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BEGIN:VEVENT
SUMMARY:Dongkwan Kim (University of Minnesota)
DTSTART;VALUE=DATE-TIME:20201001T170000Z
DTEND;VALUE=DATE-TIME:20201001T180000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/1
DESCRIPTION:Title: Robinson-Schensted correspondence for natural unit interval orders\nby Dongkwan Kim (University of Minnesota) as part of UCLA Combinatoric
s Forum\n\n\nAbstract\nStanley-Stembridge conjecture\, currently one of th
e most famous conjectures in algebraic combinatorics\, asks whether a cert
ain generating function with respect to a natural unit interval order is a
nonnegative linear combination of complete homogeneous symmetric function
s. There are many partial progress on this conjecture\, including its conn
ection with the geometry of Hessenberg varieties. \n\nIn this talk we stud
y the Schur positivity\, which is originally proved by Haiman and Gasharov
. We define an analogue of Knuth moves with respect to a natural unit inte
rval order and study its equivalence classes in terms of D graphs introduc
ed by Assaf. Then\, we show that if the given order avoids certain two sub
orders then an analogue of Robinson-Schensted correspondence is well-defin
ed\, which proves that the generating function attached to each equivalenc
e class is Schur positive. It is hoped that it proposes a new combinatoria
l aspect to investigate the Stanley-Stembridge conjectures and cohomology
of Hessenberg varieties. This work is joint with Pavlo Pylyavskyy.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Pechenik (University of Waterloo)
DTSTART;VALUE=DATE-TIME:20201008T170000Z
DTEND;VALUE=DATE-TIME:20201008T180000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
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 Forum\n\n
\nAbstract\nKnutson and Miller (2005) showed that the equivariant cohomolo
gy class of a matrix Schubert variety $X_w$ is the corresponding double Sc
hubert polynomial $S_w$. Moreover\, after Gröbner degeneration with respe
ct to any antidiagonal term order\, the resulting irreducible components a
re naturally labeled by the pipe dreams for w. In later work with Yong (20
09)\, they used diagonal term orders to obtain alternative combinatorics f
or certain $X_w$. We present further results in this direction\, with conn
ections to a neglected Schubert polynomial formula of Lascoux (2002) in te
rms of the 6-vertex ice model (recently rediscovered by Lam\, Lee\, and Sh
imozono in the guise of “bumpless pipe dreams”).\n\nNote: the talk wil
l be accessible to the general audience.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Sherman-Bennett (Harvard University/UC Berkeley)
DTSTART;VALUE=DATE-TIME:20201015T170000Z
DTEND;VALUE=DATE-TIME:20201015T180000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/3
DESCRIPTION:Title: Plabic graphs and cluster structures on positroid varieties\nby
Melissa Sherman-Bennett (Harvard University/UC Berkeley) as part of UCLA C
ombinatorics Forum\n\n\nAbstract\nOpen positroid varieties are smooth irre
ducible subvarieties of the Grassmannian\, which can be naturally defined
using "positively realizable" matroids (positroids\, for short). They wer
e first introduced by Knutson\, Lam\, and Speyer\, motivated by work of Po
stnikov on the totally nonnegative (real) Grassmannian and positroid cells
. Open positroid varieties are indexed by a number of combinatorial object
s\, including families of plabic (i.e. planar bicolored) graphs. \n\nI wil
l discuss some algebraic information plabic graphs give us about open posi
troid varieties. Together with Serhiyenko and Williams\, we showed that pl
abic graphs for an open Schubert variety $V$ (a special case of open posit
roid varieties) give seeds for a cluster algebra structure on the homogene
ous coordinate ring of $V$. Among other things\, this implies that plabic
graphs give positivity tests for elements of $V$. \n\nOur work generalize
s a result of Scott on the Grassmannian\, and confirms a longstanding folk
lore conjecture on Schubert varieties\; it was later generalized to arbitr
ary positroid varieties by Galashin and Lam. I'll also discuss recent work
with Fraser\, in which we show that relabeled plabic graphs also give see
ds for a cluster algebra structure on coordinate rings of open positroid v
arieties\, uncovering another source for positivity tests. \n\nNo knowledg
e of cluster algebras will be assumed in the talk.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swee Hong Chan (UCLA)
DTSTART;VALUE=DATE-TIME:20201022T170000Z
DTEND;VALUE=DATE-TIME:20201022T180000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/4
DESCRIPTION:Title: Sorting probability for Young diagrams\nby Swee Hong Chan (UCLA)
as part of UCLA Combinatorics Forum\n\n\nAbstract\nCan you always find tw
o elements $x$\, $y$ of a partially ordered set\, such that\, the probabil
ity that x is ordered before y when the poset is ordered randomly\, is bet
ween $1/3$ and $2/3$?\nThis is the celebrated $1/3 - 2/3$ Conjecture\, whi
ch has been called "one of the most intriguing problems in the combinatori
al theory of posets".\n\nWe will explore this conjecture for posets that a
rise from (skew-shaped) Young diagrams\, where total orderings of these po
sets correspond to standard Young tableaux. We will show that that these p
robabilities are arbitrarily close to $1/2$\, by using random walk estimat
es and the state-of-the-art hook-length formulas of Naruse. \n\nThis is a
joint work with Igor Pak and Greta Panova. This talk is aimed at a genera
l audience.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Escobar (Washington University in St. Louis)
DTSTART;VALUE=DATE-TIME:20201029T170000Z
DTEND;VALUE=DATE-TIME:20201029T180000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/5
DESCRIPTION:Title: Which Schubert varieties are Hessenberg varieties?\nby Laura Esc
obar (Washington University in St. Louis) as part of UCLA Combinatorics Fo
rum\n\n\nAbstract\nSchubert varieties are subvarieties of the flag variety
parametrized by permutations\; they induce an important basis for the coh
omology of the flag variety. Hessenberg varieties are also subvarieties of
the flag variety with connections to both algebraic combinatorics and rep
resentation theory. I will discuss joint work with Martha Precup and John
Shareshian in which we investigate which Schubert varieties in the full fl
ag variety are Hessenberg varieties.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abdul Basit (Iowa State University)
DTSTART;VALUE=DATE-TIME:20201112T180000Z
DTEND;VALUE=DATE-TIME:20201112T190000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/7
DESCRIPTION:Title: Point-box incidences and logarithmic density of semilinear graphs\nby Abdul Basit (Iowa State University) as part of UCLA Combinatorics Fo
rum\n\n\nAbstract\nZarankiewicz's problem in extremal graph theory asks fo
r the maximum number of edges in a bipartite graph on $n$ vertices which d
oes not contain a copy of $K_{k\,k}$\, the complete bipartite with $k$ ver
tices in both classes. We will consider this question for incidence graphs
of geometric objects. Significantly better bounds are known in this setti
ng\, in particular when the geometric objects are defined by systems of al
gebraic inequalities. We show even stronger bounds under the additional co
nstraint that the defining inequalities are linear. We will also discuss c
onnections of these results to combinatorial geometry and model theory. \n
\nNo background is assumed\, and the talk will be accessible to non-expert
s. Joint work with Artёm Chernikov\, Sergei Starchenko\, Terence Tao\, an
d Chieu-Minh Tran.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonah Blasiak (Drexel University)
DTSTART;VALUE=DATE-TIME:20201119T180000Z
DTEND;VALUE=DATE-TIME:20201119T190000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/8
DESCRIPTION:Title: Crystal graphs\, katabolism\, and Schur positivity\nby Jonah Bla
siak (Drexel University) as part of UCLA Combinatorics Forum\n\n\nAbstract
\nKatabolism is a mysterious operation on tableaux which involves cutting
and reassembling the pieces\nusing Schensted insertion.\nIt is featured in
several Schur positivity conjectures related to\nk-Schur functions and Ha
ll-Littlewood polynomials.\nCrystal graphs are the combinatorial skeletons
of gl_n modules and are a powerful tool for connecting representation the
ory and combinatorics. \nFor instance\, they give a beautiful explanation
of the RSK correspondence.\nUsing crystal graphs\, we uncover the mystery
behind katabolism and resolve a Schur positivity conjecture of Shimozono a
nd Weyman.\nThis talk will include many pictures of crystals and tableaux.
