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BEGIN:VEVENT
SUMMARY:Dongkwan Kim (University of Minnesota)
DTSTART:20201001T170000Z
DTEND:20201001T180000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/1
DESCRIPTION:Title: Robinson-Schensted correspondence for natural unit interval o
rders\nby Dongkwan Kim (University of Minnesota) as part of UCLA Combi
natorics Seminar\n\n\nAbstract\nStanley-Stembridge conjecture\, currently
one of the most famous conjectures in algebraic combinatorics\, asks wheth
er a certain generating function with respect to a natural unit interval o
rder is a nonnegative linear combination of complete homogeneous symmetric
functions. There are many partial progress on this conjecture\, including
its connection with the geometry of Hessenberg varieties. \n\nIn this tal
k we study the Schur positivity\, which is originally proved by Haiman and
Gasharov. We define an analogue of Knuth moves with respect to a natural
unit interval order and study its equivalence classes in terms of D graphs
introduced by Assaf. Then\, we show that if the given order avoids certai
n two suborders then an analogue of Robinson-Schensted correspondence is w
ell-defined\, which proves that the generating function attached to each e
quivalence class is Schur positive. It is hoped that it proposes a new com
binatorial aspect to investigate the Stanley-Stembridge conjectures and co
homology of Hessenberg varieties. This work is joint with Pavlo Pylyavskyy
.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Pechenik (University of Waterloo)
DTSTART:20201008T170000Z
DTEND:20201008T180000Z
DTSTAMP:20260404T095121Z
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 Se
minar\n\n\nAbstract\nKnutson and Miller (2005) showed that the equivariant
cohomology class of a matrix Schubert variety $X_w$ is the corresponding
double Schubert polynomial $S_w$. Moreover\, after Gröbner degeneration w
ith respect to any antidiagonal term order\, the resulting irreducible com
ponents are naturally labeled by the pipe dreams for w. In later work with
Yong (2009)\, they used diagonal term orders to obtain alternative combin
atorics for certain $X_w$. We present further results in this direction\,
with connections to a neglected Schubert polynomial formula of Lascoux (20
02) 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 will be accessible to the general audience.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Sherman-Bennett (Harvard University/UC Berkeley)
DTSTART:20201015T170000Z
DTEND:20201015T180000Z
DTSTAMP:20260404T095121Z
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 Combinatorics Seminar\n\n\nAbstract\nOpen positroid varieties are sm
ooth irreducible subvarieties of the Grassmannian\, which can be naturally
defined using "positively realizable" matroids (positroids\, for short).
They were first introduced by Knutson\, Lam\, and Speyer\, motivated by w
ork of Postnikov on the totally nonnegative (real) Grassmannian and positr
oid cells. Open positroid varieties are indexed by a number of combinatori
al objects\, including families of plabic (i.e. planar bicolored) graphs.
\n\nI will discuss some algebraic information plabic graphs give us about
open positroid varieties. Together with Serhiyenko and Williams\, we showe
d that plabic graphs for an open Schubert variety $V$ (a special case of o
pen positroid varieties) give seeds for a cluster algebra structure on the
homogeneous coordinate ring of $V$. Among other things\, this implies tha
t plabic graphs give positivity tests for elements of $V$. \n\nOur work g
eneralizes a result of Scott on the Grassmannian\, and confirms a longstan
ding folklore conjecture on Schubert varieties\; it was later generalized
to arbitrary positroid varieties by Galashin and Lam. I'll also discuss re
cent work with Fraser\, in which we show that relabeled plabic graphs also
give seeds for a cluster algebra structure on coordinate rings of open po
sitroid varieties\, uncovering another source for positivity tests. \n\nNo
knowledge of cluster algebras will be assumed in the talk.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swee Hong Chan (UCLA)
DTSTART:20201022T170000Z
DTEND:20201022T180000Z
DTSTAMP:20260404T095121Z
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 alway
s find two elements $x$\, $y$ of a partially ordered set\, such that\, the
probability that x is ordered before y when the poset is ordered randomly
\, is between $1/3$ and $2/3$?\nThis is the celebrated $1/3 - 2/3$ Conject
ure\, which has been called "one of the most intriguing problems in the co
mbinatorial theory of posets".\n\nWe will explore this conjecture for pose
ts that arise from (skew-shaped) Young diagrams\, where total orderings of
these posets correspond to standard Young tableaux. We will show that tha
t these probabilities are arbitrarily close to $1/2$\, by using random wal
k estimates and the state-of-the-art hook-length formulas of Naruse. \n\nT
his is a joint work with Igor Pak and Greta Panova. This talk is aimed at
a general audience.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Escobar (Washington University in St. Louis)
DTSTART:20201029T170000Z
DTEND:20201029T180000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/5
DESCRIPTION:Title: Which Schubert varieties are Hessenberg varieties?\nby La
ura Escobar (Washington University in St. Louis) as part of UCLA Combinato
rics Seminar\n\n\nAbstract\nSchubert varieties are subvarieties of the fla
g variety parametrized by permutations\; they induce an important basis fo
r the cohomology of the flag variety. Hessenberg varieties are also subvar
ieties of the flag variety with connections to both algebraic combinatoric
s and representation theory. I will discuss joint work with Martha Precup
and John Shareshian in which we investigate which Schubert varieties in th
e full flag variety are Hessenberg varieties.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abdul Basit (Iowa State University)
DTSTART:20201112T180000Z
DTEND:20201112T190000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/7
DESCRIPTION:Title: Point-box incidences and logarithmic density of semilinear gr
aphs\nby Abdul Basit (Iowa State University) as part of UCLA Combinato
rics Seminar\n\n\nAbstract\nZarankiewicz's problem in extremal graph theor
y asks for the maximum number of edges in a bipartite graph on $n$ vertice
s which does not contain a copy of $K_{k\,k}$\, the complete bipartite wit
h $k$ vertices in both classes. We will consider this question for inciden
ce graphs of geometric objects. Significantly better bounds are known in t
his setting\, in particular when the geometric objects are defined by syst
ems of algebraic inequalities. We show even stronger bounds under the addi
tional constraint that the defining inequalities are linear. We will also
discuss connections of these results to combinatorial geometry and model t
heory. \n\nNo background is assumed\, and the talk will be accessible to n
on-experts. Joint work with Artёm Chernikov\, Sergei Starchenko\, Terence
Tao\, and Chieu-Minh Tran.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonah Blasiak (Drexel University)
DTSTART:20201119T180000Z
DTEND:20201119T190000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/8
DESCRIPTION:Title: Crystal graphs\, katabolism\, and Schur positivity\nby Jo
nah Blasiak (Drexel University) as part of UCLA Combinatorics Seminar\n\n\
nAbstract\nKatabolism is a mysterious operation on tableaux which involves
cutting and reassembling the pieces\nusing Schensted insertion.\nIt is fe
atured in several Schur positivity conjectures related to\nk-Schur functio
ns and Hall-Littlewood polynomials.\nCrystal graphs are the combinatorial
skeletons of gl_n modules and are a powerful tool for connecting represent
ation theory and combinatorics. \nFor instance\, they give a beautiful exp
lanation of the RSK correspondence.\nUsing crystal graphs\, we uncover the
mystery behind katabolism and resolve a Schur positivity conjecture of Sh
imozono and Weyman.\nThis talk will include many pictures of crystals and
tableaux.\nThis is joint work with Jennifer Morse and Anna Pun.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Williams (UT Dallas)
DTSTART:20201203T180000Z
DTEND:20201203T190000Z
DTSTAMP:20260404T095121Z
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 w
ork on simultaneous cores for affine Weyl groups. In type A\, our uniform
formula recovers Drew Armstrong's conjecture for the average number of box
es in a simultaneous core. This is joint work with Marko Thiel and Eric St
ucky.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Bernardi (Brandeis University)
DTSTART:20201210T180000Z
DTEND:20201210T190000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/11
DESCRIPTION:Title: A Universal Tutte Polynomial\nby Olivier Bernardi (Brand
eis University) as part of UCLA Combinatorics Seminar\n\n\nAbstract\nWould
n't it be nice to have a polynomial expression parametrizing at once the T
utte polynomial of every matroid of a given size?\nIn this talk\, I will e
xplain how to achieve this goal. The solution involves extending the defin
ition of the Tutte polynomial from the setting of matroids to the setting
of polymatroids (this is akin to the generalization from graphs to hypergr
aphs)\, and adopting a geometric point-counting perspective. On our way\,
we will connect several notions: the activity-counting invariants of Kalma
n and Postnikov\, the point-counting invariants of Cameron and Fink\, and
the classical corank-nullity definition of the Tutte polynomial of matroid
s.\nThis is joint work with Tamas Kalman and Alex Postnikov.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swee Hong Chan (UCLA)
DTSTART:20210930T210000Z
DTEND:20210930T220000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/12
DESCRIPTION:Title: Log-concave inequalities for posets\nby Swee Hong Chan (
UCLA) as part of UCLA Combinatorics Seminar\n\nLecture held in UCLA Math S
ciences building\, room MS 3915A.\n\nAbstract\nThe study of log-concave in
equalities for combinatorial objects have seen much progress in recent yea
rs. One such progress is the solution to the strongest form of Mason's con
jecture (independently by Anari et. al. and Brándën-Huh) that the f-vect
ors of matroid independence complex is ultra-log-concave. In this talk\, w
e discuss a new proof of this result through linear algebra and discuss ge
neralizations to greedoids and posets. This is a joint work with Igor Pak.
