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BEGIN:VEVENT
SUMMARY:Anup Rao (University of Washington)
DTSTART:20200415T223000Z
DTEND:20200416T001000Z
DTSTAMP:20260404T094307Z
UID:UWCombGeom/1
DESCRIPTION:Title: Coding for sunflowers\nby Anup Rao (University of Washington
) as part of UW combinatorics and geometry seminar\n\n\nAbstract\nA sunflo
wer is a family of sets that have the same pairwise intersections. We simp
lify a recent result of Alweiss\, Lovett\, Wu and Zhang that gives an uppe
r bound on the size of every family of sets of size k that does not contai
n a sunflower. We show how to use the converse of Shannon's noiseless codi
ng theorem to give a cleaner proof of a similar bound. Our bound shows tha
t there is a constant α such that any family of $(\\alpha p \\log(pk))^k$
sets of size $k$ must contain a $p$-sunflower.\n
LOCATION:https://stable.researchseminars.org/talk/UWCombGeom/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anastasia Chavez (University of California\, Davis)
DTSTART:20200422T223000Z
DTEND:20200423T001000Z
DTSTAMP:20260404T094307Z
UID:UWCombGeom/2
DESCRIPTION:Title: Characterizing quotients of positroids\nby Anastasia Chavez
(University of California\, Davis) as part of UW combinatorics and geometr
y seminar\n\n\nAbstract\nWe characterize quotients of specific families of
positroids. Positroids are a special class of representable matroids intr
oduced by Postnikov in the study of the nonnegative part of the Grassmanni
an. Postnikov defined several combinatorial objects that index positroids.
In this talk\, we make use of two of these objects to combinatorially cha
racterize when certain positroids are quotients. Furthermore\, we conjectu
re a general rule for quotients among arbitrary positroids on the same gro
und set. This is joint work with Carolina Benedetti and Daniel Tamayo.\n\n
There is a pre-seminar (aimed at graduate students) at 3:30–4:00 PM (US
Pacific time\, UTC -7). The main talk starts at 4:10.\n
LOCATION:https://stable.researchseminars.org/talk/UWCombGeom/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rowan Rowlands (University of Washington)
DTSTART:20200429T223000Z
DTEND:20200429T233000Z
DTSTAMP:20260404T094307Z
UID:UWCombGeom/3
DESCRIPTION:Title: Combinatorics of CAT(0) cubical complexes and crossing complexes
\nby Rowan Rowlands (University of Washington) as part of UW combinato
rics and geometry seminar\n\n\nAbstract\nSimplicial complexes and cubical
complexes contain a lot of interesting combinatorics. In this talk\, we wi
ll examine special cases of each\, namely flag simplicial complexes and CA
T(0) cubical complexes\, and we will connect them by introducing the cross
ing complex. The crossing complex unlocks many deep similarities between t
hese two notions: in this talk\, we will use it to relate their $f$-vector
s\, topology and several other combinatorial properties.\n
LOCATION:https://stable.researchseminars.org/talk/UWCombGeom/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Gaetz (MIT)
DTSTART:20200513T223000Z
DTEND:20200514T001000Z
DTSTAMP:20260404T094307Z
UID:UWCombGeom/4
DESCRIPTION:Title: Separable elements and splittings of Weyl groups\nby Christi
an Gaetz (MIT) as part of UW combinatorics and geometry seminar\n\n\nAbstr
act\nThis is joint work with Yibo Gao. We introduce separable elements in
finite Weyl groups\, generalizing the well-studied class of separable per
mutations. We prove that the principal upper and lower order ideals in we
ak Bruhat order generated by a separable element are rank-symmetric and ra
nk-unimodal\, and that the product of their rank generating functions equa
ls that of the whole group\, answering an open problem of Fan Wei\, who pr
oved this result for the symmetric group.\n\nWe prove that the multiplicat
ion map from $W/V \\times V \\to W$ for a generalized quotient of the symm
etric group is always surjective when $V$ is an order ideal in right weak
