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BEGIN:VEVENT
SUMMARY:Noah Snyder (Indiana University)
DTSTART:20200420T200000Z
DTEND:20200420T210000Z
DTSTAMP:20260422T212752Z
UID:ADM-Davis/1
DESCRIPTION:Title: The exceptional knot polynomial\nby Noah Snyder (Indiana University)
as part of UC Davis algebra & discrete math seminar\n\n\nAbstract\nMany L
ie algebras fit into discrete families like $\\operatorname{GL}_n$\, $\\op
eratorname{O}_n$\, $\\operatorname{Sp}_n$. By work of Brauer\, Deligne and
others\, the corresponding planar algebras fit into continuous familes $\
\operatorname{GL}_t$ and $\\operatorname{OSp}_t$. A similar story holds fo
r quantum groups\, so we can speak of two parameter families $(\\operatorn
ame{GL}_t)_q$ and $(\\operatorname{OSp}_t)_q$. These planar algebras are t
he ones attached to the HOMFLY and Kauffman polynomials. There are a few
remaining Lie algebras which don't fit into any of the classical families:
$G_2$\, $F_4$\, $E_6$\, $E_7$\, and $E_8$. By work of Deligne\, Vogel\, a
nd Cvitanovic\, there is a conjectural 1-parameter continuous family of pl
anar algebras which interpolates between these exceptional Lie algebras. S
imilarly to the classical families\, there ought to be a 2-paramter family
of planar algebras which introduces a variable q\, and yields a new excep
tional knotpolynomial. In joint work with Scott Morrison and Dylan Thursto
n\, we give a skein theoretic description of what this knot polynomial wou
ld have to look like. In particular\, we show that any braided tensor cate
gory whose box spaces have the appropriate dimension and which satisfies s
ome mild assumptions must satisfy these exceptional skein relations.\n
LOCATION:https://researchseminars.org/talk/ADM-Davis/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Ostrik (University of Oregon)
DTSTART:20200427T200000Z
DTEND:20200427T210000Z
DTSTAMP:20260422T212752Z
UID:ADM-Davis/2
DESCRIPTION:Title: Incompressible tensor categories\nby Victor Ostrik (University of Or
egon) as part of UC Davis algebra & discrete math seminar\n\n\nAbstract\nT
his talk is based on joint work with Benson and Etingof.\nWe say that a sy
mmetric tensor category is incompressible\nif there is no symmetric tensor
functor from this category\nto a smaller tensor category. Our main result
is a construction\nof new examples of incompressible tensor categories in
positive\ncharacteristic.\n
LOCATION:https://researchseminars.org/talk/ADM-Davis/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Castillo (University of Kansas)
DTSTART:20200504T200000Z
DTEND:20200504T210000Z
DTSTAMP:20260422T212752Z
UID:ADM-Davis/3
DESCRIPTION:Title: Todd class of permutohedral variety\nby Federico Castillo (Universit
y of Kansas) as part of UC Davis algebra & discrete math seminar\n\n\nAbst
ract\nBerline and Vergne described a precise relation between the number o
f integer points of a polytope and the volumes of its faces. This relation
can be seen as a higher dimensional analogue of Pick's theorem. We study
the specific case of the permutohedron via the connection with toric varie
ties. This is joint work with Fu Liu.\n
LOCATION:https://researchseminars.org/talk/ADM-Davis/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitar Grantcharov (University of Texas)
DTSTART:20200511T200000Z
DTEND:20200511T210000Z
DTSTAMP:20260422T212752Z
UID:ADM-Davis/4
DESCRIPTION:Title: Bounded modules of direct limit Lie algebras\nby Dimitar Grantcharov