\n\nThe talk is aimed at a general audience.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Petrov (UVA and MSRI)
DTSTART:20211014T210000Z
DTEND:20211014T220000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/13
DESCRIPTION:Title: Schur rational functions\, vertex models\, and random domino
tilings\nby Leonid Petrov (UVA and MSRI) as part of UCLA Combinatoric
s Seminar\n\nLecture held in UCLA Math Sciences Building\, room MS 3915A..
\n\nAbstract\nIt is known that Schur symmetric polynomials admit a number
of generalizations (Macdonald's 1992 variations) which retain determinanta
l structure - for example\, factorial and supersymmetric Schur functions.
We describe an overarching family of Schur-like rational functions arising
as partition functions of fully inhomogeneous free fermion six vertex mod
el. These functions are indexed by partitions\, have as variables the pair
s $(x_i\,r_i)$\, $i=1\,...\,N$\, of horizontal rapidities and spin paramet
ers\; and\, moreover\, depend on vertical rapidities and spin parameters $
(y_j\,s_j)$\, $j>=1$. We establish determinantal formulas\, orthogonality\
, Cauchy identities\, and other properties of our functions. We also intro
duce random domino tiling models based on the Schur rational functions (a
la Schur processes of Okounkov-Reshetikhin 2001)\, and obtain bulk (lattic
e) asymptotics leading to a new deformation of the extended discrete sine
kernel. Based on the joint project https://arxiv.org/abs/2109.06718 with A
. Aggarwal\, A. Borodin\, and M. Wheeler.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yibo Gao (MIT)
DTSTART:20211028T170000Z
DTEND:20211028T180000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/14
DESCRIPTION:Title: The canonical bijection between pipe dreams and bumpless pip
e dreams\nby Yibo Gao (MIT) as part of UCLA Combinatorics Seminar\n\nL
ecture 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 bet
ween these two objects since bumpless pipe dreams were introduced by Lam\,
Lee and Shimozono. In this talk\, we present such a bijection and establi
sh its canonical nature by showing that it preserves Monk's rule. This is
joint work with Daoji Huang.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Terrence George (University of Michigan)
DTSTART:20211104T210000Z
DTEND:20211104T220000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/15
DESCRIPTION:Title: Electrical networks and Lagrangian Grassmannians\nby Ter
rence George (University of Michigan) as part of UCLA Combinatorics Semina
r\n\n\nAbstract\nCactus networks were introduced by Thomas Lam as a genera
lization of planar electrical networks.\nHe defined a map from these netwo
rks to a Grassmannian and showed that the image of this map lies inside th
e totally nonnegative part of this Grassmannian. We show that the image of
Lam's map consists of exactly the elements that are both totally nonnegat
ive and isotropic for a particular skew-symmetric bilinear form. This is j
oint work with Sunita Chepuri and David Speyer.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Suho Oh (Texas State)
DTSTART:20211118T220000Z
DTEND:20211118T230000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/16
DESCRIPTION:Title: Extending Shellings\nby Suho Oh (Texas State) as part of
UCLA Combinatorics Seminar\n\n\nAbstract\nShellable complexes are simplic
ial complexes with the shelling property: their facets can be ordered nice
ly\, which translates to interesting properties in algebra and combinatori
cs. Simon in 1994 conjectured that any shellable complex can be extended t
o 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 will be going over a recent joint work with M. Coleman\, A. Dochterman
n and N. Geist on proving this conjecture for a smaller class.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Josh Swanson (USC)
DTSTART:20211007T210000Z
DTEND:20211007T220000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/17
DESCRIPTION:Title: Combinatorics of harmonic polynomial differential forms\
nby Josh Swanson (USC) as part of UCLA Combinatorics Seminar\n\nLecture he
ld in UCLA Math Sciences Building\, room MS 3915A..\n\nAbstract\nA recent
conjecture of Zabrocki introduced super diagonal coinvariant algebras as a
representation-theoretic model for the Delta conjecture of Haglund--Remme
l--Wilson. Subsequent work with Wallach introduced a basis for the alterna
ting component of the super coinvariant algebra consisting of explicit har
monic polynomials in commuting and anti-commuting variables. We will discu
ss two families of relations involving these harmonics\, which are related
to Tanisaki ideals and which we call Tanisaki witness relations. This tal
k will focus on the combinatorics of these objects rather than the underly
ing abstract motivation.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolle Gonzalez (UCLA)
DTSTART:20211021T210000Z
DTEND:20211021T220000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/18
DESCRIPTION:Title: From symmetric functions\, to knots\, and back again.\nb
y Nicolle Gonzalez (UCLA) as part of UCLA Combinatorics Seminar\n\nLecture
held in UCLA Math Sciences Building\, room MS 3915A.\n\nAbstract\nFor fou
rteen years the shuffle conjecture remained open. In essence\, it gave a c
ombinatorial formula for the Frobenius character of the space of diagonal
harmonics in terms of word parking functions\, which are certain symmetric
functions that can be indexed by lattice paths. Concretely\, the conjectu
re stated that this combinatorial sum was equal to the action of the ubiqu
itous nabla operator on the nth elementary symmetric polynomial. In a star
tling paper\, Carlsson and Mellit proved this conjecture by introducing a
new algebra\, closely related to the double affine Hecke algebra\, called
$A_{q\,t}$ and defining an important polynomial action for it. This algebr
a allowed them to perform operations on symmetric functions by lifting the
corresponding structures via raising and lowering operators to certain hi
gher level polynomial rings\, performing the computations there\, and then
projecting them back. Shortly thereafter\, using parabolic flag Hilbert s
chemes\, the algebra and its representation was also realized geometricall
y by Carlsson\, Gorsky\, and Mellit\, reaffirming its connection to the wo
rk Haiman on the space of diagonal harmonics. I will introduce a topologic
al interpretation of this algebra and its representation. Namely\, I will
describe how we can realize symmetric functions and the $A_{q\,t}$ operato
rs as braid diagrams on an annulus and how many of the complicated algebra
ic relations using plethysms in the original formulation follow trivially
from isotopy of the diagrams. This paradigm not only eases many computatio
ns\, it also informs us of new operators on symmetric functions that while
natural from a topological perspective might be very difficult to see alg
ebraically\, thus yielding new light on an already rich structure. Of part
icular interest is its ability to potentially explain the many conjectures
relating the homology of the toric links and q\,t combinatorics.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:GaYee Park (UMass Amherst)
DTSTART:20211012T170000Z
DTEND:20211012T180000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/19
DESCRIPTION:Title: Minimal semi-standard skew tableaux and the Hillman-Grassl c
orrespondence\nby GaYee Park (UMass Amherst) as part of UCLA Combinato
rics Seminar\n\nLecture held in *Virtual only*.\n\nAbstract\nStandard tabl
eaux of skew shape are fundamental objects in\nenumerative and algebraic c
ombinatorics and no product formula for the\nnumber is known. In 2014\, Na
ruse gave a formula as a positive sum over\nexcited diagrams of products o
f hook-lengths. In 2018\, Morales\, Pak\, and\nPanova gave a $q$-analogue
of Naruse's formula for semi-standard tableaux\nof skew shapes. They also
showed\, partly algebraically\, that the\nHillman-Grassl map restricted to
skew shapes gave their $q$-analogue. We\nstudy the problem of making this
argument completely bijective. For a skew\nshape\, we define a new set of
semi-standard Young tableaux\, called the\nminimal SSYT\, that are equinu
merous with excited diagrams via a new\ndescription of the Hillan-Grassl b
ijection and have a version of excited\nmoves. Lastly\, we relate the mini
mal skew SSYT with the terms of the\nOkounkov-Olshanski formula for counti
ng SYT of skew shape. This is joint\nwork with Alejandro Morales and Greta
Panova.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Sherman-Bennett (University of Michigan)
DTSTART:20211116T220000Z
DTEND:20211116T230000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/20
DESCRIPTION:Title: The hypersimplex and the m=2 amplituhedron\nby Melissa S
herman-Bennett (University of Michigan) as part of UCLA Combinatorics Semi
nar\n\nLecture held in MS 6627 (!).\n\nAbstract\nI'll discuss a curious co
rrespondence between the $m=2$ amplituhedron\, a $2k$-dimensional subset o
f $\\mathrm{Gr}(k\, k+2)$\, and the hypersimplex\, an $(n-1)$-dimensional
polytope in $\\mathbb R^n$. The amplituhedron and hypersimplex are both im
ages of the totally nonnegative Grassmannian under some map (the amplituhe
dron map and the moment map\, respectively)\, but are different dimensions
and live in very different ambient spaces. I'll talk about joint work wit
h Matteo Parisi and Lauren Williams in which we give a bijection between d
ecompositions of the amplituhedron and decompositions of the hypersimplex
(originally 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 $m=2$ amp
lituhedron into Eulerian-number-many chambers\, inspired by an analogous h
ypersimplex decomposition.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marianna Russkikh (MIT)
DTSTART:20211109T180000Z
DTEND:20211109T190000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/21
DESCRIPTION:Title: Dimers and circle patterns\nby Marianna Russkikh (MIT) a
s part of UCLA Combinatorics Seminar\n\n\nAbstract\nThe dimer model is a m
odel from statistical mechanics corresponding to random perfect matchings
on graphs. Circle patterns are a class of embeddings of planar graphs such
that every face admits a circumcircle. We describe how to construct a 't-
embedding' (or a circle pattern) of a dimer planar graph using its Kastele
yn weights\, and discuss algebro-geometric properties of these embeddings.