\nThis is joint work with Jennifer Morse and Anna Pun.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Williams (UT Dallas)
DTSTART;VALUE=DATE-TIME:20201203T180000Z
DTEND;VALUE=DATE-TIME:20201203T190000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/10
DESCRIPTION:Title: Strange Expectations\nby Nathan Williams (UT Dallas) as part of
UCLA Combinatorics Forum\n\n\nAbstract\nWe extend our previous work on si
multaneous cores for affine Weyl groups. In type A\, our uniform formula r
ecovers Drew Armstrong's conjecture for the average number of boxes in a s
imultaneous core. This is joint work with Marko Thiel and Eric Stucky.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Bernardi (Brandeis University)
DTSTART;VALUE=DATE-TIME:20201210T180000Z
DTEND;VALUE=DATE-TIME:20201210T190000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/11
DESCRIPTION:Title: A Universal Tutte Polynomial\nby Olivier Bernardi (Brandeis Uni
versity) as part of UCLA Combinatorics Forum\n\n\nAbstract\nWouldn't it be
nice to have a polynomial expression parametrizing at once the Tutte poly
nomial of every matroid of a given size?\nIn this talk\, I will explain ho
w to achieve this goal. The solution involves extending the definition of
the Tutte polynomial from the setting of matroids to the setting of polyma
troids (this is akin to the generalization from graphs to hypergraphs)\, a
nd adopting a geometric point-counting perspective. On our way\, we will c
onnect several notions: the activity-counting invariants of Kalman and Pos
tnikov\, the point-counting invariants of Cameron and Fink\, and the class
ical corank-nullity definition of the Tutte polynomial of matroids.\nThis
is joint work with Tamas Kalman and Alex Postnikov.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swee Hong Chan (UCLA)
DTSTART;VALUE=DATE-TIME:20210930T210000Z
DTEND;VALUE=DATE-TIME:20210930T220000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/12
DESCRIPTION:Title: Log-concave inequalities for posets\nby Swee Hong Chan (UCLA) a
s part of UCLA Combinatorics Forum\n\nLecture held in UCLA Math Sciences b
uilding\, room MS 3915A.\n\nAbstract\nThe study of log-concave inequalitie
s for combinatorial objects have seen much progress in recent years. One s
uch progress is the solution to the strongest form of Mason's conjecture (
independently by Anari et. al. and Brándën-Huh) that the f-vectors of ma
troid independence complex is ultra-log-concave. In this talk\, we discuss
a new proof of this result through linear algebra and discuss generalizat
ions to greedoids and posets. This is a joint work with Igor Pak.\n\nThe t
alk is aimed at a general audience.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Petrov (UVA and MSRI)
DTSTART;VALUE=DATE-TIME:20211014T210000Z
DTEND;VALUE=DATE-TIME:20211014T220000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/13
DESCRIPTION:Title: Schur rational functions\, vertex models\, and random domino tiling
s\nby Leonid Petrov (UVA and MSRI) as part of UCLA Combinatorics Forum
\n\nLecture held in UCLA Math Sciences Building\, room MS 3915A..\n\nAbstr
act\nIt is known that Schur symmetric polynomials admit a number of genera
lizations (Macdonald's 1992 variations) which retain determinantal structu
re - for example\, factorial and supersymmetric Schur functions. We descri
be an overarching family of Schur-like rational functions arising as parti
tion functions of fully inhomogeneous free fermion six vertex model. These
functions are indexed by partitions\, have as variables the pairs $(x_i\,
r_i)$\, $i=1\,...\,N$\, of horizontal rapidities and spin parameters\; 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 introduce rand
om domino tiling models based on the Schur rational functions (a la Schur
processes of Okounkov-Reshetikhin 2001)\, and obtain bulk (lattice) asympt
otics leading to a new deformation of the extended discrete sine kernel. B
ased on the joint project https://arxiv.org/abs/2109.06718 with A. Aggarwa
l\, A. Borodin\, and M. Wheeler.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yibo Gao (MIT)
DTSTART;VALUE=DATE-TIME:20211028T170000Z
DTEND;VALUE=DATE-TIME:20211028T180000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/14
DESCRIPTION:Title: The canonical bijection between pipe dreams and bumpless pipe dream
s\nby Yibo Gao (MIT) as part of UCLA Combinatorics Forum\n\nLecture he
ld in *Virtual only*.\n\nAbstract\nPipe dreams and bumpless pipe dreams ar
e two combinatorial objects that enumerate Schubert polynomials\, and it h
as been an open problem to find a weight-preserving bijection between thes
e two objects since bumpless pipe dreams were introduced by Lam\, Lee and
Shimozono. In this talk\, we present such a bijection and establish its ca
nonical nature by showing that it preserves Monk's rule. This is joint wor
k with Daoji Huang.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Terrence George (University of Michigan)
DTSTART;VALUE=DATE-TIME:20211104T210000Z
DTEND;VALUE=DATE-TIME:20211104T220000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/15
DESCRIPTION:Title: Electrical networks and Lagrangian Grassmannians\nby Terrence G
eorge (University of Michigan) as part of UCLA Combinatorics Forum\n\n\nAb
stract\nCactus networks were introduced by Thomas Lam as a generalization
of planar electrical networks.\nHe defined a map from these networks to a
Grassmannian and showed that the image of this map lies inside the totally
nonnegative part of this Grassmannian. We show that the image of Lam's ma
p consists of exactly the elements that are both totally nonnegative and i
sotropic for a particular skew-symmetric bilinear form. This is joint work
with Sunita Chepuri and David Speyer.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Suho Oh (Texas State)
DTSTART;VALUE=DATE-TIME:20211118T220000Z
DTEND;VALUE=DATE-TIME:20211118T230000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/16
DESCRIPTION:Title: Extending Shellings\nby Suho Oh (Texas State) as part of UCLA C
ombinatorics Forum\n\n\nAbstract\nShellable complexes are simplicial compl
exes with the shelling property: their facets can be ordered nicely\, whic
h translates to interesting properties in algebra and combinatorics. Simon
in 1994 conjectured that any shellable complex can be extended to the k-s
keleton of a simplex while maintaining the shelling property. We go over v
arious tools and results related to this problem. In particular\, we will
be going over a recent joint work with M. Coleman\, A. Dochtermann and N.
