTART:20241108T005000Z
DTEND:20241108T013000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/54
DESCRIPTION:Title: Skein Relations for Punctured Surfaces\nby Wonwoo Kang (UIUC) a
s part of UCLA Combinatorics Seminar\n\nLecture held in UCLA Boelter hall\
, room 5436.\n\nAbstract\nSince the introduction of cluster algebras by Fo
min and Zelevinsky in 2002\, there has been substantial interest in cluste
r algebras of surface type. These algebras are particularly significant du
e to their ability to construct various combinatorial structures\, such as
snake graphs\, T-paths\, and posets\, which are useful for proving key st
ructural properties like positivity and the existence of bases. In this ta
lk\, we will begin by presenting a cluster expansion formula that utilizes
poset representatives for arcs on triangulated surfaces. Using these pose
ts and the expansion formula as tools\, we will demonstrate skein relation
s\, which resolve intersections or incompatibilities between arcs. As a re
sult\, we will demonstrate that bangles and bracelets form spanning sets a
nd exhibit linear independence\, thereby proving the existence of the bang
le and bracelet bases in punctured surfaces with boundaries and closed sur
face with genus 0. This work is done in collaboration with Esther Banaian
and Elizabeth Kelley.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Soskin (IAS)
DTSTART:20241206T012000Z
DTEND:20241206T020000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/55
DESCRIPTION:Title: Total positivity and determinantal inequalities\nby Daniel Sosk
in (IAS) as part of UCLA Combinatorics Seminar\n\nLecture held in UCLA Boe
lter hall\, room 5436.\n\nAbstract\nTotally positive matrices are matrices
in which each minor is positive. Lusztig extended the notion to reductive
Lie groups. He also proved that specialization of elements of the dual ca
nonical basis in representation theory of quantum groups at q=1 are total
ly non-negative polynomials. Thus\, it is important to investigate classes
of functions on matrices that are positive on totally positive matrices.
I will discuss several sources of such functions as well as their connecti
on to Schur positivity and Littlewood-Richardson coefficients. The main t
ools we employed are network parametrization and Temperley-Lieb immanants.
\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacques Verstraete (UCSD)
DTSTART:20250508T233000Z
DTEND:20250509T002000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/56
DESCRIPTION:Title: Recent progress in Ramsey Theory\nby Jacques Verstraete (UCSD)
as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6627.\n\nAbstr
act\nThe Ramsey number $r(s\,t)$ denotes the minimum $N$ such that in any
red-blue coloring of the edges of the complete graph $K_N$\, there exists
a red $K_s$ or a blue $K_t$. While the study of these quantities goes back
almost one hundred years\, to early papers of Ramsey and Erdős and Szeke
res\, the long-standing conjecture of Erdős that $r(s\,t)$ has order of m
agnitude close to $t^{s - 1}$ as $t \\rightarrow \\infty$ remains open in
general. It took roughly sixty years before the order of magnitude of $r(3
\,t)$ was determined by Jeong Han Kim\, who showed $r(3\,t)$ has order of
magnitude $t^2/(\\log t)$ as $t \\rightarrow \\infty$. In this talk\, we d
iscuss a variety of new techniques\, including mention of the proof that f
or some constants $a\,b > 0$ and $t \\geq 2$\,\n\\[ a\\frac{t^3}{(\\log t)
^4} \\leq r(4\,t) \\leq b\\frac{t^3}{(\\log t)^2}\,\\]\nas well as new pro
gress on other Ramsey numbers\, on Erdős-Rogers functions\, Ramsey minima
l graphs\, and on coloring hypergraphs. \n\n\nJoint work in part with Davi
d Conlon\, Sam Mattheus\, and Dhruv Mubayi.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Neville (UMich)
DTSTART:20241206T021000Z
DTEND:20241206T025000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/57
DESCRIPTION:Title: Cyclically ordered quivers\nby Scott Neville (UMich) as part of
UCLA Combinatorics Seminar\n\nLecture held in UCLA Boelter hall\, room 54
36.\n\nAbstract\nQuivers and their mutations play a fundamental role in th
e theory of cluster algebras. We focus on the problem of deciding whether
two given quivers are mutation equivalent to each other. Our approach is b
ased on introducing an additional structure of a cyclic ordering on the se
t of vertices of a quiver. This leads to new powerful invariants of quiver
mutation. These invariants can be used to show that various quivers are n
ot mutation acyclic\, i.e.\, they are not mutation equivalent to an acycli
c quiver. This talk is partially based on joint work with Sergey Fomin [ar
Xiv:2406.03604].\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jianping Pan (Arizona State Univ.)