\nThis new class of embeddings is the key for studying Miquel dynamics\, a
discrete integrable system on circle patterns: we identify Miquel dynamic
s on the space of square-grid circle patterns with the Goncharov-Kenyon di
mer dynamics and deduce the integrability of the former one and show that
the evolution is governed by cluster algebra mutations.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hunter Spink (Stanford)
DTSTART:20211202T220000Z
DTEND:20211202T230000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/22
DESCRIPTION:Title: Anti-concentration of random walks on model-theoretic defina
ble sets\nby Hunter Spink (Stanford) as part of UCLA Combinatorics Sem
inar\n\n\nAbstract\nClassical anti-concentration results show that random
walks in $\\mathbb{R}^d$ with BIG independent steps can’t concentrate in
balls much better than they can concentrate on individual points.\n\nMode
l-theoretic *definable sets* include Boolean combinations of subsets of $\
\mathbb{R}^d$ defined using equalities and inequalities of arbitrary compo
sitions of polynomials\, $e^x$\, $\\ln(x)$ and analytic functions restrict
ed to compact 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 discuss recent results which show that random walks in $\\mathbb{R}^
d$ with ARBITRARY independent steps can’t concentrate in definable sets
not containing line segments much better than they can concentrate on indi
vidual points. Time permitting\, I will discuss how these results extend t
o other groups like $\\mathrm{GL}_d(\\mathbb{R})$.\n\nJoint work with Jaco
b Fox and Matthew Kwan.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allen Knutson (Cornell)
DTSTART:20211204T000000Z
DTEND:20211204T010000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/23
DESCRIPTION:Title: The commuting scheme and generic pipe dreams\nby Allen K
nutson (Cornell) as part of UCLA Combinatorics Seminar\n\nLecture held in
! MS 5225 !.\n\nAbstract\nThe space of pairs of commuting matrices is more
mysterious than you\nmight think -- in particular\, Hochster's 1984 conje
cture that it is\nreduced remains unresolved. I'll explain how to degenera
te it to one\ncomponent of the "lower-upper scheme" {(X\,Y) : XY lower tri
angular\,\nYX upper triangular}\, a reduced complete intersection\, and ho
w to\ncompute the degree of any component as a sum over "generic pipe drea
ms".\nAs a consequence\, this recovers both the "pipe dream" and\n"bumples
s pipe dream" formulae for double Schubert polynomials.\nSome of this work
is joint with Paul Zinn-Justin.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Karpenkov (University of Liverpool)
DTSTART:20220414T210000Z
DTEND:20220414T220000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/24
DESCRIPTION:Title: Combinatorics and Geometry of Markov numbers\nby Oleg Ka
rpenkov (University of Liverpool) as part of UCLA Combinatorics Seminar\n\
nLecture held in MS 7608.\n\nAbstract\nMarkov numbers are positive solutio
ns to the Markov Diophantine equation $x^2+y^2+z^2=3xyz$. The set of Marko
v numbers can be very simple\, generated iteratively starting with the sma
llest solution $(1\,1\,1)$\, which defines a natural binary tree structure
on the set of all solutions. Markov numbers appear in the study of intege
r minima of quadratic forms\, cluster algebra\, etc.\n\nIn this talk we in
troduce generalized Markov numbers and extend the classical Markov theory.
We show that the principles hidden in Markov's theory are much broader an
d can be substantively extended beyond the limits of Markov's theory.\n\nI
n particular we discuss recursive properties for these numbers and find co
rresponding values in the Markov spectrum. Further we give a counterexampl
e to the generalized Markov uniqueness conjecture. The proposed generaliza
tion is based on geometry of numbers\, it substantively uses lattice trigo
nometry and geometric theory of continued numbers.\n\nThe talk is accessib
le to the general audience.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugene Gorsky (UC Davis)
DTSTART:20221006T210000Z
DTEND:20221006T220000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/25
DESCRIPTION:Title: Cluster structures on braid varieties\nby Eugene Gorsky
(UC Davis) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 760
8.\n\nAbstract\nGiven a positive braid\, one can define a smooth affine al
gebraic variety called the braid variety. Braid varieties generalize sever
al important varieties in Lie theory such as open Richardson and positroid
varieties. I will construct a cluster structure on a braid variety of arb
itrary type using combinatorial objects called weaves. This is a joint wor
k with Roger Casals\, Mikhail Gorsky\, Ian Le\, Linhui Shen and Jose Simen
tal.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Be'eri Greenfeld (UCSD)
DTSTART:20221027T233000Z
DTEND:20221028T001000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/26
DESCRIPTION:Title: Growth of unbounded subsets in nilpotent groups and random m
apping statistics\nby Be'eri Greenfeld (UCSD) as part of UCLA Combinat
orics Seminar\n\nLecture held in MS 6627.\n\nAbstract\nLet $G$ be an infin
ite group. Let $g(k\,n)$ be the maximum number of length-$n$ words over an
arbitrary $k$-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 fin
itely generated and residually finite then $g(k\,n)< k^n$ if and only if $
G$ is virtually nilpotent. It is then natural to ask how far $g(k\,n)$ can
get from $k^n$\; for $k$ fixed and $n$ tending to infinity\, $g(k\,n)$ is
polynomially bounded.\n\nWe quantify the Semple-Shalev Theorem at the oth
er extreme\, where $k=\\Theta(n)$. Specifically\, for a finitely generated
residually finite group $G$\, the ratio $g(k\,n)/k^n$ either tends to zer
o (if and only if $G$ is virtually abelian)\, or is greater than or equal
to an explicitly calculated optimal threshold. For higher- step free nilpo
tent groups\, this ratio tends to 1.\n\nAlong the way\, we find the probab
ility that a random function $f:[n]\\to [n]$ can be recovered from a suita
ble "inversion set"\, and geometrically interpret our results via random p
aths in $\\mathbb{Z}^n$ and the areas of their projected polygons. Finally
\, we provide a model-theoretic characterization of suboptimality of $g(k\
,n)$ by means of free sub-models and polynomial identities\, which enables
to generalize the discussion to various other classes of algebraic struct
ures.\n\nThis is a joint work with Hagai Lavner.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Colleen Robichaux (UCLA)
DTSTART:20221028T002000Z
DTEND:20221028T010000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/27
DESCRIPTION:Title: Degrees of Grothendieck polynomials and Castelnuovo-Mumford
regularity\nby Colleen Robichaux (UCLA) as part of UCLA Combinatorics
Seminar\n\nLecture held in MS 6627.\n\nAbstract\nWe give an explicit formu
la for the degree of a vexillary Grothendieck polynomial. This generalizes
a previous result of Rajchgot-Ren-Robichaux-St.Dizier-Weigandt for degree
s of symmetric Grothendieck polynomials. We apply these formulas to comput
e the Castelnuovo-Mumford regularity of certain Kazhdan-Lusztig varieties
coming from open patches of Grassmannians as well as the regularity of mix
ed one-sided ladder determinantal ideals. This is joint work with Jenna Ra
jchgot and Anna Weigandt.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (UC Davis)
DTSTART:20221028T011000Z
DTEND:20221028T015000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/28
DESCRIPTION:Title: Grid plabic graphs\, Legendrian weaves\, and (quasi-)cluster
structures\nby Daping Weng (UC Davis) as part of UCLA Combinatorics S
eminar\n\nLecture held in MS 6627.\n\nAbstract\nGiven a "grid" plabic grap
h on $\\mathbb{R}^2$\, we can construct a Legendrian link\, which is a lin
k in $\\mathbb{R}^3$ satisfying certain tangential conditions. We study a
moduli space problem associated with the Legendrian link\, and construct a
natural (quasi-)cluster structure on this moduli space using Legendrian w
eaves. In particular\, we prove that any braid variety associated with $\\
beta \\Delta$ for a 3-strand braid $\\beta$ admits cluster structures with
an explicit construction of initial seeds. We also construct Donaldson-Th
omas transformations for these moduli spaces.\n\nIn this talk\, I will int
roduce the theoretical background and describe the basic combinatorics for
constructing Legendrian weaves and the (quasi-)cluster structures from a
grid plabic graph. This is based on a joint work with Roger Casals (arXiv:
2204.13244).\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Korotkikh (MIT)
DTSTART:20221111T003000Z
DTEND:20221111T011000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/29
DESCRIPTION:Title: Spin $q$-Whittaker symmetric functions and vertex models.\nby Sergei Korotkikh (MIT) as part of UCLA Combinatorics Seminar\n\nLect
ure held in MS 6627.\n\nAbstract\nWe introduce a new family of symmetric f
unctions called spin $q$-Whittaker functions. We have found these function
s using solvable vertex model from mathematical physics and they basically
are defined by taking a specific sum over path ensembles on a square grid
. I will describe this construction from scratch and will explain how it l
eads to the following two properties. First property is the generalization
of Cauchy summation identity: an important identity from algebraic combin
atorics which encapsulates orthogonality relations for symmetric functions
. Second property is a unique structure of the vanishing points of our fun
ctions which leads to a characterization in terms of an interpolation prob
lem which is similar to the work of Okounkov from 1997 about interpolation
properties of symmetric functions. All necessary background on vertex mod
els and symmetric functions will be explained and\, time permitting\, I wi
ll also cover connections to probability and quantum groups.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Greta Panova (USC)
DTSTART:20221111T012000Z
DTEND:20221111T020000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/31
DESCRIPTION:Title: The world of poset inequalities\nby Greta Panova (USC) a
s part of UCLA Combinatorics Seminar\n\nLecture held in MS 6627.\n\nAbstra
ct\nPartially ordered sets are ubiquitous\, yet poorly understood structur
es in combinatorics. Counting their linear extensions and order preserving
maps do not have nice closed formulas and thus we can only hope to unders
tand them qualitatively or asymptotically in greater generality. In this t
alk I will show some inequalities relating linear extensions and order pre