(University of Texas) as part of UC Davis algebra & discrete math seminar
\n\n\nAbstract\nIn this talk we will discuss recent results on the categor
y of weight modules with bounded sets of weight multiplicities of the dire
ct limit Lie algebras $\\mathfrak{sl} (\\infty)$\, $\\mathfrak{o} (\\inft
y)$\, and $\\mathfrak{sp} (\\infty)$. Classification of the simple objects
and properties of the category will be provided. This is a joint work wit
h I. Penkov.\n
LOCATION:https://researchseminars.org/talk/ADM-Davis/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolle González (UCLA)
DTSTART:20200513T200000Z
DTEND:20200513T210000Z
DTSTAMP:20260422T212752Z
UID:ADM-Davis/5
DESCRIPTION:Title: $\\mathfrak{sl}_n$-homology theories obstruct ribbon concordance\nby
Nicolle González (UCLA) as part of UC Davis algebra & discrete math semi
nar\n\n\nAbstract\nIn a recent result\, Zemke showed that a ribbon concord
ance between two knots induces an injective map between their correspondin
g knot Floer homology. Shortly after\, Levine and Zemke proved the analogo
us result for ribbon concordances between links and their Khovanov homolog
y. In this talk I will explain joint work with Caprau-Lee-Lowrance-Sazdano
vic and Zhang where we generalize this construction further to show that a
link ribbon concordance induces injective maps between $\\mathfrak{sl}_n$
-homology theories for all $n \\geq 2$.\n
LOCATION:https://researchseminars.org/talk/ADM-Davis/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arseniy Sheydvasser (Graduate Center at CUNY)
DTSTART:20200518T200000Z
DTEND:20200518T210000Z
DTSTAMP:20260422T212752Z
UID:ADM-Davis/6
DESCRIPTION:Title: Algebraic invariants of hyperbolic 4-orbifolds\nby Arseniy Sheydvass
er (Graduate Center at CUNY) as part of UC Davis algebra & discrete math s
eminar\n\n\nAbstract\nGiven an algebraic subgroup G of the isometry group
of hyperbolic n-space $H^n$\, one can consider the orbifold $H^n/G$. Hyper
bolic 2- and 3-orbifolds are reasonably well-understood\; for example\, hy
perbolic 3-orbifolds correspond to orders of split quaternion algebras and
there are algorithms that make use of this structure to compute geometric
invariants of the orbifolds such as their volume\, numbers of cusps\, and
fundamental groups. However\, already hyperbolic 4-orbifolds belong to un
tamed wilds. We shall examine this frontier by introducing a class of alge
braic groups that have many of the same properties as the Bianchi groups a
nd for which we can compute some geometric invariants of the orbifolds via
algebraic invariants of rings with involution.\n
LOCATION:https://researchseminars.org/talk/ADM-Davis/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Digjoy Paul (IMSC Chennai)
DTSTART:20200526T160000Z
DTEND:20200526T170000Z
DTSTAMP:20260422T212752Z
UID:ADM-Davis/7
DESCRIPTION:Title: New approaches to the restriction problem\nby Digjoy Paul (IMSC Chen
nai) as part of UC Davis algebra & discrete math seminar\n\n\nAbstract\nGi
ven an irreducible polynomial representation $W_n$ of the general linear g
roup $GL_n$\, we can restrict it to the representations of the symmetric g
roup $S_n$ that seats inside $GL_n$ as a subgroup. The restriction problem
is to find a combinatorial interpretation of the restriction coefficient:
the multiplicity of an irreducible $S_n$ modules in such restriction of $
W_n$. This is an open problem (see OPAC 2021!) in algebraic combinatorics.
