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BEGIN:VEVENT
SUMMARY:Anup Rao (University of Washington)
DTSTART;VALUE=DATE-TIME:20200415T223000Z
DTEND;VALUE=DATE-TIME:20200416T001000Z
DTSTAMP;VALUE=DATE-TIME:20240329T005559Z
UID:UWCombGeom/1
DESCRIPTION:Title: Coding for sunflowers\nby Anup Rao (University of Washington) as pa
rt of UW combinatorics and geometry seminar\n\n\nAbstract\nA sunflower is
a family of sets that have the same pairwise intersections. We simplify a
recent result of Alweiss\, Lovett\, Wu and Zhang that gives an upper bound
on the size of every family of sets of size k that does not contain a sun
flower. We show how to use the converse of Shannon's noiseless coding theo
rem to give a cleaner proof of a similar bound. Our bound shows that there
is a constant α such that any family of $(\\alpha p \\log(pk))^k$ sets o
f size $k$ must contain a $p$-sunflower.\n
LOCATION:https://researchseminars.org/talk/UWCombGeom/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anastasia Chavez (University of California\, Davis)
DTSTART;VALUE=DATE-TIME:20200422T223000Z
DTEND;VALUE=DATE-TIME:20200423T001000Z
DTSTAMP;VALUE=DATE-TIME:20240329T005559Z
UID:UWCombGeom/2
DESCRIPTION:Title: Characterizing quotients of positroids\nby Anastasia Chavez (Univer
sity of California\, Davis) as part of UW combinatorics and geometry semin
ar\n\n\nAbstract\nWe characterize quotients of specific families of positr
oids. Positroids are a special class of representable matroids introduced
by Postnikov in the study of the nonnegative part of the Grassmannian. Pos
tnikov defined several combinatorial objects that index positroids. In thi
s talk\, we make use of two of these objects to combinatorially characteri
ze when certain positroids are quotients. Furthermore\, we conjecture a ge
neral rule for quotients among arbitrary positroids on the same ground set
. This is joint work with Carolina Benedetti and Daniel Tamayo.\n\nThere i
s 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://researchseminars.org/talk/UWCombGeom/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rowan Rowlands (University of Washington)
DTSTART;VALUE=DATE-TIME:20200429T223000Z
DTEND;VALUE=DATE-TIME:20200429T233000Z
DTSTAMP;VALUE=DATE-TIME:20240329T005559Z
UID:UWCombGeom/3
DESCRIPTION:Title: Combinatorics of CAT(0) cubical complexes and crossing complexes\nb
y Rowan Rowlands (University of Washington) as part of UW combinatorics an
d geometry seminar\n\n\nAbstract\nSimplicial complexes and cubical complex
es contain a lot of interesting combinatorics. In this talk\, we will exam
ine special cases of each\, namely flag simplicial complexes and CAT(0) cu
bical complexes\, and we will connect them by introducing the crossing com
plex. The crossing complex unlocks many deep similarities between these tw
o notions: in this talk\, we will use it to relate their $f$-vectors\, top
ology and several other combinatorial properties.\n
LOCATION:https://researchseminars.org/talk/UWCombGeom/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Gaetz (MIT)
DTSTART;VALUE=DATE-TIME:20200513T223000Z
DTEND;VALUE=DATE-TIME:20200514T001000Z
DTSTAMP;VALUE=DATE-TIME:20240329T005559Z
UID:UWCombGeom/4
DESCRIPTION:Title: Separable elements and splittings of Weyl groups\nby Christian Gaet
z (MIT) as part of UW combinatorics and geometry seminar\n\n\nAbstract\nTh
is is joint work with Yibo Gao. We introduce separable elements in finite
Weyl groups\, generalizing the well-studied class of separable permutatio
ns. We prove that the principal upper and lower order ideals in weak Bruh
at order generated by a separable element are rank-symmetric and rank-unim
odal\, and that the product of their rank generating functions equals that
of the whole group\, answering an open problem of Fan Wei\, who proved th
is result for the symmetric group.\n\nWe prove that the multiplication map
from $W/V \\times V \\to W$ for a generalized quotient of the symmetric g