Geist on proving this conjecture for a smaller class.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Josh Swanson (USC)
DTSTART;VALUE=DATE-TIME:20211007T210000Z
DTEND;VALUE=DATE-TIME:20211007T220000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/17
DESCRIPTION:Title: Combinatorics of harmonic polynomial differential forms\nby Jos
h Swanson (USC) as part of UCLA Combinatorics Forum\n\nLecture held in UCL
A Math Sciences Building\, room MS 3915A..\n\nAbstract\nA recent conjectur
e of Zabrocki introduced super diagonal coinvariant algebras as a represen
tation-theoretic model for the Delta conjecture of Haglund--Remmel--Wilson
. Subsequent work with Wallach introduced a basis for the alternating comp
onent of the super coinvariant algebra consisting of explicit harmonic pol
ynomials in commuting and anti-commuting variables. We will discuss two fa
milies of relations involving these harmonics\, which are related to Tanis
aki ideals and which we call Tanisaki witness relations. This talk will fo
cus on the combinatorics of these objects rather than the underlying abstr
act motivation.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolle Gonzalez (UCLA)
DTSTART;VALUE=DATE-TIME:20211021T210000Z
DTEND;VALUE=DATE-TIME:20211021T220000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/18
DESCRIPTION:Title: From symmetric functions\, to knots\, and back again.\nby Nicol
le Gonzalez (UCLA) as part of UCLA Combinatorics Forum\n\nLecture held in
UCLA Math Sciences Building\, room MS 3915A.\n\nAbstract\nFor fourteen yea
rs the shuffle conjecture remained open. In essence\, it gave a combinator
ial formula for the Frobenius character of the space of diagonal harmonics
in terms of word parking functions\, which are certain symmetric function
s that can be indexed by lattice paths. Concretely\, the conjecture stated
that this combinatorial sum was equal to the action of the ubiquitous nab
la operator on the nth elementary symmetric polynomial. In a startling pap
er\, Carlsson and Mellit proved this conjecture by introducing a new algeb
ra\, closely related to the double affine Hecke algebra\, called $A_{q\,t}
$ and defining an important polynomial action for it. This algebra allowed
them to perform operations on symmetric functions by lifting the correspo
nding structures via raising and lowering operators to certain higher leve
l polynomial rings\, performing the computations there\, and then projecti
ng them back. Shortly thereafter\, using parabolic flag Hilbert schemes\,
the algebra and its representation was also realized geometrically by Carl
sson\, Gorsky\, and Mellit\, reaffirming its connection to the work Haiman
on the space of diagonal harmonics. I will introduce a topological interp
retation of this algebra and its representation. Namely\, I will describe
how we can realize symmetric functions and the $A_{q\,t}$ operators as bra
id diagrams on an annulus and how many of the complicated algebraic relati
ons using plethysms in the original formulation follow trivially from isot
opy of the diagrams. This paradigm not only eases many computations\, it a
lso informs us of new operators on symmetric functions that while natural
from a topological perspective might be very difficult to see algebraicall
y\, thus yielding new light on an already rich structure. Of particular in
terest is its ability to potentially explain the many conjectures relating
the homology of the toric links and q\,t combinatorics.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:GaYee Park (UMass Amherst)
DTSTART;VALUE=DATE-TIME:20211012T170000Z
DTEND;VALUE=DATE-TIME:20211012T180000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/19
DESCRIPTION:Title: Minimal semi-standard skew tableaux and the Hillman-Grassl correspo
ndence\nby GaYee Park (UMass Amherst) as part of UCLA Combinatorics Fo
rum\n\nLecture held in *Virtual only*.\n\nAbstract\nStandard tableaux of s
kew shape are fundamental objects in\nenumerative and algebraic combinator
ics and no product formula for the\nnumber is known. In 2014\, Naruse gave
a formula as a positive sum over\nexcited diagrams of products of hook-le
ngths. 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 sha
pes 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-sta
ndard Young tableaux\, called the\nminimal SSYT\, that are equinumerous wi
th excited diagrams via a new\ndescription of the Hillan-Grassl bijection
and have a version of excited\nmoves. Lastly\, we relate the minimal skew
SSYT with the terms of the\nOkounkov-Olshanski formula for counting SYT of
skew shape. This is joint\nwork with Alejandro Morales and Greta Panova.\
n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Sherman-Bennett (University of Michigan)
DTSTART;VALUE=DATE-TIME:20211116T220000Z
DTEND;VALUE=DATE-TIME:20211116T230000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/20
DESCRIPTION:Title: The hypersimplex and the m=2 amplituhedron\nby Melissa Sherman-
Bennett (University of Michigan) as part of UCLA Combinatorics Forum\n\nLe
cture held in MS 6627 (!).\n\nAbstract\nI'll discuss a curious corresponde
nce between the $m=2$ amplituhedron\, a $2k$-dimensional subset of $\\math
rm{Gr}(k\, k+2)$\, and the hypersimplex\, an $(n-1)$-dimensional polytope
in $\\mathbb R^n$. The amplituhedron and hypersimplex are both images of t
he totally nonnegative Grassmannian under some map (the amplituhedron map
and the moment map\, respectively)\, but are different dimensions and live
in very different ambient spaces. I'll talk about joint work with Matteo
Parisi and Lauren Williams in which we give a bijection between decomposit
ions of the amplituhedron and decompositions of the hypersimplex (original
ly conjectured by Lukowski--Parisi--Williams). Along the way\, we prove th
e sign-flip description of the $m=2$ amplituhedron conjectured by Arkani-H
amed--Thomas--Trnka and give a new decomposition of the $m=2$ amplituhedro
n into Eulerian-number-many chambers\, inspired by an analogous hypersimpl
ex decomposition.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marianna Russkikh (MIT)
DTSTART;VALUE=DATE-TIME:20211109T180000Z
DTEND;VALUE=DATE-TIME:20211109T190000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/21
DESCRIPTION:Title: Dimers and circle patterns\nby Marianna Russkikh (MIT) as part