\n\nIn Polynomial Induction and the Restriction Problem\, we construct the
polynomial induction functor\, which is the right adjoint to the restrict
ion functor from the category of polynomial representations of $GL_n$ to t
he category of representations of $S_n$. This construction leads to a repr
esentation-theoretic proof of Littlewood's Plethystic formula for the rest
riction coefficient.\n\nCharacter polynomials have been used to study char
acters of families of representations of symmetric groups (see Garsia and
Goupil )\, also used in the context of FI-modules by Church\, Ellenberg\,
and Farb (see FI-modules and stability for representations of symmetric gr
oups).\n\nIn Character Polynomials and the Restriction Problem\, we comput
e character polynomial for the family of restrictions of $W_n$ as $n$ vari
es. We give an interpretation of the restriction coefficient as a moment o
f a certain character polynomial. To characterize partitions for which the
corresponding Weyl module has non zero $S_n$-invariant vectors is quite h
ard. We solve this problem for partition with two rows\, two columns\, and
for hook-partitions.\n\nThis is joint work with Sridhar Narayanan\, Amrit
anshu Prasad\, and Shraddha Srivastava.\n
LOCATION:https://researchseminars.org/talk/ADM-Davis/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iva Halacheva (Northeastern University)
DTSTART:20200601T200000Z
DTEND:20200601T210000Z
DTSTAMP:20260422T212752Z
UID:ADM-Davis/9
DESCRIPTION:Title: Self-dual puzzles in Schubert calculus branching\nby Iva Halacheva (
Northeastern University) as part of UC Davis algebra & discrete math semin
ar\n\n\nAbstract\nIn classical Schubert calculus\, Knutson and Tao’s puz
zles are a combinatorial tool that gives a positive rule for expanding the
product of two Schubert classes in equivariant cohomology of the (type A)
Grassmannian. I will describe a positive rule that uses self-dual puzzles
to compute the restriction of a Grassmannian (type A) Schubert class to t
he symplectic (type C) Grassmannian in equivariant cohomology. The proof u
ses the machinery of quantum integrable systems. I will also discuss a gen
eralization in which the Grassmannians are upgraded to their cotangent bun
dles and Schubert classes—to Segre-Schwartz-MacPherson classes. The resu
lting construction involves Lagrangian correspondences and produces a gene
ralized puzzle rule with a geometric interpretation. This is joint work wi
th Allen Knutson and Paul Zinn-Justin.\n
LOCATION:https://researchseminars.org/talk/ADM-Davis/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elijah Bodish (University of Oregon)
DTSTART:20210114T173000Z
DTEND:20210114T182000Z
DTSTAMP:20260422T212752Z
UID:ADM-Davis/10
DESCRIPTION:Title: Webs and tilting modules in type C\nby Elijah Bodish (University of
Oregon) as part of UC Davis algebra & discrete math seminar\n\n\nAbstract
\nUsing Kuperberg's $B_2/C_2$ webs\, and following Elias and Libedinsky\,
we describe a "light leaves" algorithm to construct a basis of morphisms b
etween arbitrary tensor products of fundamental representations for the Li
e algebra of type $C_2$ (and the associated quantum group). Our argument h
as very little dependence on the base field. As a result\, we prove that w
hen quantum two is invertible\, the Karoubi envelope of the $C_2$ web cate
gory is equivalent to the category of tilting modules for the divided powe
rs quantum group. Time permitting we will also discuss how the “light le
aves” basis leads to new formulas for generalized “Jones-Wenzl” proj
ectors in $C_2$ webs\, and mention work in progress with Elias\, Rose\, an
d Tatham about higher rank type $C$ webs.\n
LOCATION:https://researchseminars.org/talk/ADM-Davis/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen Griffeth (Universidad de Talca)
DTSTART:20210121T173000Z
DTEND:20210121T182000Z
DTSTAMP:20260422T212752Z
UID:ADM-Davis/11
DESCRIPTION:Title: Special parameters for rational Cherednik algebras\nby Stephen Grif
feth (Universidad de Talca) as part of UC Davis algebra & discrete math se
minar\n\n\nAbstract\nThe rational Cherednik algebra associated with a comp
lex reflection group W is a certain deformation of an algebra of different