serving maps for general posets. We will discuss various proofs\, problems
and conjectures. Based on a series of joint papers with Swee Hong Chan an
d Igor Pak.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tianyi Yu (UCSD)
DTSTART:20221130T003000Z
DTEND:20221130T011000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/32
DESCRIPTION:Title: Top degree components of Grothendieck and Lascoux polynomial
s\nby Tianyi Yu (UCSD) as part of UCLA Combinatorics Seminar\n\nLectur
e held in MS 6627.\n\nAbstract\nThe Schubert polynomials of the Symmetric
group of 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
$n!$. Another basis of this space is given by key polynomials\, which are
characters of the Demazure modules. Schubert and key polynomials are the `
`bottom layers'' of Grothendieck and Lascoux polynomials\, two inhomogeneo
us polynomials. 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 w
ay to compute 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 p
olynomials. This is a joint work with Jianping Pan.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cosmin Pohoata (IAS)
DTSTART:20221130T012000Z
DTEND:20221130T020000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/33
DESCRIPTION:Title: Convex polytopes from fewer points\nby Cosmin Pohoata (I
AS) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6627.\n\nA
bstract\nFinding the smallest integer N=ES_d(n) such that in every configu
ration of N points in R^d in general position there exist n points in conv
ex position is one of the most classical problems in extremal combinatoric
s\, known as the Erdos-Szekeres problem. In 1935\, Erdos and Szekeres famo
usly conjectured 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 recen
t proof that ES_d(n)=2^{o(n)} holds for all d≥3. Joint work with Dmitrii
Zakharov.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Gaetz (Cornell)
DTSTART:20230314T233000Z
DTEND:20230315T001000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/34
DESCRIPTION:Title: An SL(4) web basis from hourglass plabic graphs\nby Chri
stian Gaetz (Cornell) as part of UCLA Combinatorics Seminar\n\nLecture hel
d in MS 6221.\n\nAbstract\nThe SL(3) web basis is a special basis of certa
in spaces of tensor invariants developed in the late 90's by Khovanov and
Kuperberg as a tool for computing quantum link invariants. Since then this
basis has found connections and applications to cluster algebras\, canoni
cal bases\, dimer models\, and tableau combinatorics. The main open proble
m has remained: how to find a basis replicating the desirable properties o
f this basis for SL(4) and beyond? I will describe joint work with Oliver
Pechenik\, Stephan Pfannerer\, Jessica Striker\, and Josh Swanson in which
we construct such a basis for SL(4). Modified versions of plabic graphs a
nd the six-vertex model and new tableau combinatorics will appear along th
e way\, but knowledge of these topics won't be assumed in the talk.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Mazin (KSU)
DTSTART:20230315T002000Z
DTEND:20230315T010000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/35
DESCRIPTION:Title: Springer Fibers and Rational Dyck Paths\nby Mikhail Mazi
n (KSU) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6221.\
n\nAbstract\nAffine Grassmanian can be thought of as the space of linear s
ubspaces V in the space of Laurent power series C((t))\, invariant under m
ultiplication by t^n. It admits a cell decomposition with cells enumerated
by cofinite subsets in the set of non-negative integers\, invariant under
addition of n. An Affine Springer Fiber is a subvariety in the Affine Gra
ssmanian\, consisting of subspaces that are also invariant under the multi
plication by a fixed function f(t). If f(t)=t^m\, where n and m are relati
vely prime\, then the corresponding Affine Springer Fiber is particularly
well behaved: its intersection with a cell of the Affine Grassmanian is no
n-empty if and only if the corresponding subset of integers is also invari
ant under addition of m\, in which case the intersection itself is an affi
ne cell of a possibly smaller dimension. One can further see that the (m\,
n)-invariant subsets of integers are in bijection with the (m\,n)-Dyck pat
hs\, and the dimensions of cells are computed using the so-called dinv sta
tistic.\n\nIn this talk I will present a recent generalization of the abov
e construction 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)-invari
ant subsets satisfying an additional admissibility condition. Furthermore\
, such subsets turn out to be in bijection with the (m\,n)-Dyck paths\, an
d the dimensions of cells are again computed using the dinv statistic. The
talk is based on a joint work with Eugene Gorsky and Alexei Oblomkov (arX
iv:2210.12569).\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Black (UC Davis)
DTSTART:20231005T233000Z
DTEND:20231006T020000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/36
DESCRIPTION:Title: Monotone Paths on Polytopes in Combinatorics and Optimizatio
n\nby Alexander Black (UC Davis) as part of UCLA Combinatorics Seminar
\n\nLecture held in MS 6621.\n\nAbstract\nLinear programming is a core pro
blem in optimization\, and geometrically\, it is the problem of finding th
e highest point in some direction on a polytope. The standard combinatoria
l algorithm for solving linear programs is the simplex method\, which work
s by walking from vertex to vertex of the polytope along edges moving high
er at each 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 t
he main open problem in the area is to find a pivot rule that guarantees t
he path followed is always of polynomial length. In this talk\, I will dis
cuss an approach to this problem grounded in understanding the space of mo
notone paths on a polytope and pivot rules on a fixed linear program. The
key tools will be the fiber polytope construction of Billera and Sturmfels
and an analogous construction called the pivot rule polytope introduced b
y myself in joint work with De Loera\, Lütjeharms\, and Sanyal. My focus
will be on the many examples that arise from these constructions such as t
he permutahedron and associahedron.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yelena Mandelshtam (UC Berkeley)
DTSTART:20231005T233000Z
DTEND:20231006T020000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/37
DESCRIPTION:Title: Combinatorics of m=1 Grasstopes\nby Yelena Mandelshtam (
UC Berkeley) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6
621.\n\nAbstract\nThe amplituhedron is an object introduced by physicists
in 2013 arising from their study of scattering amplitudes which has garner
ed much recent attention from physicists and mathematicians alike. Mathema
tically\, it is a linear projection of a nonnegative Grassmannian to a sma
ller Grassmannian\, via a map induced by a totally positive matrix. A Gras
smann polytope\, or Grasstope\, is a generalization of the amplituhedron\,
defined to be such a projection by any matrix\, removing one of the posit
ivity conditions. In this talk\, I will discuss joint work with Dmitrii Pa
vlov and Lizzie Pratt in which we study these objects\, with hope that we
may gain new insights by broadening our horizons and studying all Grasstop
es.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Terrence George (UCLA)
DTSTART:20231005T233000Z
DTEND:20231006T020000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/38
DESCRIPTION:Title: Inverse problem for electrical networks\nby Terrence Geo
rge (UCLA) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 662
1.\n\nAbstract\nAn electrical network is a graph embedded in a disk with s
ome vertices on the boundary of the disk\, and with positive real numbers\
, called conductances\, associated to its edges. Associated to such an ele
ctrical network is its response matrix which encodes all information that
can be deduced by making electrical measurements on the boundary. I will d
iscuss how the inverse problem of recovering the conductances from the res
ponse matrix can be solved using an electrical-network version of the twis
t map on the positive Grassmannian.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chenchen Zhao (USC)
DTSTART:20231026T233000Z
DTEND:20231027T020000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/39
DESCRIPTION:Title: Kronecker product of Schur functions of square shapes\nb
y Chenchen Zhao (USC) as part of UCLA Combinatorics Seminar\n\nLecture hel
d in MS 6627.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lenny Fukshansky (Claremont McKenna College)
DTSTART:20231026T233000Z
DTEND:20231027T020000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/40
DESCRIPTION:Title: A geometric construction for integer sparse recovery\nby
Lenny Fukshansky (Claremont McKenna College) as part of UCLA Combinatoric
s Seminar\n\nLecture held in MS 6627.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Soukup (UCLA)
DTSTART:20231026T233000Z
DTEND:20231027T020000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/41
DESCRIPTION:Title: Complexity of sign imbalance and parity of linear extensions
\nby David Soukup (UCLA) as part of UCLA Combinatorics Seminar\n\nLect
ure held in MS 6621.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiliang Gao (UIUC)
DTSTART:20231117T003000Z
DTEND:20231117T030000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/42
DESCRIPTION:Title: Combinatorics of the Plucker map?\nby Shiliang Gao (UIUC
) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6621.\n\nAbs
tract\nI will discuss how Young tableaux arise from the Plucker map. Influ
ential work of Hodge from the 1940s led the way in using Grobner bases to
combinatorially study the Grassmannian. In the past decade\, the work of K
nutson-Lam-Speyer\, and more recently Galashin-Lam\, has brought to the fo
re the significance of positroid subvarieties in the Grassmannian. I will
explain how to use Young tableaux to understand these subvarieties and the
reby how to connect promotion on Young tableaux with the cyclic symmetry o
f positroid varieties. This is based on joint work with Ayah Almousa and D
aoji Huang\, see arxiv.org/abs/2309.15384.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theo Douvropoulos (Brandeis University)
DTSTART:20231117T003000Z
DTEND:20231117T030000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/43
DESCRIPTION:Title: Families of Shi-like and Catalan-like deformations of braid
and reflection arrangements\nby Theo Douvropoulos (Brandeis University
) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6621.\n\nAbs
