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BEGIN:VEVENT
SUMMARY:Joseph Bernstein (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20210425T153000Z
DTEND;VALUE=DATE-TIME:20210425T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190052Z
UID:SpringfestSerganova/1
DESCRIPTION:Title: Remark on rigidity in Lie theory (joint with Ed Shpiz)\nby
Joseph Bernstein (Tel Aviv University) as part of Springfest in honor of
Vera Serganova\n\n\nAbstract\nLet g be a finite dimensional Lie algebra ov
er a field k of characteristic 0\,\ni.e. it is a pair (L\, b) of a vector
space L and a bracket operation b. \n\n A proof of the PBW theorem is usu
ally based on a construction of a representation p of the\nLie algebra g b
y derivations of the algebra F=F(L) of formal functions on the space L\,\
nthat lifts to a faithful representation of the universal enveloping algeb
ra U(g).\n\n It turns out that one can choose such representation in a ca
nonical way.\nI will discuss how one can describe this canonical represent
ation.\n
LOCATION:https://researchseminars.org/talk/SpringfestSerganova/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Finkelberg (National Research University Higher School of
Economics)
DTSTART;VALUE=DATE-TIME:20210426T153000Z
DTEND;VALUE=DATE-TIME:20210426T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190052Z
UID:SpringfestSerganova/2
DESCRIPTION:Title: Gaiotto conjecture on quantum geometric Satake for quantum sup
ergroups\nby Michael Finkelberg (National Research University Higher S
chool of Economics) as part of Springfest in honor of Vera Serganova\n\n\n
Abstract\nThis is a joint work with Roman Travkin and Alexander Braverman.
D.Gaiotto conjectured that the category of finite dimensional representat
ions of U_q(gl(N-1|N)) is equivalent to the category of q-monodromic GL(N-
1\,C[[t]])-equivariant perverse sheaves on the determinant line bundle on
the affine Grassmannian of GL(N). I will explain an approach to this via t
he category of factorizable sheaves.\n
LOCATION:https://researchseminars.org/talk/SpringfestSerganova/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Kac (MIT)
DTSTART;VALUE=DATE-TIME:20210426T181500Z
DTEND;VALUE=DATE-TIME:20210426T191500Z
DTSTAMP;VALUE=DATE-TIME:20210514T190052Z
UID:SpringfestSerganova/3
DESCRIPTION:Title: Cyclic elements and applications\nby Victor Kac (MIT) as p
art of Springfest in honor of Vera Serganova\n\n\nAbstract\nBasic results
on cyclic elements in simple Lie algebras will be explained\, along with s
ome applications\, including normal forms of nilpotent elements and integr
ability of classical affine W-algebras.\n
LOCATION:https://researchseminars.org/talk/SpringfestSerganova/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Coulembier (University of Sydney)
DTSTART;VALUE=DATE-TIME:20210427T080000Z
DTEND;VALUE=DATE-TIME:20210427T090000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190052Z
UID:SpringfestSerganova/4
DESCRIPTION:Title: Beyond abelian envelopes\nby Kevin Coulembier (University
of Sydney) as part of Springfest in honor of Vera Serganova\n\n\nAbstract\
nWe will give a short overview of the motivation for and main examples of
abelian envelopes of rigid monoidal categories. Then we will introduce a t
heory which generalises abelian envelopes and is applicable to any rigid m
onoidal category.\n
LOCATION:https://researchseminars.org/talk/SpringfestSerganova/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iryna Kashuba (University of Sao Paulo)
DTSTART;VALUE=DATE-TIME:20210427T170000Z
DTEND;VALUE=DATE-TIME:20210427T180000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190052Z
UID:SpringfestSerganova/5
DESCRIPTION:Title: Representation type of Jordan algebras and superalgebras\n