ial operators\, with deformation parameter "c" running over a vector space
of dimension equal to the number of conjugacy classes of reflections in W
. Given a yes or no question about the structure of the Cherednik algebra
produces a subset of the parameter space consisting of those c for which t
he answer is "yes." I will discuss a number of such questions\, such as "D
oes there exist a non-trivial ideal in the Cherednik algebra?"\, "Is the t
op of the polynomial representation finite dimensional?" and "Is the Chere
dnik algebra Morita equivalent to its spherical subalgebra?" In those case
s for which explicit descriptions of the corresponding set of c are availa
ble I will discuss some of the techniques used to obtain them\, and survey
some of the most important unresolved questions. This talk is partly base
d on joint work with Charles Dunkl\, Susanna Fishel\, Daniel Juteau\, and
Elizabeth Manosalva.\n
LOCATION:https://researchseminars.org/talk/ADM-Davis/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aram Dermenjian (York University)
DTSTART:20210128T173000Z
DTEND:20210128T182000Z
DTSTAMP:20260422T212752Z
UID:ADM-Davis/12
DESCRIPTION:Title: Sign Variations and Descents\nby Aram Dermenjian (York University)
as part of UC Davis algebra & discrete math seminar\n\n\nAbstract\nIn this
talk we consider a poset structure on projective sign vectors. We show th
at the order complex of this poset is partitionable and give an interpreta
tion of the h-vector using type B descents of the type D Coxeter group.\n
LOCATION:https://researchseminars.org/talk/ADM-Davis/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Zhang (University of Georgia)
DTSTART:20210204T173000Z
DTEND:20210204T182000Z
DTSTAMP:20260422T212752Z
UID:ADM-Davis/13
DESCRIPTION:Title: Khovanov homology\, sl(N) homologies\, and ribbon concordance\nby M
elissa Zhang (University of Georgia) as part of UC Davis algebra & discret
e math seminar\n\n\nAbstract\nIn the last 20 years\, low-dimensional topol
ogists have found homology-type invariants to be very useful in the study
to knots and their relationship with the 3- and 4-manifolds they live in.
In this talk\, I will discuss the concept of "ribbon concordance" and why
we hope categorified knot invariants may help us solve some major open que
stions. This talk is based on joint work with Carmen Caprau\, Nicolle Gonz
alez\, Christine Lee\, Adam Lowrance\, and Radmila Sazdanovic on how sl(n)
homologies provide ribbon concordance obstructions. This builds off the w
ork of Adam Levine and Ian Zemke.\n
LOCATION:https://researchseminars.org/talk/ADM-Davis/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Sauermann (Institute for Advanced Study)
DTSTART:20210211T173000Z
DTEND:20210211T182000Z
DTSTAMP:20260422T212752Z
UID:ADM-Davis/14
DESCRIPTION:Title: On the extension complexity of low-dimensional polytopes\nby Lisa S
auermann (Institute for Advanced Study) as part of UC Davis algebra & disc
rete math seminar\n\n\nAbstract\nIt is sometimes possible to represent a c
omplicated polytope as a projection of a much simpler polytope. To quantif
y this phenomenon\, the extension complexity of a polytope P is defined to
be the minimum number of facets in a (possibly higher-dimensional) polyto
pe from which P can be obtained as a (linear) projection. In this talk\, w
e discuss some results on the extension complexity of random d-dimensional
polytopes (obtained as convex hulls of random points on either on the uni
t sphere or in the unit ball)\, and on the extension complexity of polygon
s with all vertices on a common circle. Joint work with Matthew Kwan and Y
ufei Zhao.\n
LOCATION:https://researchseminars.org/talk/ADM-Davis/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lauren Rose (Bard College)
DTSTART:20210218T173000Z
DTEND:20210218T182000Z
DTSTAMP:20260422T212752Z
UID:ADM-Davis/15
DESCRIPTION:Title: Generalized Spline Modules on Arbitrary Graphs\nby Lauren Rose (Bar
d College) as part of UC Davis algebra & discrete math seminar\n\n\nAbstra
ct\nGeneralized splines on a graph G with edge weighted by ideals a commut
ative ring R are R-vertex labelings such that if two vertices share an edg