of UCLA Combinatorics Forum\n\n\nAbstract\nThe dimer model is a model from
statistical mechanics corresponding to random perfect matchings on graphs
. Circle patterns are a class of embeddings of planar graphs such that eve
ry face admits a circumcircle. We describe how to construct a 't-embedding
' (or a circle pattern) of a dimer planar graph using its Kasteleyn weight
s\, and discuss algebro-geometric properties of these embeddings.\nThis ne
w class of embeddings is the key for studying Miquel dynamics\, a discrete
integrable system on circle patterns: we identify Miquel dynamics on the
space of square-grid circle patterns with the Goncharov-Kenyon dimer dynam
ics and deduce the integrability of the former one and show that the evolu
tion is governed by cluster algebra mutations.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hunter Spink (Stanford)
DTSTART;VALUE=DATE-TIME:20211202T220000Z
DTEND;VALUE=DATE-TIME:20211202T230000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/22
DESCRIPTION:Title: Anti-concentration of random walks on model-theoretic definable set
s\nby Hunter Spink (Stanford) as part of UCLA Combinatorics Forum\n\n\
nAbstract\nClassical anti-concentration results show that random walks in
$\\mathbb{R}^d$ with BIG independent steps can’t concentrate in balls mu
ch better than they can concentrate on individual points.\n\nModel-theoret
ic *definable sets* include Boolean combinations of subsets of $\\mathbb{R
}^d$ defined using equalities and inequalities of arbitrary compositions o
f polynomials\, $e^x$\, $\\ln(x)$ and analytic functions restricted to com
pact boxes. For example\, the intersection of $e^{\\sin(1/(1+(xyz)^2))+x^2
y}+zy \\geq0$ and $xyz=5$ in $\\mathbb{R}^3$.\n\nIn this talk\, I will dis
cuss recent results which show that random walks in $\\mathbb{R}^d$ with A
RBITRARY independent steps can’t concentrate in definable sets not conta
ining line segments much better than they can concentrate on individual po
ints. Time permitting\, I will discuss how these results extend to other g
roups like $\\mathrm{GL}_d(\\mathbb{R})$.\n\nJoint work with Jacob Fox and
Matthew Kwan.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allen Knutson (Cornell)
DTSTART;VALUE=DATE-TIME:20211204T000000Z
DTEND;VALUE=DATE-TIME:20211204T010000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/23
DESCRIPTION:Title: The commuting scheme and generic pipe dreams\nby Allen Knutson
(Cornell) as part of UCLA Combinatorics Forum\n\nLecture held in ! MS 5225
!.\n\nAbstract\nThe space of pairs of commuting matrices is more mysterio
us than you\nmight think -- in particular\, Hochster's 1984 conjecture tha
t it is\nreduced remains unresolved. I'll explain how to degenerate it to
one\ncomponent of the "lower-upper scheme" {(X\,Y) : XY lower triangular\,
\nYX upper triangular}\, a reduced complete intersection\, and how to\ncom
pute the degree of any component as a sum over "generic pipe dreams".\nAs
a consequence\, this recovers both the "pipe dream" and\n"bumpless pipe dr
eam" formulae for double Schubert polynomials.\nSome of this work is joint
with Paul Zinn-Justin.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Karpenkov (University of Liverpool)
DTSTART;VALUE=DATE-TIME:20220414T210000Z
DTEND;VALUE=DATE-TIME:20220414T220000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/24
DESCRIPTION:Title: Combinatorics and Geometry of Markov numbers\nby Oleg Karpenkov
(University of Liverpool) as part of UCLA Combinatorics Forum\n\nLecture
held in MS 7608.\n\nAbstract\nMarkov numbers are positive solutions to the
Markov Diophantine equation $x^2+y^2+z^2=3xyz$. The set of Markov numbers
can be very simple\, generated iteratively starting with the smallest sol
ution $(1\,1\,1)$\, which defines a natural binary tree structure on the s
et of all solutions. Markov numbers appear in the study of integer minima
of quadratic forms\, cluster algebra\, etc.\n\nIn this talk we introduce g
eneralized Markov numbers and extend the classical Markov theory. We show
that the principles hidden in Markov's theory are much broader and can be
substantively extended beyond the limits of Markov's theory.\n\nIn particu
lar we discuss recursive properties for these numbers and find correspondi
ng values in the Markov spectrum. Further we give a counterexample to the
generalized Markov uniqueness conjecture. The proposed generalization is b
ased on geometry of numbers\, it substantively uses lattice trigonometry a
nd geometric theory of continued numbers.\n\nThe talk is accessible to the
general audience.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugene Gorsky (UC Davis)
DTSTART;VALUE=DATE-TIME:20221006T210000Z
DTEND;VALUE=DATE-TIME:20221006T220000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/25
DESCRIPTION:Title: Cluster structures on braid varieties\nby Eugene Gorsky (UC Dav
is) as part of UCLA Combinatorics Forum\n\nLecture held in MS 7608.\n\nAbs
tract\nGiven a positive braid\, one can define a smooth affine algebraic v
ariety called the braid variety. Braid varieties generalize several import
ant varieties in Lie theory such as open Richardson and positroid varietie
s. I will construct a cluster structure on a braid variety of arbitrary ty
pe using combinatorial objects called weaves. This is a joint work with Ro
ger Casals\, Mikhail Gorsky\, Ian Le\, Linhui Shen and Jose Simental.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Be'eri Greenfeld (UCSD)
DTSTART;VALUE=DATE-TIME:20221027T233000Z
DTEND;VALUE=DATE-TIME:20221028T001000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/26
DESCRIPTION:Title: Growth of unbounded subsets in nilpotent groups and random mapping
statistics\nby Be'eri Greenfeld (UCSD) as part of UCLA Combinatorics F
orum\n\nLecture held in MS 6627.\n\nAbstract\nLet $G$ be an infinite group
. Let $g(k\,n)$ be the maximum number of length-$n$ words over an arbitrar
y $k$-letter subset of $G$. How does $g(k\,n)$ behave? Obviously\, $g(k\,n
)$ is at most $k^n$\, and Semple-Shalev proved that if $G$ is finitely gen
erated and residually finite then $g(k\,n)< k^n$ if and only if $G$ is vir
tually 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 polynomi
ally bounded.\n\nWe quantify the Semple-Shalev Theorem at the other extrem