roup is always surjective when $V$ is an order ideal in right weak order\;
interpreting these sets of permutations as linear extensions of 2-dimensi
onal posets gives the first direct combinatorial proof of an inequality du
e originally to Sidorenko\, answering an open problem Morales\, Pak\, and
Panova. We show that this multiplication map is a bijection if and only i
f $V$ is an order ideal in right weak order generated by a separable eleme
nt\, thereby classifying those generalized quotients which induce splittin
gs of the symmetric group\, answering a question of Björner and Wachs (19
88). All of these results are conjectured to extend to arbitrary finite W
eyl groups.\n\nNext\, we show that separable elements in $W$ are in biject
ion with the faces of all dimensions of two copies of the graph associahed
ron of the Dynkin diagram of $W$. This correspondence associates to each
separable element w a certain nested set\; we give product formulas for th
e rank generating functions of the principal upper and lower order ideals
generated by w in terms of these nested sets.\n\nFinally we show that sepa
rable elements\, although initially defined recursively\, have a non-recur
sive characterization in terms of root system pattern avoidance in the sen
se of Billey and Postnikov.\n\nThere is a pre-seminar (aimed at graduate s
tudents) at 3:30–4:00 PM (US Pacific time\, UTC -7). The main talk start
s at 4:10.\n
LOCATION:https://researchseminars.org/talk/UWCombGeom/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Graham Gordon (University of Washington)
DTSTART;VALUE=DATE-TIME:20200520T223000Z
DTEND;VALUE=DATE-TIME:20200521T001000Z
DTSTAMP;VALUE=DATE-TIME:20240329T005559Z
UID:UWCombGeom/5
DESCRIPTION:Title: Cycle type factorizations in $\\mathrm{GL}_n \\mathbb{F}_q$\nby Gra
ham Gordon (University of Washington) as part of UW combinatorics and geom
etry seminar\n\n\nAbstract\nRecent work by Huang\, Lewis\, Morales\, Reine
r\, and Stanton suggests that the regular elliptic elements of $\\mathrm{G
L}_n \\mathbb{F}_q$ are somehow analogous to the $n$-cycles of the symmetr
ic group. In 1981\, Stanley enumerated the factorizations of permutations
into products of $n$-cycles. We study the analogous problem in $\\mathrm{G
L}_n \\mathbb{F}_q$ of enumerating factorizations into products of regular
elliptic elements. More precisely\, we define a notion of cycle type 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 cycle type.
In some special cases\, we provide explicit formulas\, using a standard c
haracter-theoretic technique due to Frobenius by introducing simplified fo
rmulas for the necessary character values. We also address\, for large $q$
\, the problem of computing the probability that the product of a random t
uple of regular elliptic elements has a given cycle type. We conclude with
some results about the polynomiality of our enumerative formulas and some
open problems.\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://researchseminars.org/talk/UWCombGeom/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Helen Jenne (University of Oregon)
DTSTART;VALUE=DATE-TIME:20200506T223000Z
DTEND;VALUE=DATE-TIME:20200507T001000Z
DTSTAMP;VALUE=DATE-TIME:20240329T005559Z
UID:UWCombGeom/6
DESCRIPTION:Title: Combinatorics of the double-dimer model\nby Helen Jenne (University
of Oregon) as part of UW combinatorics and geometry seminar\n\n\nAbstract
\nIn this talk we will discuss a new result about the double-dimer model:
under certain conditions\, the partition function for double-dimer configu
rations of a planar bipartite graph satisfies an elegant recurrence\, rela
ted to the Desnanot-Jacobi identity from linear algebra. A similar identit
y for the number of dimer configurations (or perfect matchings) of a graph
was established nearly 20 years ago by Kuo and others. We will also expla
in one of the motivations for this work\, which is a problem in Donaldson-