order\; interpreting these sets of permutations as linear extensions of 2-
dimensional posets gives the first direct combinatorial proof of an inequa
lity due originally to Sidorenko\, answering an open problem Morales\, Pak
\, and Panova. We show that this multiplication map is a bijection if and
only if $V$ is an order ideal in right weak order generated by a separabl
e element\, thereby classifying those generalized quotients which induce s
plittings of the symmetric group\, answering a question of Björner and Wa
chs (1988). All of these results are conjectured to extend to arbitrary f
inite Weyl groups.\n\nNext\, we show that separable elements in $W$ are in
bijection with the faces of all dimensions of two copies of the graph ass
ociahedron of the Dynkin diagram of $W$. This correspondence associates t
o each separable element w a certain nested set\; we give product formulas
for the rank generating functions of the principal upper and lower order
ideals generated by w in terms of these nested sets.\n\nFinally we show th
at separable elements\, although initially defined recursively\, have a no
n-recursive characterization in terms of root system pattern avoidance in
the sense of Billey and Postnikov.\n\nThere is a pre-seminar (aimed at gra
duate students) at 3:30–4:00 PM (US Pacific time\, UTC -7). The main tal
k starts at 4:10.\n
LOCATION:https://stable.researchseminars.org/talk/UWCombGeom/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Graham Gordon (University of Washington)
DTSTART:20200520T223000Z
DTEND:20200521T001000Z
DTSTAMP:20260404T094307Z
UID:UWCombGeom/5
DESCRIPTION:Title: Cycle type factorizations in $\\mathrm{GL}_n \\mathbb{F}_q$\
nby Graham Gordon (University of Washington) as part of UW combinatorics a
nd geometry seminar\n\n\nAbstract\nRecent work by Huang\, Lewis\, Morales\
, Reiner\, and Stanton suggests that the regular elliptic elements of $\\m
athrm{GL}_n \\mathbb{F}_q$ are somehow analogous to the $n$-cycles of the
symmetric group. In 1981\, Stanley enumerated the factorizations of permut
ations into products of $n$-cycles. We study the analogous problem in $\\m
athrm{GL}_n \\mathbb{F}_q$ of enumerating factorizations into products of
regular elliptic elements. More precisely\, we define a notion of cycle ty
pe for $\\mathrm{GL}_n \\mathbb{F}_q$ and seek to enumerate the tuples of
a fixed number of regular elliptic elements whose product has a given cycl
e type. In some special cases\, we provide explicit formulas\, using a sta
ndard character-theoretic technique due to Frobenius by introducing simpli
fied formulas for the necessary character values. We also address\, for la
rge $q$\, the problem of computing the probability that the product of a r
andom tuple of regular elliptic elements has a given cycle type. We conclu
de with some results about the polynomiality of our enumerative formulas a
nd some open problems.\n\nThere is a pre-seminar (aimed at graduate studen
ts) at 3:30–4:00 PM (US Pacific time\, UTC -7). The main talk starts at
4:10.\n
LOCATION:https://stable.researchseminars.org/talk/UWCombGeom/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Helen Jenne (University of Oregon)
DTSTART:20200506T223000Z
DTEND:20200507T001000Z
DTSTAMP:20260404T094307Z
UID:UWCombGeom/6
DESCRIPTION:Title: Combinatorics of the double-dimer model\nby Helen Jenne (Uni
versity of Oregon) as part of UW combinatorics and geometry seminar\n\n\nA
bstract\nIn this talk we will discuss a new result about the double-dimer
model: under certain conditions\, the partition function for double-dimer
configurations of a planar bipartite graph satisfies an elegant recurrence
\, related to the Desnanot-Jacobi identity from linear algebra. A similar
identity for the number of dimer configurations (or perfect matchings) of
a graph was established nearly 20 years ago by Kuo and others. We will als
o explain one of the motivations for this work\, which is a problem in Don
aldson-Thomas and Pandharipande-Thomas theory that will be the subject of