e\, where $k=\\Theta(n)$. Specifically\, for a finitely generated residual
ly finite group $G$\, the ratio $g(k\,n)/k^n$ either tends to zero (if and
only if $G$ is virtually abelian)\, or is greater than or equal to an exp
licitly calculated optimal threshold. For higher- step free nilpotent grou
ps\, this ratio tends to 1.\n\nAlong the way\, we find the probability tha
t a random function $f:[n]\\to [n]$ can be recovered from a suitable "inve
rsion set"\, and geometrically interpret our results via random paths in $
\\mathbb{Z}^n$ and the areas of their projected polygons. Finally\, we pro
vide a model-theoretic characterization of suboptimality of $g(k\,n)$ by m
eans of free sub-models and polynomial identities\, which enables to gener
alize the discussion to various other classes of algebraic structures.\n\n
This is a joint work with Hagai Lavner.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Colleen Robichaux (UCLA)
DTSTART;VALUE=DATE-TIME:20221028T002000Z
DTEND;VALUE=DATE-TIME:20221028T010000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/27
DESCRIPTION:Title: Degrees of Grothendieck polynomials and Castelnuovo-Mumford regular
ity\nby Colleen Robichaux (UCLA) as part of UCLA Combinatorics Forum\n
\nLecture held in MS 6627.\n\nAbstract\nWe give an explicit formula for th
e degree of a vexillary Grothendieck polynomial. This generalizes a previo
us result of Rajchgot-Ren-Robichaux-St.Dizier-Weigandt for degrees of symm
etric Grothendieck polynomials. We apply these formulas to compute the Cas
telnuovo-Mumford regularity of certain Kazhdan-Lusztig varieties coming fr
om open patches of Grassmannians as well as the regularity of mixed one-si
ded ladder determinantal ideals. This is joint work with Jenna Rajchgot an
d Anna Weigandt.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (UC Davis)
DTSTART;VALUE=DATE-TIME:20221028T011000Z
DTEND;VALUE=DATE-TIME:20221028T015000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/28
DESCRIPTION:Title: Grid plabic graphs\, Legendrian weaves\, and (quasi-)cluster struct
ures\nby Daping Weng (UC Davis) as part of UCLA Combinatorics Forum\n\
nLecture held in MS 6627.\n\nAbstract\nGiven a "grid" plabic graph on $\\m
athbb{R}^2$\, we can construct a Legendrian link\, which is a link in $\\m
athbb{R}^3$ satisfying certain tangential conditions. We study a moduli sp
ace problem associated with the Legendrian link\, and construct a natural
(quasi-)cluster structure on this moduli space using Legendrian weaves. In
particular\, we prove that any braid variety associated with $\\beta \\De
lta$ for a 3-strand braid $\\beta$ admits cluster structures with an expli
cit construction of initial seeds. We also construct Donaldson-Thomas tran
sformations for these moduli spaces.\n\nIn this talk\, I will introduce th
e theoretical background and describe the basic combinatorics for construc
ting Legendrian weaves and the (quasi-)cluster structures from a grid plab
ic graph. This is based on a joint work with Roger Casals (arXiv:2204.1324
4).\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Korotkikh (MIT)
DTSTART;VALUE=DATE-TIME:20221111T003000Z
DTEND;VALUE=DATE-TIME:20221111T011000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/29
DESCRIPTION:Title: Spin $q$-Whittaker symmetric functions and vertex models.\nby S
ergei Korotkikh (MIT) as part of UCLA Combinatorics Forum\n\nLecture held
in MS 6627.\n\nAbstract\nWe introduce a new family of symmetric functions
called spin $q$-Whittaker functions. We have found these functions using s
olvable vertex model from mathematical physics and they basically are defi
ned by taking a specific sum over path ensembles on a square grid. I will
describe this construction from scratch and will explain how it leads to t
he following two properties. First property is the generalization of Cauch
y summation identity: an important identity from algebraic combinatorics w
hich encapsulates orthogonality relations for symmetric functions. Second
property is a unique structure of the vanishing points of our functions wh
ich leads to a characterization in terms of an interpolation problem which
is similar to the work of Okounkov from 1997 about interpolation properti
es of symmetric functions. All necessary background on vertex models and s
ymmetric functions will be explained and\, time permitting\, I will also c
over connections to probability and quantum groups.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Greta Panova (USC)
DTSTART;VALUE=DATE-TIME:20221111T012000Z
DTEND;VALUE=DATE-TIME:20221111T020000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/31
DESCRIPTION:Title: The world of poset inequalities\nby Greta Panova (USC) as part
of UCLA Combinatorics Forum\n\nLecture held in MS 6627.\n\nAbstract\nParti
ally ordered sets are ubiquitous\, yet poorly understood structures in com
binatorics. Counting their linear extensions and order preserving maps do
not have nice closed formulas and thus we can only hope to understand them
qualitatively or asymptotically in greater generality. In this talk I wil
l show some inequalities relating linear extensions and order preserving m
aps for general posets. We will discuss various proofs\, problems and conj
ectures. Based on a series of joint papers with Swee Hong Chan and Igor Pa
k.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tianyi Yu (UCSD)
DTSTART;VALUE=DATE-TIME:20221130T003000Z
DTEND;VALUE=DATE-TIME:20221130T011000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/32
DESCRIPTION:Title: Top degree components of Grothendieck and Lascoux polynomials\n
by Tianyi Yu (UCSD) as part of UCLA Combinatorics Forum\n\nLecture 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 a
nd has dimension $n!$. Its Hilbert series is the $q$-analogue of $n!$. Ano
ther basis of this space is given by key polynomials\, which are character
s of the Demazure modules. Schubert and key polynomials are the ``bottom l
ayers'' of Grothendieck and Lascoux polynomials\, two inhomogeneous polyno
mials. 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 t
op layer of Lascoux polynomials. We then develop a diagrammatic way to com
pute the degrees of these polynomials. Finally\, we describe the Hilbert s
eries of this space involving a classical q-analogue of the Bell numbers.