DTSTART:20241206T003000Z
DTEND:20241206T011000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/58
DESCRIPTION:Title: Pattern-avoiding polytopes and Cambrian lattices\nby Jianping P
an (Arizona State Univ.) as part of UCLA Combinatorics Seminar\n\nLecture
held in UCLA Boelter hall\, room 5436.\n\nAbstract\nIn 2017\, Davis and Sa
gan found that a pattern-avoiding Birkhoff subpolytope and an order polyto
pe have the same normalized volume. They ask whether the two polytopes are
unimodularly equivalent. We give an affirmative answer to a generalizatio
n of this question. \n\nFor each Coxeter element c in the symmetric group\
, we define a pattern-avoiding Birkhoff subpolytope\, and an order polytop
e of the heap poset of the c-sorting word of the longest permutation. We s
how the two polytopes are unimodularly equivalent. As a consequence\, we s
how the normalized volume of the pattern-avoiding Birkhoff subpolytope is
equal to the number of the longest chains in a corresponding Cambrian latt
ice. In particular\, when $c = s_1s_2…s_{n-1}$\, this resolves the quest
ion by Davis and Sagan.\n\nThis talk is based on joint work with E. Banaia
n\, S. Chepuri and E. Gunawan.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvester Zhang (UMN)
DTSTART:20250124T003000Z
DTEND:20250124T012000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/60
DESCRIPTION:Title: Rhombic Tableaux and Schubert Polynomials\nby Sylvester Zhang (
UMN) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6221.\n\n
Abstract\nWe introduce rhombic tableaux to give new combinatorial formulae
for Schubert polynomials corresponding to a partial flag variety. In the
case of Grassmanian\, rhombic tableaux recovers (reverse) semistandard You
ng tableaux. We discuss extensions to Stanley symmetric functions and K-th
eory\, and give a generalization of Bender-Knuth involution. This talk is
based on joint work with Ilani Axelrod-Freed and Jiyang Gao.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yassine El Maazouz (CalTech)
DTSTART:20250124T013000Z
DTEND:20250124T022000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/61
DESCRIPTION:Title: The positive orthogonal Grassmannian\nby Yassine El Maazouz (Ca
lTech) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6221.\n
\nAbstract\nThe Plücker positive region $\\text{OGr}_+(k\,2k)$ of the ort
hogonal Grassmannian emerged as the positive geometry behind the ABJM scat
tering amplitudes. We initiate the study of the positive orthogonal Grassm
annian $\\text{OGr}_+(k\,n)$ for general values of $k$ and $n$. We determi
ne the boundary structure of the quadric $\\text{OGr}_+(1\,n)$ in $\\mathb
b{P}^{(n-1)}_+$ and show that it is a positive geometry. We show that $\\t
ext{OGr}_+(k\,2k+1)$ is isomorphic to $\\text{OGr}_+(k+1\,2k+2)$ and conne
ct its combinatorial structure to matchings on $[2k+2]$. Finally\, we show
that in the case $n>2k+1$\, the positroid cells of $\\text{Gr}_+(k\,n)$ d
o not induce a CW cell decomposition of $\\text{OGr}_+(k\,n)$. This was jo
int work with Yelena Mandelshtam.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grant Barkley (Harvard)
DTSTART:20250221T003000Z
DTEND:20250221T030000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/62
DESCRIPTION:Title: The combinatorial invariance conjecture\nby Grant Barkley (Harv
ard) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6221.\n\n
Abstract\nLet $u$ and $v$ be two permutations of the numbers $1\,\\ldots\,
n$. Associated to $u$ and $v$ is a polynomial $P_{uv}$\, called the $\\tex
tit{Kazhdan-Lusztig polynomial}$\, which encodes numerical invariants that
are central in geometric representation theory. The coefficients of $P_{u
v}$ simultaneously describe the singularities of Schubert varieties\, the
structure of Hecke algebras\, and the representation theory of Lie algebra
s. Associated to $u$ and $v$ is another object\, the $\\textit{Bruhat grap
h}$ of $(u\,v)$\, which is a directed graph describing the transpositions
