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BEGIN:VEVENT
SUMMARY:Noah Snyder (Indiana University)
DTSTART:20200420T200000Z
DTEND:20200420T210000Z
DTSTAMP:20260404T094506Z
UID:ADM-Davis/1
DESCRIPTION:Title: The exceptional knot polynomial\nby Noah Snyder (Indiana Univ
ersity) as part of UC Davis algebra & discrete math seminar\n\n\nAbstract\
nMany Lie algebras fit into discrete families like $\\operatorname{GL}_n$\
, $\\operatorname{O}_n$\, $\\operatorname{Sp}_n$. By work of Brauer\, Deli
gne and others\, the corresponding planar algebras fit into continuous fam
iles $\\operatorname{GL}_t$ and $\\operatorname{OSp}_t$. A similar story h
olds for quantum groups\, so we can speak of two parameter families $(\\op
eratorname{GL}_t)_q$ and $(\\operatorname{OSp}_t)_q$. These planar algebra
s are the ones attached to the HOMFLY and Kauffman polynomials. There are
a few remaining Lie algebras which don't fit into any of the classical fa
milies: $G_2$\, $F_4$\, $E_6$\, $E_7$\, and $E_8$. By work of Deligne\, Vo
gel\, and Cvitanovic\, there is a conjectural 1-parameter continuous famil
y of planar algebras which interpolates between these exceptional Lie alge
bras. Similarly to the classical families\, there ought to be a 2-paramter
family of planar algebras which introduces a variable q\, and yields a ne
w exceptional knotpolynomial. In joint work with Scott Morrison and Dylan
Thurston\, we give a skein theoretic description of what this knot polynom
ial would have to look like. In particular\, we show that any braided tens
or category whose box spaces have the appropriate dimension and which sati
sfies some mild assumptions must satisfy these exceptional skein relations
.\n
LOCATION:https://stable.researchseminars.org/talk/ADM-Davis/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Ostrik (University of Oregon)
DTSTART:20200427T200000Z
DTEND:20200427T210000Z
DTSTAMP:20260404T094506Z
UID:ADM-Davis/2
DESCRIPTION:Title: Incompressible tensor categories\nby Victor Ostrik (Universit
y of Oregon) as part of UC Davis algebra & discrete math seminar\n\n\nAbst
ract\nThis talk is based on joint work with Benson and Etingof.\nWe say th
at a symmetric 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 catego
ries in positive\ncharacteristic.\n
LOCATION:https://stable.researchseminars.org/talk/ADM-Davis/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Castillo (University of Kansas)
DTSTART:20200504T200000Z
DTEND:20200504T210000Z
DTSTAMP:20260404T094506Z
UID:ADM-Davis/3
DESCRIPTION:Title: Todd class of permutohedral variety\nby Federico Castillo (Un
iversity of Kansas) as part of UC Davis algebra & discrete math seminar\n\
n\nAbstract\nBerline and Vergne described a precise relation between the n
umber of integer points of a polytope and the volumes of its faces. This r
elation can be seen as a higher dimensional analogue of Pick's theorem. We
study the specific case of the permutohedron via the connection with tori
c varieties. This is joint work with Fu Liu.\n
LOCATION:https://stable.researchseminars.org/talk/ADM-Davis/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitar Grantcharov (University of Texas)
DTSTART:20200511T200000Z
DTEND:20200511T210000Z
DTSTAMP:20260404T094506Z
UID:ADM-Davis/4
DESCRIPTION:Title: Bounded modules of direct limit Lie algebras\nby Dimitar Gran
tcharov (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
category of weight modules with bounded sets of weight multiplicities of t
he direct limit Lie algebras $\\mathfrak{sl} (\\infty)$\, $\\mathfrak{o}
(\\infty)$\, and $\\mathfrak{sp} (\\infty)$. Classification of the simple
objects and properties of the category will be provided. This is a joint w
ork with I. Penkov.\n
LOCATION:https://stable.researchseminars.org/talk/ADM-Davis/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolle González (UCLA)