\nThe talk does not assume knowledge of Grothendieck or Lascoux polynomial
s. This is a joint work with Jianping Pan.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cosmin Pohoata (IAS)
DTSTART;VALUE=DATE-TIME:20221130T012000Z
DTEND;VALUE=DATE-TIME:20221130T020000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/33
DESCRIPTION:Title: Convex polytopes from fewer points\nby Cosmin Pohoata (IAS) as
part of UCLA Combinatorics Forum\n\nLecture held in MS 6627.\n\nAbstract\n
Finding the smallest integer N=ES_d(n) such that in every configuration of
N points in R^d in general position there exist n points in convex positi
on is one of the most classical problems in extremal combinatorics\, known
as the Erdos-Szekeres problem. In 1935\, Erdos and Szekeres famously conj
ectured that ES_2(n)=2^{n−2}+1 holds\, which was nearly settled by Suk i
n 2016\, who showed that ES_2(n)≤2^{n+o(n)}. We discuss a recent proof t
hat ES_d(n)=2^{o(n)} holds for all d≥3. Joint work with Dmitrii Zakharov
.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Gaetz (Cornell)
DTSTART;VALUE=DATE-TIME:20230314T233000Z
DTEND;VALUE=DATE-TIME:20230315T001000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/34
DESCRIPTION:Title: An SL(4) web basis from hourglass plabic graphs\nby Christian G
aetz (Cornell) as part of UCLA Combinatorics Forum\n\nLecture held in MS 6
221.\n\nAbstract\nThe SL(3) web basis is a special basis of certain 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 ha
s found connections and applications to cluster algebras\, canonical bases
\, dimer models\, and tableau combinatorics. The main open problem has rem
ained: how to find a basis replicating the desirable properties of this ba
sis for SL(4) and beyond? I will describe joint work with Oliver Pechenik\
, Stephan Pfannerer\, Jessica Striker\, and Josh Swanson in which we const
ruct such a basis for SL(4). Modified versions of plabic graphs and the si
x-vertex model and new tableau combinatorics will appear along the way\, b
ut knowledge of these topics won't be assumed in the talk.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Mazin (KSU)
DTSTART;VALUE=DATE-TIME:20230315T002000Z
DTEND;VALUE=DATE-TIME:20230315T010000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/35
DESCRIPTION:Title: Springer Fibers and Rational Dyck Paths\nby Mikhail Mazin (KSU)
as part of UCLA Combinatorics Forum\n\nLecture held in MS 6221.\n\nAbstra
ct\nAffine Grassmanian can be thought of as the space of linear subspaces
V in the space of Laurent power series C((t))\, invariant under multiplica
tion by t^n. It admits a cell decomposition with cells enumerated by cofin
ite subsets in the set of non-negative integers\, invariant under addition
of n. An Affine Springer Fiber is a subvariety in the Affine Grassmanian\
, consisting of subspaces that are also invariant under the multiplication
by a fixed function f(t). If f(t)=t^m\, where n and m are relatively prim
e\, then the corresponding Affine Springer Fiber is particularly well beha
ved: its intersection with a cell of the Affine Grassmanian is non-empty i
f and only if the corresponding subset of integers is also invariant under
addition of m\, in which case the intersection itself is an affine cell o
f a possibly smaller dimension. One can further see that the (m\,n)-invari
ant subsets of integers are in bijection with the (m\,n)-Dyck paths\, and
the dimensions of cells are computed using the so-called dinv statistic.\n
\nIn this talk I will present a recent generalization of the above constru
ction to the case when m and n are not relatively prime and f(t)=t^m+t^{m+
1}. Turns out that the Springer Fiber in this case is again well-behaved\,
with the non-empty intersections enumerated by the (m\,n)-invariant subse
ts satisfying an additional admissibility condition. Furthermore\, such su
bsets turn out to be in bijection with the (m\,n)-Dyck paths\, and the dim
ensions of cells are again computed using the dinv statistic. The talk is
based on a joint work with Eugene Gorsky and Alexei Oblomkov (arXiv:2210.1
2569).\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Black (UC Davis)
DTSTART;VALUE=DATE-TIME:20231005T233000Z
DTEND;VALUE=DATE-TIME:20231006T020000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/36
DESCRIPTION:Title: Monotone Paths on Polytopes in Combinatorics and Optimization\n
by Alexander Black (UC Davis) as part of UCLA Combinatorics Forum\n\nLectu
re held in MS 6621.\n\nAbstract\nLinear programming is a core problem in o
ptimization\, and geometrically\, it is the problem of finding the highest
point in some direction on a polytope. The standard combinatorial algorit
hm for solving linear programs is the simplex method\, which works by walk
ing from vertex to vertex of the polytope along edges moving higher at eac
h step. We call such a walk a monotone path. There are many ways for the s
implex method to choose monotone paths called pivot rules\, and the main o
pen problem in the area is to find a pivot rule that guarantees the path f
ollowed is always of polynomial length. In this talk\, I will discuss an a
pproach to this problem grounded in understanding the space of monotone pa
ths 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 a
nalogous construction called the pivot rule polytope introduced by myself
in joint work with De Loera\, Lütjeharms\, and Sanyal. My focus will be o
n the many examples that arise from these constructions such as the permut
ahedron and associahedron.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yelena Mandelshtam (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20231005T233000Z
DTEND;VALUE=DATE-TIME:20231006T020000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/37
DESCRIPTION:Title: Combinatorics of m=1 Grasstopes\nby Yelena Mandelshtam (UC Berk
eley) as part of UCLA Combinatorics Forum\n\nLecture held in MS 6621.\n\nA
bstract\nThe amplituhedron is an object introduced by physicists in 2013 a
rising from their study of scattering amplitudes which has garnered much r
ecent attention from physicists and mathematicians alike. Mathematically\,
it is a linear projection of a nonnegative Grassmannian to a smaller Gras
smannian\, via a map induced by a totally positive matrix. A Grassmann pol
ytope\, or Grasstope\, is a generalization of the amplituhedron\, defined
to be such a projection by any matrix\, removing one of the positivity con
ditions. In this talk\, I will discuss joint work with Dmitrii Pavlov and
Lizzie Pratt in which we study these objects\, with hope that we may gain
new insights by broadening our horizons and studying all Grasstopes.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Terrence George (UCLA)
DTSTART;VALUE=DATE-TIME:20231005T233000Z
DTEND;VALUE=DATE-TIME:20231006T020000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/38
DESCRIPTION:Title: Inverse problem for electrical networks\nby Terrence George (UC
LA) as part of UCLA Combinatorics Forum\n\nLecture held in MS 6621.\n\nAbs
tract\nAn electrical network is a graph embedded in a disk with some verti
ces on the boundary of the disk\, and with positive real numbers\, called
conductances\, associated to its edges. Associated to such an electrical n
etwork is its response matrix which encodes all information that can be de
duced by making electrical measurements on the boundary. I will discuss ho
w the inverse problem of recovering the conductances from the response mat
rix can be solved using an electrical-network version of the twist map on
the positive Grassmannian.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chenchen Zhao (USC)
DTSTART;VALUE=DATE-TIME:20231026T233000Z
DTEND;VALUE=DATE-TIME:20231027T020000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/39