taking $u$ to $v$. \nThe $\\textit{combinatorial invariance conjecture}$ (
CIC) of Dyer and Lusztig asserts that the Bruhat graph of $(u\,v)$ uniquel
y determines $P_{uv}$. Recently\, Geordie Williamson and Google DeepMind a
pplied machine learning techniques to this problem. Using those techniques
\, they conjectured an explicit recursion that would compute $P_{uv}$ from
the Bruhat graph and thereby prove the CIC. In joint work with Christian
Gaetz\, we prove the Williamson-DeepMind conjecture in the case where $u$
is the identity permutation. Along the way\, we prove two new identities f
or the Kazhdan--Lusztig $R$ polynomials\, one of which implies new cases o
f the CIC.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Miranda (UCLA)
DTSTART:20250221T013000Z
DTEND:20250221T022000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/63
DESCRIPTION:Title: Flexible Periodic Surfaces\nby Robert Miranda (UCLA) as part of
UCLA Combinatorics Seminar\n\nLecture held in MS 6221.\n\nAbstract\nA pol
yhedral surface has a n-dimensional flex if there exists a continuous fami
ly of realizations $\\{Q_t : t \\in [0\,1]^n\\}$ which are pairwise noniso
morphic. Gaifullin and Gaifullin showed that if a 2-periodic polyhedral su
rface in is homeomorphic to a plane\, then it can have at most a 1-dimensi
onal periodic flex. Glazyrin and Pak later found an example of a 2-periodi
c polyhedral surface\, not homeomorphic to a plane\, which has a full 3-di
mensional periodic flex. In this talk\, we present a new construction for
a flexible 3-periodic polyhedral surfaces\, and discuss generalizations to
higher dimensions.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ada Stelzer (UIUC)
DTSTART:20250307T003000Z
DTEND:20250307T030000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/64
DESCRIPTION:Title: Crystals\, standard monomials\, and filtered RSK\nby Ada Stelze
r (UIUC) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6221.
\n\nAbstract\nConsider a variety $X$ in the space of matrices\, stable und
er the action of a product of general linear groups by row and column oper
ations. How does its coordinate ring decompose as a direct sum of irreduci
ble representations? We argue that this question is effectively studied by
imposing a crystal graph structure on the standard monomials of the defin
ing ideal of $X$ (with respect to some term order). For the standard monom
ials of "bicrystalline" ideals\, we obtain such a crystal structure from t
he crystal graph on monomials introduced by Danilov–Koshevoi and van Lee
uwen. This yields an explicit combinatorial rule we call "filtered RSK" fo
r their irreducible representation multiplicities. In this talk\, we will
explain our rule and show that Schubert determinantal ideals (among others
) are bicrystalline. Based on joint work with Abigail Price and Alexander
Yong\, https://arxiv.org/abs/2403.09938\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Esther Banaian (UC Riverside)
DTSTART:20250307T013000Z
DTEND:20250307T022000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/65
DESCRIPTION:Title: Positivity and Structure of Generalized Cluster Algebras\nby Es
ther Banaian (UC Riverside) as part of UCLA Combinatorics Seminar\n\nLectu
re held in MS 6221.\n\nAbstract\nMotivated by relations amongst lambda len
gths on an orbifold\, Chekhov and Shapiro introduced generalized cluster a
lgebras\, which have the same structure as ordinary cluster algebras but w
hose mutation polynomials can have arbitrarily many terms. We focus on gen
eralized cluster algebras which arise from orbifolds and exhibit combinato
rial expansion formulas for their cluster variables. These expressions can
be phrased in terms of perfect matching of certain graphs (an analogue of
the snake graphs from Musiker-Schiffler-Williams) or in terms of order id
eals of a poset. The formulas make the positivity of the cluster variables
evident and also can be used as a tool to prove structural properties suc