tract\nThe Shi arrangement $Shi_n$ is a deformation of the braid arrangeme
nt $Br_n$ and was introduced by Shi to study Kazhdan-Lusztig cells (that t
urn out to be unions of the regions of $Shi_n$). It has remarkable numerol
ogical and structural properties: it has $(n+1)^{n-1}$-many regions that c
an be naturally labeled by parking functions or trees\; it has analogs for
all Weyl groups\; its characteristic polynomial factors with positive int
eger roots.\n\nWe will present recent work\, joint with Olivier Bernardi\,
where we give an $n$-parameter family of deformations of the braid arrang
ement $Br_n$ that generalize the Shi arrangement $Shi_n$. They share many
of the remarkable properties of $Shi_n$\, in particular they come with pro
duct formulas for their characteristic polynomials\, and their regions are
naturally labeled by Cayley trees. We will present a parallel story for C
atalan-like deformations\, generalizations to other Weyl groups\, and appl
ications on the theory of parking spaces.\n\nWe will finish with the origi
nal motivation for this construction\, which was the study of coxeter theo
retic invariants on restrictions of reflection arrangements and associated
multi-arrangements.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Grebík (UCLA)
DTSTART:20231117T003000Z
DTEND:20231117T030000Z
DTSTAMP:20260404T095121Z
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\nAbstract\nOne of fundamental notions of graph theory is the chromatic i
ndex $\\chi'(G)$ of a graph $G$ which is the smallest number of colors nee
ded to color all edges of $G$ so that every two edges that intersect have
different 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 col
oring. In this talk I will discuss edge colorings from the perspective of
the LOCAL model of distributed computing. In particular\, I will talk abou
t what happens when we try to replace the sequential algorithm by a distri
buted one.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daoji Huang (UMN)
DTSTART:20240202T003000Z
DTEND:20240202T030000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/45
DESCRIPTION:Title: Tableaux theory inspired methods for Schubert calculus\n
by Daoji Huang (UMN) as part of UCLA Combinatorics Seminar\n\nLecture held
in MS 6621.\n\nAbstract\nThe classical Littlewood-Richardson (LR) coeffic
ients are special cases of Schubert structure constants\, for which many c
ombinatorial interpretations are known. The theory of symmetric functions
and combinatorics of Young tableaux provide a combinatorial toolbox for ma
ny different but related rules for the LR coefficients. In this talk\, I w
ill explain the basic ideas to lift many components of the classical theor
y to the context of Schubert structure constants\, as well as the obstruct
ions and challenges to solving the full problems using these methods.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasu Tewari (U of Toronto)
DTSTART:20240202T003000Z
DTEND:20240202T030000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/46
DESCRIPTION:Title: The ideal of quasisymmetric polynomials\nby Vasu Tewari
(U of Toronto) as part of UCLA Combinatorics Seminar\n\nLecture held in MS
6621.\n\nAbstract\nWith an eye toward mimicking the combinatorial theory
of Schubert polynomials\, I will describe a new perspective on the quotien
t of the polynomial ring modulo the ideal $QSym_n^+$ of quasisymmetric pol
ynomials. This involves two simple operators-- trimming and blossoming-- a
cting on the polynomial ring. The trimming operators are degree-lowering o
perators that are a mild modification of divided difference operators (cen
tral to Lascoux-Schützenberger's construction of Schubert polynomials). W
e identify a basis that may be considered an appropriate analogue to Schub
ert polynomials with regard to these operators. The blossoming operators
are degree-increasing operators that grow volume polynomials of certain cu
bes decomposing the permutahedron.\n\nJoint work with Philippe Nadeau (Lyo
n/CNRS) and Hunter Spink (UofT).\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karim Adiprasito (IMJ-PRG)
DTSTART:20240223T003000Z
DTEND:20240223T030000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/47
DESCRIPTION:Title: Efficiently encoding configuration spaces\nby Karim Adip
rasito (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 complem
ent of a configuration space\, naturally a neat algebraic variety\, by a s
maller than naïve number of algebraic constraints\, in an attempt to deep
en our understanding of the work of Haiman. We also translate this to var
ieties that merely resemble configuration spaces. Joint work with Itaï Be
n Yacoov and Ehud Hrushovski.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brendan Pawlowski
DTSTART:20240223T003000Z
DTEND:20240223T030000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/49
DESCRIPTION:Title: The fraction of an $S_n$-orbit on a hyperplane\nby Brend
an Pawlowski as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6
621.\n\nAbstract\nFix a point in $\\mathbb{R}^n$ with distinct coordinates
and consider the $S_n$-orbit obtained by permuting its coordinates. Huang
\, McKinnon\, 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 orbi
t. We explain\nhow to prove their conjecture using the Sperner property fo
r Bruhat\norder and bounds on q-binomial coefficients.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amanda Schwartz (UMich)
DTSTART:20241018T000000Z
DTEND:20241018T021500Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/50
DESCRIPTION:Title: The HOMFLY Polynomial of a Forest Quiver\nby Amanda Schw
artz (UMich) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6
221.\n\nAbstract\nThe HOMFLY polynomial of a link is a two-variable link i
nvariant which was introduced in the 1980s. It can be defined recursively
using a skein relation and specializes to other link invariants such as th
e Alexander polynomial and Jones polynomial. In this talk\, we will begin
by defining the HOMFLY polynomial of a forest quiver via a recursive defin
ition on the underlying graph of the quiver. Then\, we will discuss how th
e HOMFLY polynomial of a forest quiver is related to the HOMFLY polynomial
of certain plabic links. In particular\, given any connected plabic graph
$G$ whose quiver $Q_G$ is a forest quiver\, the HOMFLY polynomial of the
associated plabic link is in fact equal to the HOMFLY polynomial of the qu
iver $Q_G$. We will sketch a proof of this result and also discuss a close
d-form expression for the Alexander polynomial of a forest quiver.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steven Karp (Notre Dame)
DTSTART:20241018T000000Z
DTEND:20241018T021500Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/51
DESCRIPTION:Title: Positivity in real Schubert calculus\nby Steven Karp (No
tre Dame) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 6221
.\n\nAbstract\nSchubert calculus involves studying intersection problems a
mong linear subspaces of C^n. A classical example of a Schubert problem is
to find all 2-dimensional subspaces of C^4 which intersect 4 given 2-dime
nsional 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 p
roblems has the remarkable property that all of its complex solutions are
real. This conjecture inspired a lot of work in the area\, including its p
roof by Mukhin-Tarasov-Varchenko in 2009. I will present a strengthening o
f this result which resolves some conjectures of Sottile\, Eremenko\, Mukh
in-Tarasov\, and myself\, based on surprising connections with total posit
ivity\, the representation theory of symmetric groups\, symmetric function
s\, and the KP hierarchy. This is joint work with Kevin Purbhoo\, and with
Evgeny Mukhin and Vitaly Tarasov.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catherine Babecki (CalTech)
DTSTART:20241018T000000Z
DTEND:20241018T021500Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/52
DESCRIPTION:Title: Spectrahedral Geometry of Graph Sparsifiers\nby Catherin
e Babecki (CalTech) as part of UCLA Combinatorics Seminar\n\nLecture held
in MS 6221.\n\nAbstract\nWe propose an approach to graph sparsification ba
sed on the idea of preserving the smallest k eigenvalues and eigenvectors
of the graph Laplacian. This is motivated by the fact that small eigenvalu
es and their associated eigenvectors tend to be more informative of the gl
obal structure and geometry of the graph than larger eigenvalues and their
eigenvectors. The set of all weighted subgraphs of a graph G that have th
e same first k eigenvalues (and eigenvectors) as G is the intersection of
a polyhedron with a cone of positive semidefinite matrices. We discuss the
geometry of these sets and deduce the natural scale of k. Various familie
s of graphs illustrate our construction.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Swanson (USC)
DTSTART:20241108T000000Z
DTEND:20241108T004000Z
DTSTAMP:20260404T095121Z
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 p
owerful 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 pl
abic graphs. In this talk\, I will explain how our basis naturally models
the geometry of the affine building $\\Delta(\\SL(4)^\\vee)$. Specifically
\, duals of move-equivalence classes of basis webs assemble to form remark
able 3D simplicial complexes we call pockets\, which in turn generically e
xtend the irreducible components of Satake fibers. Special cases correspon
d to plane partitions\, alternating sign matrices\, tilings of the Aztec d
iamond\, and more. Joint with Christian Gaetz\, Jessica Striker\, and Haih
an Wu.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wonwoo Kang (UIUC)
DTSTART:20241108T005000Z
DTEND:20241108T013000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/54
DESCRIPTION:Title: Skein Relations for Punctured Surfaces\nby Wonwoo Kang (
UIUC) as part of UCLA Combinatorics Seminar\n\nLecture held in UCLA Boelte
r hall\, room 5436.\n\nAbstract\nSince the introduction of cluster algebra
s by Fomin and Zelevinsky in 2002\, there has been substantial interest in
cluster algebras of surface type. These algebras are particularly signifi
cant due to their ability to construct various combinatorial structures\,
such as snake graphs\, T-paths\, and posets\, which are useful for proving
key structural properties like positivity and the existence of bases. In
this talk\, we will begin by presenting a cluster expansion formula that u
tilizes poset representatives for arcs on triangulated surfaces. Using the
se posets and the expansion formula as tools\, we will demonstrate skein r
elations\, which resolve intersections or incompatibilities between arcs.