DESCRIPTION:Title: Kronecker product of Schur functions of square shapes\nby Chenc
hen Zhao (USC) as part of UCLA Combinatorics Forum\n\nLecture held in MS 6
627.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lenny Fukshansky (Claremont McKenna College)
DTSTART;VALUE=DATE-TIME:20231026T233000Z
DTEND;VALUE=DATE-TIME:20231027T020000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/40
DESCRIPTION:Title: A geometric construction for integer sparse recovery\nby Lenny
Fukshansky (Claremont McKenna College) as part of UCLA Combinatorics Forum
\n\nLecture held in MS 6627.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Soukup (UCLA)
DTSTART;VALUE=DATE-TIME:20231026T233000Z
DTEND;VALUE=DATE-TIME:20231027T020000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/41
DESCRIPTION:Title: Complexity of sign imbalance and parity of linear extensions\nb
y David Soukup (UCLA) as part of UCLA Combinatorics Forum\n\nLecture held
in MS 6621.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiliang Gao (UIUC)
DTSTART;VALUE=DATE-TIME:20231117T003000Z
DTEND;VALUE=DATE-TIME:20231117T030000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/42
DESCRIPTION:Title: Combinatorics of the Plucker map?\nby Shiliang Gao (UIUC) as pa
rt of UCLA Combinatorics Forum\n\nLecture held in MS 6621.\n\nAbstract\nI
will discuss how Young tableaux arise from the Plucker map. Influential wo
rk of Hodge from the 1940s led the way in using Grobner bases to combinato
rially study the Grassmannian. In the past decade\, the work of Knutson-La
m-Speyer\, and more recently Galashin-Lam\, has brought to the fore the si
gnificance of positroid subvarieties in the Grassmannian. I will explain h
ow to use Young tableaux to understand these subvarieties and thereby how
to connect promotion on Young tableaux with the cyclic symmetry of positro
id varieties. This is based on joint work with Ayah Almousa and Daoji Huan
g\, see arxiv.org/abs/2309.15384.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theo Douvropoulos (Brandeis University)
DTSTART;VALUE=DATE-TIME:20231117T003000Z
DTEND;VALUE=DATE-TIME:20231117T030000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/43
DESCRIPTION:Title: Families of Shi-like and Catalan-like deformations of braid and ref
lection arrangements\nby Theo Douvropoulos (Brandeis University) as pa
rt of UCLA Combinatorics Forum\n\nLecture held in MS 6621.\n\nAbstract\nTh
e Shi arrangement $Shi_n$ is a deformation of the braid arrangement $Br_n$
and was introduced by Shi to study Kazhdan-Lusztig cells (that turn out t
o be unions of the regions of $Shi_n$). It has remarkable numerological an
d structural properties: it has $(n+1)^{n-1}$-many regions that can be nat
urally labeled by parking functions or trees\; it has analogs for all Weyl
groups\; its characteristic polynomial factors with positive integer root
s.\n\nWe will present recent work\, joint with Olivier Bernardi\, where we
give an $n$-parameter family of deformations of the braid arrangement $Br
_n$ that generalize the Shi arrangement $Shi_n$. They share many of the re
markable properties of $Shi_n$\, in particular they come with product form
ulas for their characteristic polynomials\, and their regions are naturall
y labeled by Cayley trees. We will present a parallel story for Catalan-li
ke deformations\, generalizations to other Weyl groups\, and applications
on the theory of parking spaces.\n\nWe will finish with the original motiv
ation for this construction\, which was the study of coxeter theoretic inv
ariants on restrictions of reflection arrangements and associated multi-ar
rangements.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Grebík (UCLA)
DTSTART;VALUE=DATE-TIME:20231117T003000Z
DTEND;VALUE=DATE-TIME:20231117T030000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/44
DESCRIPTION:Title: Edge colorings and distributed computing\nby Jan Grebík (UCLA)
as part of UCLA Combinatorics Forum\n\nLecture held in MS 6621.\n\nAbstra
ct\nOne of fundamental notions of graph theory is the chromatic index $\\c
hi'(G)$ of a graph $G$ which is the smallest number of colors needed to co
lor 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 i
s enough\, where $\\Delta$ is the maximum degree of $G$. In fact\, there i
s a polynomial time sequential algorithm that produces such a coloring. In
this talk I will discuss edge colorings from the perspective of the LOCAL
model of distributed computing. In particular\, I will talk about what ha
ppens when we try to replace the sequential algorithm by a distributed one
.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daoji Huang (UMN)
DTSTART;VALUE=DATE-TIME:20240202T003000Z
DTEND;VALUE=DATE-TIME:20240202T030000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/45
DESCRIPTION:Title: Tableaux theory inspired methods for Schubert calculus\nby Daoj
i Huang (UMN) as part of UCLA Combinatorics Forum\n\nLecture held in MS 66
21.\n\nAbstract\nThe classical Littlewood-Richardson (LR) coefficients are
special cases of Schubert structure constants\, for which many combinator
ial interpretations are known. The theory of symmetric functions and combi
natorics of Young tableaux provide a combinatorial toolbox for many differ
ent but related rules for the LR coefficients. In this talk\, I will expla
in the basic ideas to lift many components of the classical theory to the
context of Schubert structure constants\, as well as the obstructions and
challenges to solving the full problems using these methods.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasu Tewari (U of Toronto)
DTSTART;VALUE=DATE-TIME:20240202T003000Z
DTEND;VALUE=DATE-TIME:20240202T030000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/46
DESCRIPTION:Title: The ideal of quasisymmetric polynomials\nby Vasu Tewari (U of T
oronto) as part of UCLA Combinatorics Forum\n\nLecture held in MS 6621.\n\
nAbstract\nWith an eye toward mimicking the combinatorial theory of Schube
rt polynomials\, I will describe a new perspective on the quotient of the
polynomial ring modulo the ideal $QSym_n^+$ of quasisymmetric polynomials.
This involves two simple operators-- trimming and blossoming-- acting on
the polynomial ring. The trimming operators are degree-lowering operators
that are a mild modification of divided difference operators (central to L
ascoux-Schützenberger's construction of Schubert polynomials). We identif
y a basis that may be considered an appropriate analogue to Schubert polyn
omials with regard to these operators. The blossoming operators are degre
e-increasing operators that grow volume polynomials of certain cubes decom
posing the permutahedron.\n\nJoint work with Philippe Nadeau (Lyon/CNRS) a
nd Hunter Spink (UofT).\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karim Adiprasito (IMJ-PRG)
DTSTART;VALUE=DATE-TIME:20240223T003000Z
DTEND;VALUE=DATE-TIME:20240223T030000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/47
DESCRIPTION:Title: Efficiently encoding configuration spaces\nby Karim Adiprasito
(IMJ-PRG) as part of UCLA Combinatorics Forum\n\nLecture held in MS 6621.\
n\nAbstract\nWe discuss how difficult it is to encode the complement of a
configuration space\, naturally a neat algebraic variety\, by a smaller th
an naïve number of algebraic constraints\, in an attempt to deepen our un
derstanding of the work of Haiman. We also translate this to varieties th
at merely resemble configuration spaces. Joint work with Itaï Ben Yacoov
and Ehud Hrushovski.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brendan Pawlowski
DTSTART;VALUE=DATE-TIME:20240223T003000Z
DTEND;VALUE=DATE-TIME:20240223T030000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/49
DESCRIPTION:Title: The fraction of an $S_n$-orbit on a hyperplane\nby Brendan Pawl