DTSTART:20200513T200000Z
DTEND:20200513T210000Z
DTSTAMP:20260404T094506Z
UID:ADM-Davis/5
DESCRIPTION:Title: $\\mathfrak{sl}_n$-homology theories obstruct ribbon concordance<
/a>\nby Nicolle González (UCLA) as part of UC Davis algebra & discrete ma
th seminar\n\n\nAbstract\nIn a recent result\, Zemke showed that a ribbon
concordance between two knots induces an injective map between their corre
sponding knot Floer homology. Shortly after\, Levine and Zemke proved the
analogous result for ribbon concordances between links and their Khovanov
homology. In this talk I will explain joint work with Caprau-Lee-Lowrance-
Sazdanovic 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://stable.researchseminars.org/talk/ADM-Davis/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arseniy Sheydvasser (Graduate Center at CUNY)
DTSTART:20200518T200000Z
DTEND:20200518T210000Z
DTSTAMP:20260404T094506Z
UID:ADM-Davis/6
DESCRIPTION:Title: Algebraic invariants of hyperbolic 4-orbifolds\nby Arseniy Sh
eydvasser (Graduate Center at CUNY) as part of UC Davis algebra & discrete
math seminar\n\n\nAbstract\nGiven an algebraic subgroup G of the isometry
group of hyperbolic n-space $H^n$\, one can consider the orbifold $H^n/G$
. Hyperbolic 2- and 3-orbifolds are reasonably well-understood\; for examp
le\, hyperbolic 3-orbifolds correspond to orders of split quaternion algeb
ras and there are algorithms that make use of this structure to compute ge
ometric invariants of the orbifolds such as their volume\, numbers of cusp
s\, and fundamental groups. However\, already hyperbolic 4-orbifolds belon
g to untamed wilds. We shall examine this frontier by introducing a class
of algebraic groups that have many of the same properties as the Bianchi g
roups and for which we can compute some geometric invariants of the orbifo
lds via algebraic invariants of rings with involution.\n
LOCATION:https://stable.researchseminars.org/talk/ADM-Davis/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Digjoy Paul (IMSC Chennai)
DTSTART:20200526T160000Z
DTEND:20200526T170000Z
DTSTAMP:20260404T094506Z
UID:ADM-Davis/7
DESCRIPTION:Title: New approaches to the restriction problem\nby Digjoy Paul (IM
SC Chennai) as part of UC Davis algebra & discrete math seminar\n\n\nAbstr
act\nGiven an irreducible polynomial representation $W_n$ of the general l
inear group $GL_n$\, we can restrict it to the representations of the symm
etric group $S_n$ that seats inside $GL_n$ as a subgroup. The restriction
problem is to find a combinatorial interpretation of the restriction coeff
icient: the multiplicity of an irreducible $S_n$ modules in such restricti
on of $W_n$. This is an open problem (see OPAC 2021!) in algebraic combina
torics.\n\nIn Polynomial Induction and the Restriction Problem\, we constr
uct the polynomial induction functor\, which is the right adjoint to the r
estriction functor from the category of polynomial representations of $GL_
n$ to the category of representations of $S_n$. This construction leads to
a representation-theoretic proof of Littlewood's Plethystic formula for t
he restriction coefficient.\n\nCharacter polynomials have been used to stu
dy characters of families of representations of symmetric groups (see Gars
ia and Goupil )\, also used in the context of FI-modules by Church\, Ellen
berg\, and Farb (see FI-modules and stability for representations of symme
tric groups).\n\nIn Character Polynomials and the Restriction Problem\, we
compute character polynomial for the family of restrictions of $W_n$ as $
n$ varies. We give an interpretation of the restriction coefficient as a m
oment of a certain character polynomial. To characterize partitions for wh
ich the corresponding Weyl module has non zero $S_n$-invariant vectors is