As a result\, we will demonstrate that bangles and bracelets form spanning
sets and exhibit linear independence\, thereby proving the existence of t
he bangle and bracelet bases in punctured surfaces with boundaries and clo
sed surface with genus 0. This work is done in collaboration with Esther B
anaian and Elizabeth Kelley.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Soskin (IAS)
DTSTART:20241206T012000Z
DTEND:20241206T020000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/55
DESCRIPTION:Title: Total positivity and determinantal inequalities\nby Dani
el Soskin (IAS) as part of UCLA Combinatorics Seminar\n\nLecture held in U
CLA Boelter hall\, room 5436.\n\nAbstract\nTotally positive matrices are m
atrices in which each minor is positive. Lusztig extended the notion to re
ductive Lie groups. He also proved that specialization of elements of the
dual canonical basis in representation theory of quantum groups at q=1 ar
e totally non-negative polynomials. Thus\, it is important to investigate
classes of functions on matrices that are positive on totally positive mat
rices. I will discuss several sources of such functions as well as their c
onnection to Schur positivity and Littlewood-Richardson coefficients. The
main tools we employed are network parametrization and Temperley-Lieb imm
anants.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacques Verstraete (UCSD)
DTSTART:20250508T233000Z
DTEND:20250509T002000Z
DTSTAMP:20260404T095121Z
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
\nAbstract\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 go
es back almost one hundred years\, to early papers of Ramsey and Erdős an
d Szekeres\, the long-standing conjecture of Erdős that $r(s\,t)$ has ord
er of magnitude close to $t^{s - 1}$ as $t \\rightarrow \\infty$ remains o
pen 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 or
der of magnitude $t^2/(\\log t)$ as $t \\rightarrow \\infty$. In this talk
\, we discuss a variety of new techniques\, including mention of the proof
that for 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 progress on other Ramsey numbers\, on Erdős-Rogers functions\, Ramsey
minimal graphs\, and on coloring hypergraphs. \n\n\nJoint work in part wi
th David Conlon\, Sam Mattheus\, and Dhruv Mubayi.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Neville (UMich)
DTSTART:20241206T021000Z
DTEND:20241206T025000Z
DTSTAMP:20260404T095121Z
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 5436.\n\nAbstract\nQuivers and their mutations play a fundamental rol
e in the theory of cluster algebras. We focus on the problem of deciding w
hether two given quivers are mutation equivalent to each other. Our approa
ch is based on introducing an additional structure of a cyclic ordering on
the set of vertices of a quiver. This leads to new powerful invariants of
quiver mutation. These invariants can be used to show that various quiver
s are not mutation acyclic\, i.e.\, they are not mutation equivalent to an
acyclic quiver. This talk is partially based on joint work with Sergey Fo
min [arXiv:2406.03604].\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jianping Pan (Arizona State Univ.)
DTSTART:20241206T003000Z
DTEND:20241206T011000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/58
DESCRIPTION:Title: Pattern-avoiding polytopes and Cambrian lattices\nby Jia
nping Pan (Arizona State Univ.) as part of UCLA Combinatorics Seminar\n\nL
ecture held in UCLA Boelter hall\, room 5436.\n\nAbstract\nIn 2017\, Davis
and Sagan found that a pattern-avoiding Birkhoff subpolytope and an order
polytope have the same normalized volume. They ask whether the two polyto
pes are unimodularly equivalent. We give an affirmative answer to a genera
lization of this question. \n\nFor each Coxeter element c in the symmetric
group\, we define a pattern-avoiding Birkhoff subpolytope\, and an order
polytope of the heap poset of the c-sorting word of the longest permutatio
n. We show the two polytopes are unimodularly equivalent. As a consequence
\, we show the normalized volume of the pattern-avoiding Birkhoff subpolyt
ope is equal to the number of the longest chains in a corresponding Cambri
an lattice. In particular\, when $c = s_1s_2…s_{n-1}$\, this resolves th
e question by Davis and Sagan.\n\nThis talk is based on joint work with E.
Banaian\, S. Chepuri and E. Gunawan.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvester Zhang (UMN)
DTSTART:20250124T003000Z
DTEND:20250124T012000Z
DTSTAMP:20260404T095121Z
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 62
21.\n\nAbstract\nWe introduce rhombic tableaux to give new combinatorial f
ormulae for Schubert polynomials corresponding to a partial flag variety.
In the case of Grassmanian\, rhombic tableaux recovers (reverse) semistand
ard Young tableaux. We discuss extensions to Stanley symmetric functions a
nd K-theory\, and give a generalization of Bender-Knuth involution. This t
alk is based on joint work with Ilani Axelrod-Freed and Jiyang Gao.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yassine El Maazouz (CalTech)
DTSTART:20250124T013000Z
DTEND:20250124T022000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/61
DESCRIPTION:Title: The positive orthogonal Grassmannian\nby Yassine El Maaz
ouz (CalTech) as part of UCLA Combinatorics Seminar\n\nLecture held in MS
6221.\n\nAbstract\nThe Plücker positive region $\\text{OGr}_+(k\,2k)$ of
the orthogonal Grassmannian emerged as the positive geometry behind the AB
JM scattering amplitudes. We initiate the study of the positive orthogonal
Grassmannian $\\text{OGr}_+(k\,n)$ for general values of $k$ and $n$. We
determine the boundary structure of the quadric $\\text{OGr}_+(1\,n)$ in $
\\mathbb{P}^{(n-1)}_+$ and show that it is a positive geometry. We show th
at $\\text{OGr}_+(k\,2k+1)$ is isomorphic to $\\text{OGr}_+(k+1\,2k+2)$ an
d connect its combinatorial structure to matchings on $[2k+2]$. Finally\,
we show that in the case $n>2k+1$\, the positroid cells of $\\text{Gr}_+(k
\,n)$ do not induce a CW cell decomposition of $\\text{OGr}_+(k\,n)$. This
was joint work with Yelena Mandelshtam.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grant Barkley (Harvard)
DTSTART:20250221T003000Z
DTEND:20250221T030000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/62
DESCRIPTION:Title: The combinatorial invariance conjecture\nby Grant Barkle
y (Harvard) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 62
21.\n\nAbstract\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
$\\textit{Kazhdan-Lusztig polynomial}$\, which encodes numerical invarian
ts that are central in geometric representation theory. The coefficients o
f $P_{uv}$ simultaneously describe the singularities of Schubert varieties
\, the structure of Hecke algebras\, and the representation theory of Lie
algebras. Associated to $u$ and $v$ is another object\, the $\\textit{Bruh
at graph}$ of $(u\,v)$\, which is a directed graph describing the transpos
itions taking $u$ to $v$. \nThe $\\textit{combinatorial invariance conject
ure}$ (CIC) of Dyer and Lusztig asserts that the Bruhat graph of $(u\,v)$
uniquely determines $P_{uv}$. Recently\, Geordie Williamson and Google Dee
pMind applied machine learning techniques to this problem. Using those tec
hniques\, they conjectured an explicit recursion that would compute $P_{uv
}$ from the Bruhat graph and thereby prove the CIC. In joint work with Chr
istian Gaetz\, we prove the Williamson-DeepMind conjecture in the case whe
re $u$ is the identity permutation. Along the way\, we prove two new ident
ities for the Kazhdan--Lusztig $R$ polynomials\, one of which implies new
cases of the CIC.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Miranda (UCLA)
DTSTART:20250221T013000Z
DTEND:20250221T022000Z
DTSTAMP:20260404T095121Z
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 polyhedral surface has a n-dimensional flex if there exists a continuo
us family of realizations $\\{Q_t : t \\in [0\,1]^n\\}$ which are pairwise
nonisomorphic. Gaifullin and Gaifullin showed that if a 2-periodic polyhe
dral surface in is homeomorphic to a plane\, then it can have at most a 1-
dimensional periodic flex. Glazyrin and Pak later found an example of a 2-
periodic polyhedral surface\, not homeomorphic to a plane\, which has a fu
ll 3-dimensional periodic flex. In this talk\, we present a new constructi
on for a flexible 3-periodic polyhedral surfaces\, and discuss generalizat
ions to higher dimensions.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ada Stelzer (UIUC)
DTSTART:20250307T003000Z
DTEND:20250307T030000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/64
DESCRIPTION:Title: Crystals\, standard monomials\, and filtered RSK\nby Ada
Stelzer (UIUC) as part of UCLA Combinatorics Seminar\n\nLecture held in M
S 6221.\n\nAbstract\nConsider a variety $X$ in the space of matrices\, sta
ble under the action of a product of general linear groups by row and colu
mn operations. How does its coordinate ring decompose as a direct sum of i
rreducible representations? We argue that this question is effectively stu
died by imposing a crystal graph structure on the standard monomials of th
e defining ideal of $X$ (with respect to some term order). For the standar
d monomials of "bicrystalline" ideals\, we obtain such a crystal structure
from the crystal graph on monomials introduced by Danilov–Koshevoi and
van Leeuwen. This yields an explicit combinatorial rule we call "filtered
RSK" for their irreducible representation multiplicities. In this talk\, w
e will explain our rule and show that Schubert determinantal ideals (among
others) are bicrystalline. Based on joint work with Abigail Price and Ale
xander Yong\, https://arxiv.org/abs/2403.09938\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Esther Banaian (UC Riverside)
DTSTART:20250307T013000Z
DTEND:20250307T022000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/65
DESCRIPTION:Title: Positivity and Structure of Generalized Cluster Algebras
\nby Esther Banaian (UC Riverside) as part of UCLA Combinatorics Seminar\n
\nLecture held in MS 6221.\n\nAbstract\nMotivated by relations amongst lam
bda lengths on an orbifold\, Chekhov and Shapiro introduced generalized cl
uster algebras\, which have the same structure as ordinary cluster algebra
s but whose mutation polynomials can have arbitrarily many terms. We focus
on generalized cluster algebras which arise from orbifolds and exhibit co
mbinatorial expansion formulas for their cluster variables. These expressi
ons can be phrased in terms of perfect matching of certain graphs (an anal
ogue of the snake graphs from Musiker-Schiffler-Williams) or in terms of o
rder ideals of a poset. The formulas make the positivity of the cluster va
riables evident and also can be used as a tool to prove structural propert