owski as part of UCLA Combinatorics Forum\n\nLecture held in MS 6621.\n\nA
bstract\nFix a point in $\\mathbb{R}^n$ with distinct coordinates and cons
ider the $S_n$-orbit obtained by permuting its coordinates. Huang\, McKinn
on\, and Satriano conjectured that a hyperplane other than $x_1 + ... + x_
n = 0$ can contain at most $2⌊n/2⌋(n-2)!$ points of this orbit. We exp
lain\nhow to prove their conjecture using the Sperner property for Bruhat\
norder and bounds on q-binomial coefficients.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amanda Schwartz (UMich)
DTSTART;VALUE=DATE-TIME:20241018T000000Z
DTEND;VALUE=DATE-TIME:20241018T021500Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/50
DESCRIPTION:Title: The HOMFLY Polynomial of a Forest Quiver\nby Amanda Schwartz (U
Mich) as part of UCLA Combinatorics Forum\n\nLecture held in MS 6221.\n\nA
bstract\nThe HOMFLY polynomial of a link is a two-variable link invariant
which was introduced in the 1980s. It can be defined recursively using a s
kein relation and specializes to other link invariants such as the Alexand
er polynomial and Jones polynomial. In this talk\, we will begin by defini
ng the HOMFLY polynomial of a forest quiver via a recursive definition on
the underlying graph of the quiver. Then\, we will discuss how the HOMFLY
polynomial of a forest quiver is related to the HOMFLY polynomial of certa
in plabic links. In particular\, given any connected plabic graph $G$ whos
e quiver $Q_G$ is a forest quiver\, the HOMFLY polynomial of the associate
d plabic link is in fact equal to the HOMFLY polynomial of the quiver $Q_G
$. We will sketch a proof of this result and also discuss a closed-form ex
pression for the Alexander polynomial of a forest quiver.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steven Karp (Notre Dame)
DTSTART;VALUE=DATE-TIME:20241018T000000Z
DTEND;VALUE=DATE-TIME:20241018T021500Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/51
DESCRIPTION:Title: Positivity in real Schubert calculus\nby Steven Karp (Notre Dam
e) as part of UCLA Combinatorics Forum\n\nLecture held in MS 6221.\n\nAbst
ract\nSchubert calculus involves studying intersection problems among line
ar 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-dimensional s
ubspaces nontrivially (it turns out there are 2 of them). In the 1990's\,
B. and M. Shapiro conjectured that a certain family of Schubert problems h
as the remarkable property that all of its complex solutions are real. Thi
s conjecture inspired a lot of work in the area\, including its proof by M
ukhin-Tarasov-Varchenko in 2009. I will present a strengthening of this re
sult which resolves some conjectures of Sottile\, Eremenko\, Mukhin-Taraso
v\, and myself\, based on surprising connections with total positivity\, t
he representation theory of symmetric groups\, symmetric functions\, and t
he KP hierarchy. This is joint work with Kevin Purbhoo\, and with Evgeny M
ukhin and Vitaly Tarasov.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catherine Babecki (CalTech)
DTSTART;VALUE=DATE-TIME:20241018T000000Z
DTEND;VALUE=DATE-TIME:20241018T021500Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/52
DESCRIPTION:Title: Spectrahedral Geometry of Graph Sparsifiers\nby Catherine Babec
ki (CalTech) as part of UCLA Combinatorics Forum\n\nLecture held in MS 622
1.\n\nAbstract\nWe propose an approach to graph sparsification based on th
e idea of preserving the smallest k eigenvalues and eigenvectors of the gr
aph Laplacian. This is motivated by the fact that small eigenvalues and th
eir associated eigenvectors tend to be more informative of the global stru
cture and geometry of the graph than larger eigenvalues and their eigenvec
tors. The set of all weighted subgraphs of a graph G that have the same fi
rst k eigenvalues (and eigenvectors) as G is the intersection of a polyhed
ron with a cone of positive semidefinite matrices. We discuss the geometry
of these sets and deduce the natural scale of k. Various families of grap
hs illustrate our construction.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Swanson (USC)
DTSTART;VALUE=DATE-TIME:20241108T000000Z
DTEND;VALUE=DATE-TIME:20241108T004000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/53
DESCRIPTION:Title: Webs\, pockets\, and buildings\nby Joshua Swanson (USC) as part
of UCLA Combinatorics Forum\n\nLecture held in UCLA Boelter hall\, room 5
436.\n\nAbstract\nWebs are certain diagrams which are part of a powerful g
raphical calculus arising from quantum groups and knot invariants. Gaetz\,
Pechenik\, Pfannerer\, Striker\, and I recently introduced a web basis fo
r $U_q(\\mathfrak{sl}_4)$ using the new framework of hourglass plabic grap
hs. In this talk\, I will explain how our basis naturally models the geome
try of the affine building $\\Delta(\\SL(4)^\\vee)$. Specifically\, duals
of move-equivalence classes of basis webs assemble to form remarkable 3D s
implicial complexes we call pockets\, which in turn generically extend the
irreducible components of Satake fibers. Special cases correspond to plan
e partitions\, alternating sign matrices\, tilings of the Aztec diamond\,
and more. Joint with Christian Gaetz\, Jessica Striker\, and Haihan Wu.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wonwoo Kang (UIUC)
DTSTART;VALUE=DATE-TIME:20241108T005000Z
DTEND;VALUE=DATE-TIME:20241108T013000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/54
DESCRIPTION:Title: Skein Relations for Punctured Surfaces\nby Wonwoo Kang (UIUC) a
s part of UCLA Combinatorics Forum\n\nLecture held in UCLA Boelter hall\,
room 5436.\n\nAbstract\nSince the introduction of cluster algebras by Fomi
n and Zelevinsky in 2002\, there has been substantial interest in cluster
algebras of surface type. These algebras are particularly significant due
to their ability to construct various combinatorial structures\, such as s
nake graphs\, T-paths\, and posets\, which are useful for proving key stru
ctural properties like positivity and the existence of bases. In this talk
\, we will begin by presenting a cluster expansion formula that utilizes p
oset representatives for arcs on triangulated surfaces. Using these posets
and the expansion formula as tools\, we will demonstrate skein relations\
, which resolve intersections or incompatibilities between arcs. As a resu
lt\, we will demonstrate that bangles and bracelets form spanning sets and
exhibit linear independence\, thereby proving the existence of the bangle
and bracelet bases in punctured surfaces with boundaries and closed surfa
ce with genus 0. This work is done in collaboration with Esther Banaian an
d Elizabeth Kelley.\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Soskin (IAS)
DTSTART;VALUE=DATE-TIME:20241206T003000Z
DTEND;VALUE=DATE-TIME:20241206T030000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/55
DESCRIPTION:by Daniel Soskin (IAS) as part of UCLA Combinatorics Forum\n\n
Lecture held in UCLA Boelter hall\, room 5436.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Neville (UMich)
DTSTART;VALUE=DATE-TIME:20241206T003000Z
DTEND;VALUE=DATE-TIME:20241206T030000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/57
DESCRIPTION:by Scott Neville (UMich) as part of UCLA Combinatorics Forum\n
\nLecture held in UCLA Boelter hall\, room 5436.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jianping Pan (Arizona State University)
DTSTART;VALUE=DATE-TIME:20241206T003000Z
DTEND;VALUE=DATE-TIME:20241206T030000Z
DTSTAMP;VALUE=DATE-TIME:20241112T133929Z
UID:ucla_comb_sem/58
DESCRIPTION:by Jianping Pan (Arizona State University) as part of UCLA Com
binatorics Forum\n\nLecture held in UCLA Boelter hall\, room 5436.\nAbstra
ct: TBA\n
LOCATION:https://researchseminars.org/talk/ucla_comb_sem/58/
END:VEVENT
END:VCALENDAR