quite hard. We solve this problem for partition with two rows\, two column
s\, and for hook-partitions.\n\nThis is joint work with Sridhar Narayanan\
, Amritanshu Prasad\, and Shraddha Srivastava.\n
LOCATION:https://stable.researchseminars.org/talk/ADM-Davis/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iva Halacheva (Northeastern University)
DTSTART:20200601T200000Z
DTEND:20200601T210000Z
DTSTAMP:20260404T094506Z
UID:ADM-Davis/9
DESCRIPTION:Title: Self-dual puzzles in Schubert calculus branching\nby Iva Hala
cheva (Northeastern University) as part of UC Davis algebra & discrete mat
h seminar\n\n\nAbstract\nIn classical Schubert calculus\, Knutson and Tao
’s puzzles are a combinatorial tool that gives a positive rule for expan
ding 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 cl
ass to the symplectic (type C) Grassmannian in equivariant cohomology. The
proof uses the machinery of quantum integrable systems. I will also discu
ss a generalization in which the Grassmannians are upgraded to their cotan
gent bundles and Schubert classes—to Segre-Schwartz-MacPherson classes.
The resulting construction involves Lagrangian correspondences and produce
s a generalized puzzle rule with a geometric interpretation. This is joint
work with Allen Knutson and Paul Zinn-Justin.\n
LOCATION:https://stable.researchseminars.org/talk/ADM-Davis/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elijah Bodish (University of Oregon)
DTSTART:20210114T173000Z
DTEND:20210114T182000Z
DTSTAMP:20260404T094506Z
UID:ADM-Davis/10
DESCRIPTION:Title: Webs and tilting modules in type C\nby Elijah Bodish (Univer
sity of Oregon) as part of UC Davis algebra & discrete math seminar\n\n\nA
bstract\nUsing Kuperberg's $B_2/C_2$ webs\, and following Elias and Libedi
nsky\, we describe a "light leaves" algorithm to construct a basis of morp
hisms between arbitrary tensor products of fundamental representations for
the Lie algebra of type $C_2$ (and the associated quantum group). Our arg
ument has very little dependence on the base field. As a result\, we prove
that when quantum two is invertible\, the Karoubi envelope of the $C_2$ w
eb category is equivalent to the category of tilting modules for the divid
ed powers quantum group. Time permitting we will also discuss how the “l
ight leaves” basis leads to new formulas for generalized “Jones-Wenzl
” projectors in $C_2$ webs\, and mention work in progress with Elias\, R
ose\, and Tatham about higher rank type $C$ webs.\n
LOCATION:https://stable.researchseminars.org/talk/ADM-Davis/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen Griffeth (Universidad de Talca)
DTSTART:20210121T173000Z
DTEND:20210121T182000Z
DTSTAMP:20260404T094506Z
UID:ADM-Davis/11
DESCRIPTION:Title: Special parameters for rational Cherednik algebras\nby Steph
en Griffeth (Universidad de Talca) as part of UC Davis algebra & discrete
math seminar\n\n\nAbstract\nThe rational Cherednik algebra associated with
a complex reflection group W is a certain deformation of an algebra of di
fferential operators\, with deformation parameter "c" running over a vecto
r space of dimension equal to the number of conjugacy classes of reflectio
ns in W. Given a yes or no question about the structure of the Cherednik a
lgebra produces a subset of the parameter space consisting of those c for
which the answer is "yes." I will discuss a number of such questions\, suc
h as "Does there exist a non-trivial ideal in the Cherednik algebra?"\, "I
s the top of the polynomial representation finite dimensional?" and "Is th
e Cherednik algebra Morita equivalent to its spherical subalgebra?" In tho
se cases for which explicit descriptions of the corresponding set of c are
available I will discuss some of the techniques used to obtain them\, and
survey some of the most important unresolved questions. This talk is part