e in G\, the vertex labels are congruent modulo the edge ideal. When R is
a principal ideal domain\, we introduce collapsing operations that reduces
any simple graph to a single vertex and carries along the edge ideal info
rmation. This corresponds to a sequence of surjective maps between the ass
ociated spline modules\, and leads to an explicit construction of an R-mod
ule basis in terms of the edge ideals. We also solve an interpolation prob
lem\, i.e. given a partial vertex labeling\, when can it can be extended t
o a generalized spline?\n\n\n\nZoom: 994 0826 8795 Contact mjvazirani@ucda
vis.edu for Password\n
LOCATION:https://researchseminars.org/talk/ADM-Davis/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Rose (UNC Chapel Hill)
DTSTART:20210311T173000Z
DTEND:20210311T182000Z
DTSTAMP:20260422T212752Z
UID:ADM-Davis/16
DESCRIPTION:Title: Type C Webs\nby David Rose (UNC Chapel Hill) as part of UC Davis al
gebra & discrete math seminar\n\n\nAbstract\nIn his seminal 1996 paper\, K
uperberg gives presentations for the categories of finite-dimensional repr
esentations of quantum groups associated to rank 2 simple complex Lie alge
bras (as braided pivotal categories). Such presentations underly construct
ions of invariants in low-dimensional topology\; in particular\, they serv
e as a "foundation" for various link homology theories. Kuperberg also pos
es the following problem: to find analogous descriptions of these categori
es for quantum groups of higher rank. In 2012\, Cautis-Kamnitzer-Morrison
solved this problem in type A using skew Howe duality\, a technique that d
oes not extend (at least in a straightforward way) to give a solution in o
ther types.\n\nIn this talk\, we will present a solution to Kuperberg's pr
oblem in type C. Our proof combines results on pivotal categories and quan
tum group representations with diagrammatic/topological analogues of theor
ems concerning reduced expressions in the symmetric group. Time permitting
\, we'll discuss some future directions. This work is joint with Bodish\,
Elias\, and Tatham (on the arXiv soon!) and builds on previous work with T
atham (https://arxiv.org/abs/2006.02491).\n\n\n\nZoom password hint: It is
our current year \, equivalently the next term in the sequence 1718\, 181
9\, 1920\,...\n\n\n\nPlease contact mjvazirani@ucdavis.edu if you need the
Zoom link/password (or see the hint above). Zoom: 994 0826 8795\n
LOCATION:https://researchseminars.org/talk/ADM-Davis/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sachin Gautam (Ohio State University)
DTSTART:20210225T173000Z
DTEND:20210225T182000Z
DTSTAMP:20260422T212752Z
UID:ADM-Davis/17
DESCRIPTION:Title: R-matrices and Yangians\nby Sachin Gautam (Ohio State University) a
s part of UC Davis algebra & discrete math seminar\n\n\nAbstract\nAn R-mat
rix is a solution to the Yang-Baxter equation (YBE)\, a central object in
Statistical Mechanics\, discovered in 1970's. The R-matrix also features p
rominently in the theory of quantum groups formulated in the eighties. In
recent years\, many areas of mathematics and physics have found methods to
construct R-matrices and solve the associated integrable system.\n\nIn th
is talk I will present one such method\, which produces meromorphic soluti
ons to (YBE) starting from the representation theory of a family of quantu
m groups called Yangians. Our techniques give (i) a constructive proof of
the existence of the universal R-matrix of Yangians\, which was obtained v
ia cohomological methods by Drinfeld in 1983\, and (ii) prove that Drinfel
d's universal R-matrix is analytically well behaved. This talk is based on
joint works with Valerio Toledano Laredo and Curtis Wendlandt.\n\n\n\nPle
ase contact mjvazirani@ucdavis.edu if you need the Zoom link/password. Zoo
m: 994 0826 8795\n
LOCATION:https://researchseminars.org/talk/ADM-Davis/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anastasia Chavez (UC Davis)
DTSTART:20210304T173000Z
DTEND:20210304T182000Z
DTSTAMP:20260422T212752Z
UID:ADM-Davis/18
DESCRIPTION:by Anastasia Chavez (UC Davis) as part of UC Davis algebra & d
iscrete math seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ADM-Davis/18/
END:VEVENT
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