by Iryna Kashuba (University of Sao Paulo) as part of Springfest in honor
of Vera Serganova\n\n\nAbstract\nWe will review recent and classical resul
ts on the representations of finite dimensional Jordan algebras and supera
lgebras. We will weigh the pros against the cons of using the Tits-Kantor-
Koecher construction for this problem.\n\nJoint with Representation Theory
and Mathematical Physics Seminar\n
LOCATION:https://researchseminars.org/talk/SpringfestSerganova/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Volodymyr Mazorchuk (Uppsala University)
DTSTART;VALUE=DATE-TIME:20210428T153000Z
DTEND;VALUE=DATE-TIME:20210428T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190052Z
UID:SpringfestSerganova/6
DESCRIPTION:Title: Simple modules for Lie algebras and superalgebras\nby Volo
dymyr Mazorchuk (Uppsala University) as part of Springfest in honor of Ver
a Serganova\n\n\nAbstract\nIn this talk I will try to survey the state of
the art for the problem of classification of simple modules for complex Li
e algebras and superalgebras. The main emphasis will be on some recent tec
hniques and results on how to reduce the Lie superalgebra problem to the L
ie algebra problem.\n
LOCATION:https://researchseminars.org/talk/SpringfestSerganova/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Pevtsova (University of Washington)
DTSTART;VALUE=DATE-TIME:20210428T181500Z
DTEND;VALUE=DATE-TIME:20210428T191500Z
DTSTAMP;VALUE=DATE-TIME:20210514T190052Z
UID:SpringfestSerganova/7
DESCRIPTION:Title: Support and tensor product property for integrable Hopf algebr
as\nby Julia Pevtsova (University of Washington) as part of Springfest
in honor of Vera Serganova\n\n\nAbstract\nI’ll describe the hypersurfac
e approach to the theory of support varieties for finite dimensional Hopf
algebras. The idea comes from commutative algebra going back to the work o
f Eisenbud\, Avramov-Buchweitz and Avramov-Iyengar. It has been recently i
mplemented in two different non-commutative contexts: finite supergroup sc
hemes in a joint project with D. Benson\, S. Iyengar and H. Krause and non
-braided settings such as small quantum borels in a joint project with C.
Negron.\n
LOCATION:https://researchseminars.org/talk/SpringfestSerganova/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thorsten Heidersdorf (University of Bonn)
DTSTART;VALUE=DATE-TIME:20210429T153000Z
DTEND;VALUE=DATE-TIME:20210429T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190052Z
UID:SpringfestSerganova/8
DESCRIPTION:Title: Character formulas and the DS functor\nby Thorsten Heiders
dorf (University of Bonn) as part of Springfest in honor of Vera Serganova
\n\n\nAbstract\nI will report on joint work with Maria Gorelik on obtainin
g good character formulas for irreducible representations of Lie superalge
bras in terms of Euler characters. We prove a formula relating the Euler c
haracters to Kac-Wakimoto terms and determine the image of super versions
of the Euler characters under the functor ds induced by the Duflo-Serganov
a functor DS on the supercharacter ring.\n
LOCATION:https://researchseminars.org/talk/SpringfestSerganova/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jon Brundan (University of Oregon)
DTSTART;VALUE=DATE-TIME:20210429T181500Z
DTEND;VALUE=DATE-TIME:20210429T191500Z
DTSTAMP;VALUE=DATE-TIME:20210514T190052Z
UID:SpringfestSerganova/9
DESCRIPTION:Title: Okounkov-Vershik approach to representations of the partition
category\nby Jon Brundan (University of Oregon) as part of Springfest
in honor of Vera Serganova\n\n\nAbstract\nI will report on joint work with
Max Vargas revisiting the representation theory of the partition category
. Our approach is similar in spirit to the Okounkov-Vershik approach to re
presentation theory of symmetric groups\, with the Jucys-Murphy elements r