ly based on joint work with Charles Dunkl\, Susanna Fishel\, Daniel Juteau
\, and Elizabeth Manosalva.\n
LOCATION:https://stable.researchseminars.org/talk/ADM-Davis/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aram Dermenjian (York University)
DTSTART:20210128T173000Z
DTEND:20210128T182000Z
DTSTAMP:20260404T094506Z
UID:ADM-Davis/12
DESCRIPTION:Title: Sign Variations and Descents\nby Aram Dermenjian (York Unive
rsity) as part of UC Davis algebra & discrete math seminar\n\n\nAbstract\n
In this talk we consider a poset structure on projective sign vectors. We
show that the order complex of this poset is partitionable and give an int
erpretation of the h-vector using type B descents of the type D Coxeter gr
oup.\n
LOCATION:https://stable.researchseminars.org/talk/ADM-Davis/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Zhang (University of Georgia)
DTSTART:20210204T173000Z
DTEND:20210204T182000Z
DTSTAMP:20260404T094506Z
UID:ADM-Davis/13
DESCRIPTION:Title: Khovanov homology\, sl(N) homologies\, and ribbon concordance\nby Melissa Zhang (University of Georgia) as part of UC Davis algebra &
discrete math seminar\n\n\nAbstract\nIn the last 20 years\, low-dimensiona
l topologists have found homology-type invariants to be very useful in the
study to knots and their relationship with the 3- and 4-manifolds they li
ve in. In this talk\, I will discuss the concept of "ribbon concordance" a
nd why we hope categorified knot invariants may help us solve some major o
pen questions. This talk is based on joint work with Carmen Caprau\, Nicol
le Gonzalez\, Christine Lee\, Adam Lowrance\, and Radmila Sazdanovic on ho
w sl(n) homologies provide ribbon concordance obstructions. This builds of
f the work of Adam Levine and Ian Zemke.\n
LOCATION:https://stable.researchseminars.org/talk/ADM-Davis/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Sauermann (Institute for Advanced Study)
DTSTART:20210211T173000Z
DTEND:20210211T182000Z
DTSTAMP:20260404T094506Z
UID:ADM-Davis/14
DESCRIPTION:Title: On the extension complexity of low-dimensional polytopes\nby
Lisa Sauermann (Institute for Advanced Study) as part of UC Davis algebra
& discrete math seminar\n\n\nAbstract\nIt is sometimes possible to repres
ent a complicated polytope as a projection of a much simpler polytope. To
quantify this phenomenon\, the extension complexity of a polytope P is def
ined to be the minimum number of facets in a (possibly higher-dimensional)
polytope from which P can be obtained as a (linear) projection. In this t
alk\, we discuss some results on the extension complexity of random d-dime
nsional polytopes (obtained as convex hulls of random points on either on
the unit sphere or in the unit ball)\, and on the extension complexity of
polygons with all vertices on a common circle. Joint work with Matthew Kwa
n and Yufei Zhao.\n
LOCATION:https://stable.researchseminars.org/talk/ADM-Davis/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lauren Rose (Bard College)
DTSTART:20210218T173000Z
DTEND:20210218T182000Z
DTSTAMP:20260404T094506Z
UID:ADM-Davis/15
DESCRIPTION:Title: Generalized Spline Modules on Arbitrary Graphs\nby Lauren Ro
se (Bard College) as part of UC Davis algebra & discrete math seminar\n\n\
nAbstract\nGeneralized splines on a graph G with edge weighted by ideals a
commutative ring R are R-vertex labelings such that if two vertices share
an edge in G\, the vertex labels are congruent modulo the edge ideal. Whe
n R is a principal ideal domain\, we introduce collapsing operations that
reduces any simple graph to a single vertex and carries along the edge ide
al information. This corresponds to a sequence of surjective maps between
the associated spline modules\, and leads to an explicit construction of a