a forthcoming paper with Gautam Webb and Ben Young.\n\nThere is a pre-semi
nar (aimed at graduate students) at 3:30–4:00 PM (US Pacific time\, UTC
-7). The main talk starts at 4:10.\n
LOCATION:https://stable.researchseminars.org/talk/UWCombGeom/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Griffin (University of Washington)
DTSTART:20200527T223000Z
DTEND:20200528T001000Z
DTSTAMP:20260404T094307Z
UID:UWCombGeom/7
DESCRIPTION:Title: Ordered set partitions\, Garsia-Procesi modules\, and rank varie
ties\nby Sean Griffin (University of Washington) as part of UW combina
torics and geometry seminar\n\n\nAbstract\nCoinvariant rings $R_n$ are a w
ell-studied family of rings with rich connections to the combinatorics of
the symmetric group $S_n$. Two remarkable families of graded rings which g
eneralize the coinvariant rings are:\n\n• The cohomology rings of Spring
er fibers $R_\\lambda$\, whose $S_n$-module structure coincides with the d
ual Hall-Littlewood functions under the graded Frobenius characteristic ma
p.\n\n• The generalized coinvariant rings $R_{n\,k}$ of Haglund\, Rhoade
s\, and Shimozono\, which give a representation-theoretic interpretation o
f the expression in the Delta Conjecture when $t=0$. \n\nIn this talk\, we
introduce a family of graded rings $R_{n\,\\lambda\,s}$ which are a commo
n generalization of $R_\\lambda$ and $R_{n\,k}$. We then generalize many o
f the previously known formulas for $R_{\\lambda}$ and $R_{n\,k}$ to our s
etting. Finally\, we show how our results can be applied to Eisenbud-Saltm
an rank varieties\, generalizing work of De Concini-Procesi and Tanisaki.\
n\nThere is a pre-seminar (aimed at graduate students) at 3:30–4:00 PM (
US Pacific time\, UTC -7). The main talk starts at 4:10.\n
LOCATION:https://stable.researchseminars.org/talk/UWCombGeom/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jayadev Athreya (University of Washington)
DTSTART:20200617T223000Z
DTEND:20200618T001000Z
DTSTAMP:20260404T094307Z
UID:UWCombGeom/8
DESCRIPTION:Title: Counting tripods on the torus\nby Jayadev Athreya (Universit
y of Washington) as part of UW combinatorics and geometry seminar\n\n\nAbs
tract\nMotivated by some questions on spectral networks arising from physi
cs\, we study a counting problem for certain immersed graphs on tori. We w
ill explain all relevant terms and our results and proof are essentially v
ia elementary methods.\n\nThere is a pre-seminar (aimed at graduate studen
ts) at 3:30–4:00 PM (US Pacific time\, UTC -7). The main talk starts at
4:10.\n
LOCATION:https://stable.researchseminars.org/talk/UWCombGeom/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandro Morales (University of Massachusetts\, Amherst)
DTSTART:20200603T223000Z
DTEND:20200604T001000Z
DTSTAMP:20260404T094307Z
UID:UWCombGeom/9
DESCRIPTION:Title: Factorization problems in complex reflection groups\nby Alej
andro Morales (University of Massachusetts\, Amherst) as part of UW combin
atorics and geometry seminar\n\n\nAbstract\nThe study of factorizations in
the symmetric group is related to combinatorial objects like graphs embed
ded on surfaces and non-crossing partitions. We consider analogues for com
plex reflections groups of certain factorization problems of permutations
first studied by Jackson\, Schaeffer\, Vassilieva and Bernardi. Instead of
counting factorizations of a long cycle given the number of cycles of eac
h factor\, we count factorizations of Coxeter elements by fixed space dime
nsion of each factor. We show combinatorially that\, as with permutations\
, the generating function counting these factorizations has nice coefficie
nts after an appropriate change of basis. This is joint work with Joel Lew
is.\n\nThere is a pre-seminar (aimed at graduate students) at 3:30–4:00
PM (US Pacific time\, UTC -7). The main talk starts at 4:10.\n
LOCATION:https://stable.researchseminars.org/talk/UWCombGeom/9/
END:VEVENT
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