ies such as linear independence of cluster monomials. Time-permitting\, we
will also discuss how these expansion formulas illuminate a connection be
tween these cluster variables and indecomposable modules of a finite-dimen
sional algebra. This talk is based on past and current works with Wonwoo K
ang\, Ezgi Kantarci Oguz\, Elizabeth Kelley\, Yadira Valdivieso\, and Emin
e Yildirim.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaku Liu (UW)
DTSTART:20250410T233000Z
DTEND:20250411T022000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/66
DESCRIPTION:Title: A regular unimodular triangulation of the matroid base polyt
ope\nby Gaku Liu (UW) as part of UCLA Combinatorics Seminar\n\nLecture
held in MS 6627.\n\nAbstract\nWe produce the first regular unimodular tri
angulation of an arbitrary matroid base polytope. We then extend our tri
angulation to integral generalized permutahedra. Prior to this work it was
unknown whether each matroid base polytope admitted a unimodular cover. I
will also discuss connections to other open problems in matroid theory\,
namely White's conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Martinez (UCLA)
DTSTART:20250411T003000Z
DTEND:20250411T012000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/67
DESCRIPTION:Title: Affine Deodhar Diagrams and Rational Dyck Paths\nby Thom
as Martinez (UCLA) as part of UCLA Combinatorics Seminar\n\nLecture held i
n MS 6627.\n\nAbstract\nGiven a bounded affine permutation $f$\, we introd
uce affine Deodhar diagrams for $f$\, similar to affine pipe dreams introd
uced by Snider. We explore combinatorial moves between these diagrams and\
, as an application\, use these moves to establish a bijection between Deo
dhar diagrams and rational Dyck paths for a special class of bounded affin
e permutations. This resolves an open problem posed by Galashin and Lam.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Gladkov (UCLA)
DTSTART:20250509T003000Z
DTEND:20250509T012000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/68
DESCRIPTION:Title: Gadgets in percolation\nby Nikita Gladkov (UCLA) as part
of UCLA Combinatorics Seminar\n\nLecture held in MS 6627.\n\nAbstract\nSu
ppose that\, due to a marathon\, each street in Los Angeles has a 1/2 chan
ce of being closed. With nothing better to do\, your n friends\, who live
in different parts of the city\, try to figure out which subgroups can sti
ll assemble. We explore the possible distributions over the set of resulti
ng partitions based on computer experiments and discuss the known inequali
ties.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daoji Huang (IAS)
DTSTART:20250529T233000Z
DTEND:20250530T002000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/69
DESCRIPTION:Title: Affine Robinson--Schensted correspondence via growth diagram
s\nby Daoji Huang (IAS) as part of UCLA Combinatorics Seminar\n\nLectu
re 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 encoded in Viennot's shadow line construction and equivalently by Fomi
n's growth diagrams\, whose geometric interpretation\, which connects to S
pringer theory\, is given by van Leeuwen. Motivated by Kazhdan--Lusztig th
eory\, Shi introduced the analogue of the Robinson--Schensted corresponden
ce for the affine Weyl group of type A via an insertion algorithm. We gene
ralize Fomin's growth diagram and Viennot's shadow line construction to th
e affine setting\, recover and refine Shi's correspondence\, and give geom
etric interpretations in the style of van Leeuwen. This is ongoing joint w
ork with Sylvester Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Galashin (UCLA)
DTSTART:20250530T003000Z
DTEND:20250530T012000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/71
DESCRIPTION:Title: Amplituhedra and origami\nby Pavel Galashin (UCLA) as pa
rt of UCLA Combinatorics Seminar\n\nLecture held in MS 6221.\n\nAbstract\n
I will explain a proof of the BCFW triangulation conjecture which states t
hat the cells appearing in the Britto–Cachazo–Feng–Witten (BCFW) rec
ursion triangulate the amplituhedron (in full generality at all loop level
s). The key ingredient is a relation to origami crease patterns which are
planar graphs with faces colored black and white\, embedded in the plane s
o that the sum of black (equivalently\, white) angles at each vertex is 18
0°. Along the way\, we prove conjectures of Chelkak–Laslier–Russkikh
and Kenyon–Lam–Ramassamy–Russkikh on the existence of such origami e
mbeddings of arbitrary planar graphs\, which originated from the works of
Kenyon and Smirnov on the conformal invariance of the dimer and Ising mode
ls.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamás Kátay (UCLA)
DTSTART:20251202T000000Z
DTEND:20251202T010000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/72
DESCRIPTION:Title: Elusive properties of countably infinite graphs\nby Tam
ás Kátay (UCLA) as part of UCLA Combinatorics Seminar\n\nLecture held in
MS 5147.\n\nAbstract\nA graph property is elusive (or evasive) if any alg
orithm testing it by asking questions of the form "Is there an edge betwee
n vertices x and y?" must\, in the worst case\, examine all pairs of verti
ces. Elusive properties of finite graphs have been extensively studied sin
ce the 70s. For infinite graphs\, they were first studied by Csernák and
Soukup in 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 countab
ly infinite case.\n\n\nJoint work with Márton Elekes and Anett Kocsis. 80
% of the talk requires only very elementary knowledge in graph theory.\n\n
joint talk with the UCLA Logic Colloquium\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oriol Solé-Pi (MIT)
DTSTART:20251020T230000Z
DTEND:20251021T000000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/73
DESCRIPTION:Title: Graph structure and soficity\nby Oriol Solé-Pi (MIT) as
part of UCLA Combinatorics Seminar\n\nLecture held in MS 5147.\n\nAbstrac
t\nA random rooted graph is said to be sofic if it is the Benjamini-Schram
m limit of a sequence of finite graphs. Perhaps surprisingly\, our underst
anding of which graphs are sofic is still quite limited. For starters\, so
fic graphs are known to possess a certain property known as unimodularity.
(Unimodular random rooted graphs can also be encoded by graphings of pmp
Borel equivalence relations.) However\, in a recent breakthrough\, Bowen\,
Chapman\, Lubotzky and Vidick have shown that not all unimodular graphs a
re sofic. In this talk\, I will give an overview of what is known in the o
ther direction: Which additional conditions on the graph are known to impl
y soficity? Two important properties which I will talk about here are hype
rfiniteness and treeability. Then\, I will discuss a novel result along th
ese lines: For any finite graph H\, every one-ended\, unimodular graph whi
ch does not have H as a minor must be sofic. The proof of this result proc
eeds by showing that all unimodular graphs of this kind are "almost" treea
ble.\n\njoint talk with the UCLA Logic Colloquium\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvester Zhang (UCLA)
DTSTART:20251009T210000Z
DTEND:20251009T220000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/74
DESCRIPTION:Title: Mixed Pipedreams\nby Sylvester Zhang (UCLA) as part of U
CLA Combinatorics Seminar\n\nLecture held in MS 5203.\n\nAbstract\nI will
discuss the combinatorics of skew semistandard Young tableaux and their co
nnection to Richardson varieties in the Grassmannian\, and introduce mixed
pipedreams\, a combinatorial model for Lenart-Sottile’s skew Schubert p
olynomials. These polynomials correspond to Richardson varieties in the fu
ll flag variety. This talk is based on on-going work with Tianyi Yu and Ji
yang Gao.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Soskin (UCLA)
DTSTART:20251016T210000Z
DTEND:20251016T220000Z
DTSTAMP:20260404T095121Z
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 called a Lorentzian matrix if it has at most one positive eigenvalue.
One out of the many examples of Lorentzian matrices is given by mixed volu
mes\n$$v_{ij} = V (P_i\, P_j \, K_1\,\\ldots\, K_{n−2})\,$$ of convex bo
dies $K_1\, \\ldots\, K_{n−2}\, P_1\, \\ldots\, P_m ⊂ \\mathbb{R}^n$.
Classical 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
special case of the reverse Khovanskii–Teissier inequalities\, whose va
riants appear in Brunn–Minkowski theory\, and in works of Weil.\n\n\nMul
tiplicative inequalities have been studied in matrix entries and minors fo
r Totally positive and Positive semidefinite matrices\, as well as for reg
ular functions defined on positive loci of cluster varieties. I will discu
ss recent results on multiplicative inequities in entries of Lorentzian ma
trices\, Alexandrov–Fenchel and reverse Khovanskii–Teissier inequaliti
es are simple examples of those (joint work with D.Huang\, J.Huh\, and B.W
ang\, 2025+). We show that the set of multiplicative generators of inequal
ities in matrix entries of Lorentzian matrices correspond to the extreme r
ays of the dual cone of the so called Cut cone. Cut cone was thoroughly st
udied by M.Deza and M.Laurent in the context of metric geometry\, graph th
eory\, and combinatorial optimization. In particular\, we discover new fam
ilies of inequalities which are in some sense stronger than previously kno
wn\, as well as we study the optimal multiplicative constants for such ine
qualities. The main tools we employed are multi-variable calculus\, linear
algebra and Gromov’s $\\delta$-hyperbolic metrics on n points. I will a
lso present two conjectures observing phenomena aligned with previous stud
ies of multiplicative inequalities mentioned earlier.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Gagnon (USC)
DTSTART:20251106T230000Z
DTEND:20251107T000000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/77
DESCRIPTION:Title: Quasisymmetric and Coxeter flag varieties\nby Lucas Gagn
on (USC) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 5203.
\n\nAbstract\nIn algebraic combinatorics\, the terms $\\textit{Coxeter--Ca
talan}$ and $\\textit{quasisymmetric}$ describe two common philosophies fo
r generalizing classical objects and deepening results. One area where n
either philosophy has made serious headway is the Schubert calculus of the
complete flag variety. In this talk I will introduce a toric complex $\
\mathrm{QFl}$ inside the complete flag variety which is simultaneously a q
uasisymmetric and Coxeter-Catalan generalization. In the remaining ti
me I will convince you that: (i) $\\mathrm{QFl}$ is the `right' generaliza
tion\, because its combinatorics are nice enough to do actual computations
\; and (ii) $\\mathrm{QFl}$ is an `interesting' generalization because it
is still connected to classical Schubert calculus. Based on work with N.