n R-module basis in terms of the edge ideals. We also solve an interpolati
on problem\, i.e. given a partial vertex labeling\, when can it can be ext
ended to a generalized spline?\n\n\n\nZoom: 994 0826 8795 Contact mjvazira
ni@ucdavis.edu for Password\n
LOCATION:https://stable.researchseminars.org/talk/ADM-Davis/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Rose (UNC Chapel Hill)
DTSTART:20210311T173000Z
DTEND:20210311T182000Z
DTSTAMP:20260404T094506Z
UID:ADM-Davis/16
DESCRIPTION:Title: Type C Webs\nby David Rose (UNC Chapel Hill) as part of UC D
avis algebra & discrete math seminar\n\n\nAbstract\nIn his seminal 1996 pa
per\, Kuperberg gives presentations for the categories of finite-dimension
al representations of quantum groups associated to rank 2 simple complex L
ie algebras (as braided pivotal categories). Such presentations underly co
nstructions of invariants in low-dimensional topology\; in particular\, th
ey serve as a "foundation" for various link homology theories. Kuperberg a
lso poses the following problem: to find analogous descriptions of these c
ategories for quantum groups of higher rank. In 2012\, Cautis-Kamnitzer-Mo
rrison solved this problem in type A using skew Howe duality\, a technique
that does not extend (at least in a straightforward way) to give a soluti
on in other types.\n\nIn this talk\, we will present a solution to Kuperbe
rg's problem in type C. Our proof combines results on pivotal categories a
nd quantum group representations with diagrammatic/topological analogues o
f theorems concerning reduced expressions in the symmetric group. Time per
mitting\, we'll discuss some future directions. This work is joint with Bo
dish\, Elias\, and Tatham (on the arXiv soon!) and builds on previous work
with Tatham (https://arxiv.org/abs/2006.02491).\n\n\n\nZoom password hint
: It is our current year \, equivalently the next term in the sequence 171
8\, 1819\, 1920\,...\n\n\n\nPlease contact mjvazirani@ucdavis.edu if you n
eed the Zoom link/password (or see the hint above). Zoom: 994 0826 8795\n
LOCATION:https://stable.researchseminars.org/talk/ADM-Davis/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sachin Gautam (Ohio State University)
DTSTART:20210225T173000Z
DTEND:20210225T182000Z
DTSTAMP:20260404T094506Z
UID:ADM-Davis/17
DESCRIPTION:Title: R-matrices and Yangians\nby Sachin Gautam (Ohio State Univer
sity) as part of UC Davis algebra & discrete math seminar\n\n\nAbstract\nA
n R-matrix is a solution to the Yang-Baxter equation (YBE)\, a central obj
ect in Statistical Mechanics\, discovered in 1970's. The R-matrix also fea
tures prominently in the theory of quantum groups formulated in the eighti
es. In recent years\, many areas of mathematics and physics have found met
hods to construct R-matrices and solve the associated integrable system.\n
\nIn this talk I will present one such method\, which produces meromorphic
solutions to (YBE) starting from the representation theory of a family of
quantum groups called Yangians. Our techniques give (i) a constructive pr
oof of the existence of the universal R-matrix of Yangians\, which was obt
ained via cohomological methods by Drinfeld in 1983\, and (ii) prove that
Drinfeld's universal R-matrix is analytically well behaved. This talk is b
ased on joint works with Valerio Toledano Laredo and Curtis Wendlandt.\n\n
\n\nPlease contact mjvazirani@ucdavis.edu if you need the Zoom link/passwo
rd. Zoom: 994 0826 8795\n
LOCATION:https://stable.researchseminars.org/talk/ADM-Davis/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anastasia Chavez (UC Davis)
DTSTART:20210304T173000Z
DTEND:20210304T182000Z
DTSTAMP:20260404T094506Z
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://stable.researchseminars.org/talk/ADM-Davis/18/
END:VEVENT
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