h as linear independence of cluster monomials. Time-permitting\, we will a
lso discuss how these expansion formulas illuminate a connection between t
hese cluster variables and indecomposable modules of a finite-dimensional
algebra. This talk is based on past and current works with Wonwoo Kang\, E
zgi Kantarci Oguz\, Elizabeth Kelley\, Yadira Valdivieso\, and Emine Yildi
rim.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaku Liu (UW)
DTSTART:20250410T233000Z
DTEND:20250411T022000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/66
DESCRIPTION:Title: A regular unimodular triangulation of the matroid base polytope
\nby Gaku Liu (UW) as part of UCLA Combinatorics Seminar\n\nLecture held i
n MS 6627.\n\nAbstract\nWe produce the first regular unimodular triangulat
ion of an arbitrary matroid base polytope. We then extend our triangulat
ion to integral generalized permutahedra. Prior to this work it was unknow
n whether each matroid base polytope admitted a unimodular cover. I will a
lso discuss connections to other open problems in matroid theory\, namely
White's conjecture.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Martinez (UCLA)
DTSTART:20250411T003000Z
DTEND:20250411T012000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/67
DESCRIPTION:Title: Affine Deodhar Diagrams and Rational Dyck Paths\nby Thomas Mart
inez (UCLA) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 66
27.\n\nAbstract\nGiven a bounded affine permutation $f$\, we introduce a
ffine Deodhar diagrams for $f$\, similar to affine pipe dreams introduced
by Snider. We explore combinatorial moves between these diagrams and\, as
an application\, use these moves to establish a bijection between Deodhar
diagrams and rational Dyck paths for a special class of bounded affine per
mutations. This resolves an open problem posed by Galashin and Lam.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Gladkov (UCLA)
DTSTART:20250509T003000Z
DTEND:20250509T012000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/68
DESCRIPTION:Title: Gadgets in percolation\nby Nikita Gladkov (UCLA) as part of UCL
A Combinatorics Seminar\n\nLecture held in MS 6627.\n\nAbstract\nSuppose t
hat\, due to a marathon\, each street in Los Angeles has a 1/2 chance of b
eing closed. With nothing better to do\, your n friends\, who live in diff
erent parts of the city\, try to figure out which subgroups can still asse
mble. We explore the possible distributions over the set of resulting part
itions based on computer experiments and discuss the known inequalities.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daoji Huang (IAS)
DTSTART:20250529T233000Z
DTEND:20250530T002000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/69
DESCRIPTION:Title: Affine Robinson--Schensted correspondence via growth diagrams\n
by Daoji Huang (IAS) as part of UCLA Combinatorics Seminar\n\nLecture held
in MS 6221.\n\nAbstract\nThe Robinson--Schensted correspondence is one of
the most fundamental tools in algebraic combinatorics. Besides the usual
introduction as a combinatorial algorithm\, this correspondence can be enc
oded in Viennot's shadow line construction and equivalently by Fomin's gro
wth diagrams\, whose geometric interpretation\, which connects to Springer
theory\, is given by van Leeuwen. Motivated by Kazhdan--Lusztig theory\,
Shi introduced the analogue of the Robinson--Schensted correspondence for
the affine Weyl group of type A via an insertion algorithm. We generalize
Fomin's growth diagram and Viennot's shadow line construction to the affin
e setting\, recover and refine Shi's correspondence\, and give geometric i
nterpretations in the style of van Leeuwen. This is ongoing joint work wit
h Sylvester Zhang.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Galashin (UCLA)
DTSTART:20250530T003000Z
DTEND:20250530T012000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/71
DESCRIPTION:Title: Amplituhedra and origami\nby Pavel Galashin (UCLA) as part of U