Bergeron\, P. Nadeau\, H. Spink\, and V. Tewari.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swee Hong Chan (Rutgers)
DTSTART:20251120T220000Z
DTEND:20251120T230000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/79
DESCRIPTION:Title: Spanning trees and continued fractions\nby Swee Hong Cha
n (Rutgers) as part of UCLA Combinatorics Seminar\n\nLecture held in MS 52
03.\n\nAbstract\nConsider the set of positive integers representing the nu
mber of spanning trees in simple graphs with n vertices. How quickly can t
his set grow as a function of n? In this talk\, we discuss a proof of the
exponential growth of this set\, which resolves an open problem of Sedlac
ek from 1966. The proof uses a connection with continued fractions and adv
ances towards Zaremba’s conjecture in number theory. This is joint work
with Alex Kontorovich and Igor Pak. This talk is intended for general audi
ence.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sinai Robins (University of São Paulo)
DTSTART:20251023T210000Z
DTEND:20251023T220000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/80
DESCRIPTION:Title: The Siegel-Bombieri method in the geometry of numbers\, thro
ugh the lens of Fourier\nby Sinai Robins (University of São Paulo) as
part of UCLA Combinatorics Seminar\n\nLecture held in MS 5203.\n\nAbstrac
t\nWe extend some classical results in the geometry of numbers\, obtained
by C. L. Siegel (1935)\, and E. Bombieri (1962)\, both of whom extended Mi
nkowski’s first theorem for convex\, centrally symmetric bodies. A dis
crete version of these results allows us to give some discrete analogues o
f the Siegel-Bombieri formulas\, for any finite set of integer points in E
uclidean space\, using finite covariograms. We’ll give visual examples
\, with pictures in dimension 2. On the other hand\, a continuous applic
ation of these results allows us to shed additional light on the enumerati
on of lattice points in polytopes in $\\mathbb{R}^d$\, and more generally
in compact subsets of $\\mathbb{R}^d$. This is joint work with Michel Fale
iros.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Skopenkov (KAUST)
DTSTART:20260129T220000Z
DTEND:20260129T230000Z
DTSTAMP:20260404T095121Z
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\nAbstract\nIncidence theorems about points and lines in the plane are at
the core of projective geometry\, and their automated proofs are studied
in mathematical logic. One approach to such proofs\, which originated from
Coxeter/Greitzer’s proof of Pappus’ theorem\, is multiple application
s of Menelaus's theorem. Richter-Gebert\, Fomin\, and Pylyavskyy visualize
d them using triangulated surfaces. We investigate which incidence theorem
s can or cannot be proved in this way. We show that\, in addition to trian
gulated surfaces\, one can use simplicial complexes satisfying a certain e
xcision property. This property holds\, for instance\, for the generalizat
ion of gropes that we provide. We introduce a hierarchy of classes of theo
rems based on the underlying topological spaces. We show that this hierarc
hy does not collapse over R by considering the same theorems over finite f
ields. This is joint work with P. Pylyavskyy.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tianyi Yu (UQAM)
DTSTART:20260219T220000Z
DTEND:20260219T230000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/82
DESCRIPTION:Title: A positive combinatorial formula for the double Edelman--Gre
ene coefficients\nby Tianyi Yu (UQAM) as part of UCLA Combinatorics Se
minar\n\nLecture held in MS 6201.\n\nAbstract\nLam\, Lee\, and Shimozono i
ntroduced the double Stanley symmetric functions in their study of the equ
ivariant geometry of the affine Grassmannian.They proved that the associat
ed double Edelman--Greene coefficients\, the double Schur expansion coeffi
cients of these functions\, are positive\, a result later refined by Ander
son. They further asked for a combinatorial proof of this positivity. In t
his paper\, we provide the first such proof\, together with a combinatoria
l formula that manifests the finer positivity established by Anderson. Our
formula is built from two combinatorial models: bumpless pipedreams and i
ncreasing chains in the Bruhat order. The proof relies on three key ingred
ients: a correspondence between these two models\, a natural subdivision o
f bumpless pipedreams\, and a symmetry property of increasing chains. This
talk is based on joint work with Jack Chou.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fan Zhou (Columbia)
DTSTART:20260122T220000Z
DTEND:20260122T230000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/83
DESCRIPTION:Title: Categorifying Jacobi-Trudi\nby Fan Zhou (Columbia) as pa
rt of UCLA Combinatorics Seminar\n\nLecture held in MS 6201.\n\nAbstract\n
The Jacobi-Trudi determinant identity is a famous formula for the Schur po
lynomials\, which are central to the study of symmetric polynomials and ar
ise as "shadows" of simple representations of symmetric groups. A determin
ant can\, of course\, be written as an alternating sum of products of entr
ies in the matrix\; a natural question is then whether this alternating su
m can be lifted\, or ‘categorified'\, into a resolution such that the Eu
ler-Frobenius characteristic of the resolution recovers this determinant i
dentity. In other words\, it is natural to wonder if this determinant iden
tity is simply a ‘numerical shadow' of a deeper fact regarding modules\;
this type of ‘allegory-of-the-cave'-esque story is known as a ‘catego
rification'. In this talk we will outline a categorification of the Jacobi
-Trudi determinant identity using “KLR algebras”.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrés R. Vindas Meléndez (Harvey Mudd)
DTSTART:20260205T220000Z
DTEND:20260205T230000Z
DTSTAMP:20260404T095121Z
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 p
olynomial of a given graph $G=(V\,E)$\, namely\, $\\chi_G^\\lambda(q\,n):=
\n\\sum_{{\\text{proper colorings} c:V\\to[n]}} q^{ \\sum_{ v \\in V } \\l
ambda_v c(v) }$\, where $\\lambda \\in \\mathbb{Z}^V$ is a fixed linear f
orm. Via work of Chapoton (2016) on $q$-Ehrhart polynomials\, $\\chi_G^\\l
ambda(q\,n)$ turns out to be a polynomial in the $q$-integer $[n]_q$\, wit
h coefficients that are rational functions in $q$. Additionally\, we prove
structural results for $\\chi_G^\\lambda(q\,n)$ and exhibit connections t
o neighboring concepts\, e.g.\, chromatic symmetric functions and the arit
hmetic of order polytopes. We offer a strengthened version of Stanley's co
njecture that the chromatic symmetric function distinguishes trees\, which
leads to an analogue of $P$-partitions for graphs. This is joint work wit
h Esme Bajo (San Diego Miramar College) and Matthias Beck (San Francisco S
tate).\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuhan Jiang (UC Berkeley)
DTSTART:20260312T210000Z
DTEND:20260312T220000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/85
DESCRIPTION:Title: A basis of the alternating diagonal coinvariants and a decom
position of $m$-Dyck paths\nby Yuhan Jiang (UC Berkeley) as part of UC
LA Combinatorics Seminar\n\nLecture held in MS 6201.\n\nAbstract\nThe ring
of diagonal coinvariants is widely studied in the context of the shuffle
conjecture\, and its alternating part exhibits $q\,t$-Catalan combinatoric
s. We construct an explicit vector space basis in terms of bivariate Vande
rmonde determinants for the alternating component of the diagonal coinvari
ant ring $DR_n$\, answering a question of Stump. As a Corollary\, we recov
er the combinatorial formula of the $q\,t$-Catalan numbers. Moreover\, we
construct a decomposition of an $m$-Dyck path into an $m$-tuple of Dyck pa
ths such that the area sequence and bounce sequence of the $m$-Dyck path i
s entrywise the sum of the area sequences and bounce sequences of the Dyck
paths in the tuple. We conjecture that this decomposition gives a basis f
or the alternating component of the generalized diagonal coinvariants $DR_
n^{(m)}$.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abhishek Dhawan (UIUC)
DTSTART:20260402T210000Z
DTEND:20260402T220000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/86
DESCRIPTION:Title: Independent sets in $K_{t\,t\,t}$-free graphs\nby Abhish
ek Dhawan (UIUC) as part of UCLA Combinatorics Seminar\n\nLecture held in
MS 6201.\n\nAbstract\nAjtai\, Erdös\, Komlós\, and Szemerédi conjecture
d in 1981 that for every graph $F$\, every $n$-vertex $F$-free graph of av
erage degree $d$ contains an independent set of size $\\Omega(n \\log d/d)
$. The largest class of graphs for which this was previously known was est
ablished by Alon\, Krivelevich\, and Sudakov in 1999\, who proved it for t
he so-called almost bipartite graphs\, namely subgraphs of $K_{1\,t\,t}$.
We prove the conjecture for all $3$-colorable graphs $F$\, i.e.\, subgraph
s of $K_{t\,t\,t}$\, representing the first progress on the problem in mor
e than 25 years. More precisely\, we show that every $n$-vertex $K_{t\,t\,
t}$-free graph of average degree $d$ contains an independent set of size a
t least $(1 − o(1))n \\log d/d$\, matching Shearer's celebrated bound fo
r triangle-free graphs (the case $t = 1$) and thereby yielding a substanti
al strengthening of it. We develop a new variant of the Rödl nibble metho
d to prove this result\, which is of independent interest.\n\nThis talk is
based on joint work with Oliver Janzer and Abhishek Methuku.\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Bernshteyn (UCLA)
DTSTART:20260507T210000Z
DTEND:20260507T220000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/87
DESCRIPTION:by Anton Bernshteyn (UCLA) as part of UCLA Combinatorics Semin
ar\n\nLecture held in MS 6201.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Ovenhouse (MSU)
DTSTART:20260423T210000Z
DTEND:20260423T220000Z
DTSTAMP:20260404T095121Z
UID:ucla_comb_sem/88
DESCRIPTION:by Nick Ovenhouse (MSU) as part of UCLA Combinatorics Seminar\
n\nLecture held in MS 6201.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ucla_comb_sem/88/
END:VEVENT
END:VCALENDAR