eplaced by Enyang-Jucys-Murphy elements. Our techniques recover all of the
results of Comes and Ostrik from their work on the Deligne category Rep(S
_t)\, and we can do a little bit more besides.\n
LOCATION:https://researchseminars.org/talk/SpringfestSerganova/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yasmine Fittouhi and Anthony Joseph (Weizmann Institute of Science
)
DTSTART;VALUE=DATE-TIME:20210503T153000Z
DTEND;VALUE=DATE-TIME:20210503T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190052Z
UID:SpringfestSerganova/10
DESCRIPTION:Title: Components of the nilfibre in type $A$ for Parabolic Action\nby Yasmine Fittouhi and Anthony Joseph (Weizmann Institute of Science)
as part of Springfest in honor of Vera Serganova\n\n\nAbstract\nLet $G$ b
e a simple algebraic group\, $P$ a parabolic subgroup and $\\mathfrak m$ t
he nilradical of its Lie algebra $\\mathfrak p$. A theorem of Richardson s
ays that $P$ has a dense orbit in $\\mathfrak m$.\n\nAs a consequence the
invariant algebra $\\mathbb C[\\mathfrak m]^{P'}$ is polynomial. Thus one
may ask if this action admits a Weierstrass section\, that is to say a lin
ear subvariety $e+V$ of $\\mathfrak m$ such that restriction of invariants
defines an isomorphism onto $\\mathbb C[e+V]$.\nIn type $A$\, a proposal
for the generators was given by Benlolo and Sanderson and verified by Jose
ph and Melnikov. \n\nIn previous work this was used to construct a Weierst
rass section (in type $A$) but by heavy combinatorics. \nThe nilfibre $\\
mathscr N$ (for this action) is the zero set in $\\mathfrak m$ of $\\mathb
b C[\\mathfrak m]^{P'}_+$. It is generally not irreducible. \nFrom the c
omputed Weierstrass section we obtained a ``canonical'' component of $\\ma
thscr N$ and show it to be a ``B saturation set''.\nHere it is suggested t
hat the remaining components take a similar form and in turn lead to furth
er non-equivalent Weierstrass sections.\nHopefully this will be a template
for constructing Weierstrass sections in general type. \nPreliminary comp
utations are reported.\n
LOCATION:https://researchseminars.org/talk/SpringfestSerganova/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Etingof (MIT)
DTSTART;VALUE=DATE-TIME:20210503T181500Z
DTEND;VALUE=DATE-TIME:20210503T191500Z
DTSTAMP;VALUE=DATE-TIME:20210514T190052Z
UID:SpringfestSerganova/11
DESCRIPTION:Title: New examples of incompressible symmetric tensor categories in
positive characteristic\nby Pavel Etingof (MIT) as part of Springfest
in honor of Vera Serganova\n\n\nAbstract\nI'll describe generalizations $
{\\rm Ver}_{p^n}$\, ${\\rm Ver}_{p^n}^+$ of the incompressible abelian sym
metric tensor categories defined in my joint work with D. Benson (arXiv:18
07.05549) for $p=2$ and by Gelfand-Kazhdan and Georgiev-Mathieu in 1990s f
or $n=1$. Namely\, ${\\rm Ver}_{p^n}$ is the abelian envelope of the quoti
ent of the category of tilting modules for $SL_2(\\bf k)$ by the $n$-th St
einberg module\, and ${\\rm Ver}_{p^n}^+$ is its subcategory generated by
$PGL_2(\\bf k)$-modules. The categories ${\\rm Ver}_{p^n}$ are reductions
to characteristic $p$ of Verlinde braided tensor categories in characteris
tic zero\, which explains the notation. I will try to describe the structu
re of these categories in detail\, and in particular explain that they cat
egorify the real cyclotomic rings $\\mathbb{Z}[2\\cos(2\\pi/p^n)]$\, and t
hat ${\\rm Ver}_{p^n}$ embeds into ${\\rm Ver}_{p^{n+1}}$. We conjecture t
hat every symmetric tensor category of moderate growth over $\\bf k$ admit
s a fiber functor to the union ${\\rm Ver}_{p^\\infty}$ of the nested sequ
ence ${\\rm Ver}_{p}\\subset {\\rm Ver}_{p^2}\\subset\\cdots$. This would
provide a positive characteristic analog of Deligne's theorem in character