Thomas and Pandharipande-Thomas theory that will be the subject of a forth
coming paper with Gautam Webb and Ben Young.\n\nThere is a pre-seminar (ai
med at graduate students) at 3:30–4:00 PM (US Pacific time\, UTC -7). Th
e main talk starts at 4:10.\n
LOCATION:https://researchseminars.org/talk/UWCombGeom/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Griffin (University of Washington)
DTSTART;VALUE=DATE-TIME:20200527T223000Z
DTEND;VALUE=DATE-TIME:20200528T001000Z
DTSTAMP;VALUE=DATE-TIME:20240329T005559Z
UID:UWCombGeom/7
DESCRIPTION:Title: Ordered set partitions\, Garsia-Procesi modules\, and rank varieties\nby Sean Griffin (University of Washington) as part of UW combinatorics
and geometry seminar\n\n\nAbstract\nCoinvariant rings $R_n$ are a well-stu
died family of rings with rich connections to the combinatorics of the sym
metric group $S_n$. Two remarkable families of graded rings which generali
ze the coinvariant rings are:\n\n• The cohomology rings of Springer fibe
rs $R_\\lambda$\, whose $S_n$-module structure coincides with the dual Hal
l-Littlewood functions under the graded Frobenius characteristic map.\n\n
• The generalized coinvariant rings $R_{n\,k}$ of Haglund\, Rhoades\, an
d Shimozono\, which give a representation-theoretic interpretation of the
expression in the Delta Conjecture when $t=0$. \n\nIn this talk\, we intro
duce a family of graded rings $R_{n\,\\lambda\,s}$ which are a common gene
ralization of $R_\\lambda$ and $R_{n\,k}$. We then generalize many of the
previously known formulas for $R_{\\lambda}$ and $R_{n\,k}$ to our setting
. Finally\, we show how our results can be applied to Eisenbud-Saltman ran
k varieties\, generalizing work of De Concini-Procesi and Tanisaki.\n\nThe
re is a pre-seminar (aimed at graduate students) at 3:30–4:00 PM (US Pac
ific time\, UTC -7). The main talk starts at 4:10.\n
LOCATION:https://researchseminars.org/talk/UWCombGeom/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jayadev Athreya (University of Washington)
DTSTART;VALUE=DATE-TIME:20200617T223000Z
DTEND;VALUE=DATE-TIME:20200618T001000Z
DTSTAMP;VALUE=DATE-TIME:20240329T005559Z
UID:UWCombGeom/8
DESCRIPTION:Title: Counting tripods on the torus\nby Jayadev Athreya (University of Wa
shington) as part of UW combinatorics and geometry seminar\n\n\nAbstract\n
Motivated by some questions on spectral networks arising from physics\, we
study a counting problem for certain immersed graphs on tori. We will exp
lain all relevant terms and our results and proof are essentially via elem
entary methods.\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://researchseminars.org/talk/UWCombGeom/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandro Morales (University of Massachusetts\, Amherst)
DTSTART;VALUE=DATE-TIME:20200603T223000Z
DTEND;VALUE=DATE-TIME:20200604T001000Z
DTSTAMP;VALUE=DATE-TIME:20240329T005559Z
UID:UWCombGeom/9
DESCRIPTION:Title: Factorization problems in complex reflection groups\nby Alejandro M
orales (University of Massachusetts\, Amherst) as part of UW combinatorics
and geometry seminar\n\n\nAbstract\nThe study of factorizations in the sy
mmetric group is related to combinatorial objects like graphs embedded on
surfaces and non-crossing partitions. We consider analogues for complex re
flections groups of certain factorization problems of permutations first s
tudied by Jackson\, Schaeffer\, Vassilieva and Bernardi. Instead of counti
ng factorizations of a long cycle given the number of cycles of each facto
r\, we count factorizations of Coxeter elements by fixed space dimension o
f each factor. We show combinatorially that\, as with permutations\, the g
enerating function counting these factorizations has nice coefficients aft
er an appropriate change of basis. This is joint work with Joel Lewis.\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://researchseminars.org/talk/UWCombGeom/9/
END:VEVENT
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