CLA Combinatorics Seminar\n\nLecture held in MS 6221.\n\nAbstract\nI will
explain a proof of the BCFW triangulation conjecture which states that the
cells appearing in the Britto–Cachazo–Feng–Witten (BCFW) recursion
triangulate the amplituhedron (in full generality at all loop levels). The
key ingredient is a relation to origami crease patterns which are planar
graphs with faces colored black and white\, embedded in the plane so that
the sum of black (equivalently\, white) angles at each vertex is 180°. Al
ong the way\, we prove conjectures of Chelkak–Laslier–Russkikh and Ken
yon–Lam–Ramassamy–Russkikh on the existence of such origami embeddin
gs of arbitrary planar graphs\, which originated from the works of Kenyon
and Smirnov on the conformal invariance of the dimer and Ising models.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamás Kátay (UCLA)
DTSTART:20251202T000000Z
DTEND:20251202T010000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/72
DESCRIPTION:Title: Elusive properties of countably infinite graphs\nby Tamás Kát
ay (UCLA) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 5147
.\n\nAbstract\nA graph property is elusive (or evasive) if any algorithm t
esting it by asking questions of the form "Is there an edge between vertic
es x and y?" must\, in the worst case\, examine all pairs of vertices. Elu
sive properties of finite graphs have been extensively studied since the 7
0s. For infinite graphs\, they were first studied by Csernák and Soukup i
n 2021. I will give a brief introduction to elusive properties via games\,
and then I will talk about some of our new results in the countably infin
ite case.\n\n\nJoint work with Márton Elekes and Anett Kocsis. 80% of the
talk requires only very elementary knowledge in graph theory.\n\njoint ta
lk with the UCLA Logic Colloquium\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oriol Solé-Pi (MIT)
DTSTART:20251020T230000Z
DTEND:20251021T000000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/73
DESCRIPTION:Title: Graph structure and soficity\nby Oriol Solé-Pi (MIT) as part o
f UCLA Combinatorics Seminar\n\nLecture held in MS 5147.\n\nAbstract\nA ra
ndom rooted graph is said to be sofic if it is the Benjamini-Schramm limit
of a sequence of finite graphs. Perhaps surprisingly\, our understanding
of which graphs are sofic is still quite limited. For starters\, sofic gra
phs are known to possess a certain property known as unimodularity. (Unimo
dular random rooted graphs can also be encoded by graphings of pmp Borel e
quivalence relations.) However\, in a recent breakthrough\, Bowen\, Chapma
n\, Lubotzky and Vidick have shown that not all unimodular graphs are sofi
c. In this talk\, I will give an overview of what is known in the other di
rection: Which additional conditions on the graph are known to imply sofic
ity? Two important properties which I will talk about here are hyperfinite
ness and treeability. Then\, I will discuss a novel result along these lin
es: For any finite graph H\, every one-ended\, unimodular graph which does
not have H as a minor must be sofic. The proof of this result proceeds by
showing that all unimodular graphs of this kind are "almost" treeable.\n\
njoint talk with the UCLA Logic Colloquium\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvester Zhang (UCLA)
DTSTART:20251009T210000Z
DTEND:20251009T220000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/74
DESCRIPTION:Title: Mixed Pipedreams\nby Sylvester Zhang (UCLA) as part of UCLA Com
binatorics Seminar\n\nLecture held in MS 5203.\n\nAbstract\nI will discuss
the combinatorics of skew semistandard Young tableaux and their connectio
n to Richardson varieties in the Grassmannian\, and introduce mixed pipedr
eams\, a combinatorial model for Lenart-Sottile’s skew Schubert polynomi
als. These polynomials correspond to Richardson varieties in the full flag
variety. This talk is based on on-going work with Tianyi Yu and Jiyang Ga
o.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Soskin (UCLA)