istic zero and a generalization of the result of arXiv:1503.01492\, which
shows that this conjecture holds for fusion categories (in which case the
fiber functor lands in ${\\rm Ver}_p$). This is joint work with D. Benson
and V. Ostrik.\n
LOCATION:https://researchseminars.org/talk/SpringfestSerganova/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Penkov (Jacobs University Bremen)
DTSTART;VALUE=DATE-TIME:20210504T153000Z
DTEND;VALUE=DATE-TIME:20210504T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190052Z
UID:SpringfestSerganova/12
DESCRIPTION:Title: Bounded weight modules at infinity\nby Ivan Penkov (Jacob
s University Bremen) as part of Springfest in honor of Vera Serganova\n\n\
nAbstract\nIn this talk\, I present a recent classification of simple bou
nded weight modules for the Lie algebras $sl(\\infty)$\, $o(\\infty)$\, $s
p(\\infty)$ (joint work with D. Grantcharov\, exploiting an unpublished id
ea of I. Dimitrov) and will discuss their primitive ideals (bounded primit
ive ideals). I will also present some results from a current joint work wi
th D. Grantcharov and V. Serganova on the category of simple bounded weigh
t modules for the Lie superalgebra $osp(n|m)$ where $m$ or $n$ equals $\\i
nfty$.\n
LOCATION:https://researchseminars.org/talk/SpringfestSerganova/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Ostrik (University of Oregon)
DTSTART;VALUE=DATE-TIME:20210504T181500Z
DTEND;VALUE=DATE-TIME:20210504T191500Z
DTSTAMP;VALUE=DATE-TIME:20210514T190052Z
UID:SpringfestSerganova/13
DESCRIPTION:Title: Frobenius exact symmetric tensor categories\nby Victor Os
trik (University of Oregon) as part of Springfest in honor of Vera Sergano
va\n\n\nAbstract\nI will report on a joint work in progress with K.Coulemb
ier and P.Etingof. We give a characterization of symmetric tensor categori
es over fields of positive characteristic which admit an exact tensor func
tor to the Verlinde category\; in particular we give a characterization of
Tannakian categories. A crucial\ningredient of this characterization is e
xactness of the Frobenius twist functor which mimics the Frobenius twist f
or representations of algebraic groups.\n
LOCATION:https://researchseminars.org/talk/SpringfestSerganova/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catharina Stroppel (University of Bonn)
DTSTART;VALUE=DATE-TIME:20210505T153000Z
DTEND;VALUE=DATE-TIME:20210505T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190052Z
UID:SpringfestSerganova/14
DESCRIPTION:Title: Based tilting theory\nby Catharina Stroppel (University o
f Bonn) as part of Springfest in honor of Vera Serganova\n\n\nAbstract\nIn
this talk I would like to talk about based quasihereditary algebras and g
eneralisations thereof and describe the corresponding theory of tilting mo
dules and Ringel duality\, some kind of based tilting theory. We give a ge
neral setup in which one can study both semiinfinite highest weight catego
ries as well as examples of algebras with triangular decompositions. Impor
tant examples arise in practise when the notion of highest weight categori
es is weakened to categories with (nice) stratifications. We will in parti
cular study such categories when the strata are symmetric and describe the
relevance to the representation theory.\n
LOCATION:https://researchseminars.org/talk/SpringfestSerganova/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vyacheslav Futorny (University of Sao Paulo)
DTSTART;VALUE=DATE-TIME:20210505T181500Z
DTEND;VALUE=DATE-TIME:20210505T191500Z
DTSTAMP;VALUE=DATE-TIME:20210514T190052Z
UID:SpringfestSerganova/15
DESCRIPTION:Title: Strongly tame Gelfand-Tsetlin modules for Lie (super)algebras
and vertex algebras \nby Vyacheslav Futorny (University of Sao Pa
ulo) as part of Springfest in honor of Vera Serganova\n\n\nAbstract\nFor L
ie algebras and superalgebras in type A we will discuss infinite-dimensio
nal simple modules which admit a basis of Gelfand-Tsetlin tableaux and th
e action via the classical Gelfand-Tsetlin formulas based on recent joint
results with L.E.Ramirez\, V.Serganova and J.Zhang. We will also describe
the connection with the admissible representations of simple affine verte
x algebras.\n
LOCATION:https://researchseminars.org/talk/SpringfestSerganova/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siddhartha Sahi (Rutgers University)
DTSTART;VALUE=DATE-TIME:20210506T153000Z
DTEND;VALUE=DATE-TIME:20210506T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190052Z
UID:SpringfestSerganova/16
DESCRIPTION:Title: Interpolation polynomials\, Capelli operators\, and Lie super
algebras\nby Siddhartha Sahi (Rutgers University) as part of Springfes
t in honor of Vera Serganova\n\n\nAbstract\nThe interpolation polynomials
are a family of inhomogeneous symmetric polynomials that are characterized
by rather simple vanishing (interpolation) conditions. They were introduc
ed by the speaker in connection with joint work with Bertram Kostant on th
e eigenvalues of generalized Capelli-type operators associated to Jordan a
lgebras. Of particular interest is a one parameter subfamily\, which was s
tudied by Friedrich Knop and the speaker\, and by Okunkov-Olshanski\, and
which is closely related to Jack polynomials and Macdonald polynomials.\n\
nWe will describe two recent developments in this direction. The first set
of results is joint work with Hadi Salmasian and Vera Serganova\, which s
olves the Capelli eigenvalue problem in the setting of Lie superalgebras a
nd Jordan superalgebras. The second is joint work with Yusra Naqvi and Emi
ly Sergel\, which proves a long-conjectured positivity property of interpo
lation polynomials.\n
LOCATION:https://researchseminars.org/talk/SpringfestSerganova/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arkady Vaintrob (University of Oregon)
DTSTART;VALUE=DATE-TIME:20210506T181500Z
DTEND;VALUE=DATE-TIME:20210506T191500Z
DTSTAMP;VALUE=DATE-TIME:20210514T190052Z
UID:SpringfestSerganova/17
DESCRIPTION:Title: Mirror symmetry for invertible singularities\nby Arkady V
aintrob (University of Oregon) as part of Springfest in honor of Vera Serg
anova\n\n\nAbstract\nA cohomological field theory (CohFT) is an algebraic
structure underlying the properties of the Gromov-Witten invariants and qu
antum cohomology of projective varieties. For a quasi-homogeneous polynomi
al W with an isolated singularity at the origin there are several known co
nstructions of CohFTs\, the so-called A- and B- Landau-Ginzburg (LG) model
s. The corresponding invariants play a prominent role in various mirror sy
mmetry correspondences connecting LG models with other kinds of quantum in
variants. If the polynomial W is invertible (i.e. when the number of monom
ials in W is equal to the number of variables)\, then the dual polynomial
W' with the transposed matrix of exponents also has an isolated singularit
y\, and we can talk about relations between LG models for W and W'. Corres
pondences of this type were first considered by physicists Berglund and Hu
ebsch in the early 1990s\, but their mathematical understanding was develo
ped only recently. I will talk about a joint work with Weyong He\, Alexand
er Polishchuk\, and Yefeng Shen on a mirror symmetry theorem connecting a
B-model of W and a A-model of W' based\, respectively\, on Saito's theory
of primitive forms and on the CohFT constructed in my earlier work with Po
lishchuk using categories of matrix factorizations.\n
LOCATION:https://researchseminars.org/talk/SpringfestSerganova/17/
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