DTSTART:20251016T210000Z
DTEND:20251016T220000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/75
DESCRIPTION:Title: Multiplicative inequalities for Lorentzian matrices\nby Daniel
Soskin (UCLA) as part of UCLA Combinatorics Seminar\n\nLecture held in MS
5203.\n\nAbstract\nA symmetric matrix with nonnegative real entries is cal
led a Lorentzian matrix if it has at most one positive eigenvalue. One out
of the many examples of Lorentzian matrices is given by mixed volumes\n$$
v_{ij} = V (P_i\, P_j \, K_1\,\\ldots\, K_{n−2})\,$$ of convex bodies $K
_1\, \\ldots\, K_{n−2}\, P_1\, \\ldots\, P_m ⊂ \\mathbb{R}^n$. Classic
al Alexandrov–Fenchel inequality claims that $v_{ij}^2 ≥ v_{ii}v_{jj}$
. A more general inequality $v_{ki}v_{kj} \\geq v_{kk}v_{ij}$ is a specia
l case of the reverse Khovanskii–Teissier inequalities\, whose variants
appear in Brunn–Minkowski theory\, and in works of Weil.\n\n\nMultiplica
tive inequalities have been studied in matrix entries and minors for Total
ly positive and Positive semidefinite matrices\, as well as for regular fu
nctions defined on positive loci of cluster varieties. I will discuss rece
nt results on multiplicative inequities in entries of Lorentzian matrices\
, Alexandrov–Fenchel and reverse Khovanskii–Teissier inequalities are
simple examples of those (joint work with D.Huang\, J.Huh\, and B.Wang\, 2
025+). We show that the set of multiplicative generators of inequalities i
n matrix entries of Lorentzian matrices correspond to the extreme rays of
the dual cone of the so called Cut cone. Cut cone was thoroughly studied b
y M.Deza and M.Laurent in the context of metric geometry\, graph theory\,
and combinatorial optimization. In particular\, we discover new families o
f inequalities which are in some sense stronger than previously known\, as
well as we study the optimal multiplicative constants for such inequaliti
es. The main tools we employed are multi-variable calculus\, linear algebr
a and Gromov’s $\\delta$-hyperbolic metrics on n points. I will also pre
sent two conjectures observing phenomena aligned with previous studies of
multiplicative inequalities mentioned earlier.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Gagnon (USC)
DTSTART:20251106T230000Z
DTEND:20251107T000000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/77
DESCRIPTION:Title: Quasisymmetric and Coxeter flag varieties\nby Lucas Gagnon (USC
) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 5203.\n\nAbs
tract\nIn algebraic combinatorics\, the terms $\\textit{Coxeter--Catalan}$
and $\\textit{quasisymmetric}$ describe two common philosophies for gener
alizing classical objects and deepening results. One area where neither
philosophy has made serious headway is the Schubert calculus of the comple
te flag variety. In this talk I will introduce a toric complex $\\mathrm
{QFl}$ inside the complete flag variety which is simultaneously a quasisym
metric and Coxeter-Catalan generalization. In the remaining time I wi
ll convince you that: (i) $\\mathrm{QFl}$ is the `right' generalization\,
because its combinatorics are nice enough to do actual computations\; and
(ii) $\\mathrm{QFl}$ is an `interesting' generalization because it is stil
l connected to classical Schubert calculus. Based on work with N. Berger
on\, P. Nadeau\, H. Spink\, and V. Tewari.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swee Hong Chan (Rutgers)
DTSTART:20251120T220000Z
DTEND:20251120T230000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/79
DESCRIPTION:Title: Spanning trees and continued fractions\nby Swee Hong Chan (Rutg
ers) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 5203.\n\n
Abstract\nConsider the set of positive integers representing the number of
spanning trees in simple graphs with n vertices. How quickly can this set
grow as a function of n? In this talk\, we discuss a proof of the expone
ntial growth of this set\, which resolves an open problem of Sedlacek from
1966. The proof uses a connection with continued fractions and advances t
owards Zaremba’s conjecture in number theory. This is joint work with Al
ex Kontorovich and Igor Pak. This talk is intended for general audience.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sinai Robins (University of São Paulo)
DTSTART:20251023T210000Z
DTEND:20251023T220000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/80
DESCRIPTION:Title: The Siegel-Bombieri method in the geometry of numbers\, through the
lens of Fourier\nby Sinai Robins (University of São Paulo) as part o
f UCLA Combinatorics Seminar\n\nLecture held in MS 5203.\n\nAbstract\nWe e
xtend some classical results in the geometry of numbers\, obtained by C. L
. Siegel (1935)\, and E. Bombieri (1962)\, both of whom extended Minkowski
’s first theorem for convex\, centrally symmetric bodies. A discrete v
ersion of these results allows us to give some discrete analogues of the S
iegel-Bombieri formulas\, for any finite set of integer points in Euclidea
n space\, using finite covariograms. We’ll give visual examples\, with
pictures in dimension 2. On the other hand\, a continuous application o
f these results allows us to shed additional light on the enumeration of l
attice points in polytopes in $\\mathbb{R}^d$\, and more generally in comp
act subsets of $\\mathbb{R}^d$. This is joint work with Michel Faleiros.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Skopenkov (KAUST)
DTSTART:20260129T220000Z
DTEND:20260129T230000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/81
DESCRIPTION:Title: Incidences\, tilings\, and fields\nby Mikhail Skopenkov (KAUST)
as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6201.\n\nAbst
ract\nIncidence theorems about points and lines in the plane are at the co
re of projective geometry\, and their automated proofs are studied in math
ematical logic. One approach to such proofs\, which originated from Coxete
r/Greitzer’s proof of Pappus’ theorem\, is multiple applications of Me
nelaus's theorem. Richter-Gebert\, Fomin\, and Pylyavskyy visualized them
using triangulated surfaces. We investigate which incidence theorems can o
r cannot be proved in this way. We show that\, in addition to triangulated
surfaces\, one can use simplicial complexes satisfying a certain excision
property. This property holds\, for instance\, for the generalization of
gropes that we provide. We introduce a hierarchy of classes of theorems ba
sed on the underlying topological spaces. We show that this hierarchy does
not collapse over R by considering the same theorems over finite fields.
This is joint work with P. Pylyavskyy.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tianyi Yu (UQAM)
DTSTART:20260219T220000Z
DTEND:20260219T230000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/82
DESCRIPTION:Title: A positive combinatorial formula for the double Edelman--Greene coe
fficients\nby Tianyi Yu (UQAM) as part of UCLA Combinatorics Seminar\n
\nLecture held in MS 6201.\n\nAbstract\nLam\, Lee\, and Shimozono introduc
ed the double Stanley symmetric functions in their study of the equivarian
t geometry of the affine Grassmannian.They proved that the associated doub
le Edelman--Greene coefficients\, the double Schur expansion coefficients
of these functions\, are positive\, a result later refined by Anderson. Th
ey further asked for a combinatorial proof of this positivity. In this pap
er\, we provide the first such proof\, together with a combinatorial formu
la that manifests the finer positivity established by Anderson. Our formul
a is built from two combinatorial models: bumpless pipedreams and increasi
ng chains in the Bruhat order. The proof relies on three key ingredients:
a correspondence between these two models\, a natural subdivision of bumpl
ess pipedreams\, and a symmetry property of increasing chains. This talk i
s based on joint work with Jack Chou.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fan Zhou (Columbia)
DTSTART:20260122T220000Z
DTEND:20260122T230000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/83
DESCRIPTION:Title: Categorifying Jacobi-Trudi\nby Fan Zhou (Columbia) as part of U
CLA Combinatorics Seminar\n\nLecture held in MS 6201.\n\nAbstract\nThe Jac
obi-Trudi determinant identity is a famous formula for the Schur polynomia
ls\, which are central to the study of symmetric polynomials and arise as
"shadows" of simple representations of symmetric groups. A determinant can
\, of course\, be written as an alternating sum of products of entries in
the matrix\; a natural question is then whether this alternating sum can b
e lifted\, or ‘categorified'\, into a resolution such that the Euler-Fro
benius characteristic of the resolution recovers this determinant identity
. In other words\, it is natural to wonder if this determinant identity is
simply a ‘numerical shadow' of a deeper fact regarding modules\; this t
ype of ‘allegory-of-the-cave'-esque story is known as a ‘categorificat
ion'. In this talk we will outline a categorification of the Jacobi-Trudi
determinant identity using “KLR algebras”.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrés R. Vindas Meléndez (Harvey Mudd)
DTSTART:20260205T220000Z
DTEND:20260205T230000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/84
DESCRIPTION:Title: q-Chromatic polynomials\nby Andrés R. Vindas Meléndez (Harvey
Mudd) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6201.\n
\nAbstract\nWe introduce and study a $q$-version of the chromatic polynomi
al of a given graph $G=(V\,E)$\, namely\, $\\chi_G^\\lambda(q\,n):=\n\\sum
_{{\\text{proper colorings} c:V\\to[n]}} q^{ \\sum_{ v \\in V } \\lambda_v
c(v) }$\, where $\\lambda \\in \\mathbb{Z}^V$ is a fixed linear form. Vi
a work of Chapoton (2016) on $q$-Ehrhart polynomials\, $\\chi_G^\\lambda(q
\,n)$ turns out to be a polynomial in the $q$-integer $[n]_q$\, with coeff
icients that are rational functions in $q$. Additionally\, we prove struct
ural results for $\\chi_G^\\lambda(q\,n)$ and exhibit connections to neigh
boring concepts\, e.g.\, chromatic symmetric functions and the arithmetic
of order polytopes. We offer a strengthened version of Stanley's conjectur
e that the chromatic symmetric function distinguishes trees\, which leads
to an analogue of $P$-partitions for graphs. This is joint work with Esme
Bajo (San Diego Miramar College) and Matthias Beck (San Francisco State).\
n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuhan Jiang (UC Berkeley)
DTSTART:20260312T210000Z
DTEND:20260312T220000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/85
DESCRIPTION:Title: A basis of the alternating diagonal coinvariants and a decompositio
n of $m$-Dyck paths\nby Yuhan Jiang (UC Berkeley) as part of UCLA Comb
inatorics Seminar\n\nLecture held in MS 6201.\n\nAbstract\nThe ring of dia
gonal coinvariants is widely studied in the context of the shuffle conject
ure\, and its alternating part exhibits $q\,t$-Catalan combinatorics. We c
onstruct an explicit vector space basis in terms of bivariate Vandermonde
determinants for the alternating component of the diagonal coinvariant rin
g $DR_n$\, answering a question of Stump. As a Corollary\, we recover the
combinatorial formula of the $q\,t$-Catalan numbers. Moreover\, we constru
ct a decomposition of an $m$-Dyck path into an $m$-tuple of Dyck paths suc
h that the area sequence and bounce sequence of the $m$-Dyck path is entry
wise the sum of the area sequences and bounce sequences of the Dyck paths
in the tuple. We conjecture that this decomposition gives a basis for the
alternating component of the generalized diagonal coinvariants $DR_n^{(m)}
$.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abhishek Dhawan (UIUC)
DTSTART:20260402T210000Z
DTEND:20260402T220000Z
DTSTAMP:20260314T084834Z
UID:ucla_comb_sem/86
DESCRIPTION:by Abhishek Dhawan (UIUC) as part of UCLA Combinatorics Semina
r\n\nLecture held in MS 6201.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/86/
END:VEVENT
END:VCALENDAR