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SUMMARY:Maxence Mayrand (University of Toronto)
DTSTART;VALUE=DATE-TIME:20200903T185000Z
DTEND;VALUE=DATE-TIME:20200903T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034607Z
UID:GPRTatNU/1
DESCRIPTION:Title: Symplectic reduction along a submanifold and the Moore-
Tachikawa TQFT\nby Maxence Mayrand (University of Toronto) as part of Geom
etry\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nIn 2011\
, Moore and Tachikawa conjectured the existence of certain complex Hamilto
nian varieties which generate two-dimensional TQFTs where the target categ
ory has complex reductive groups as objects and holomorphic symplectic var
ieties as arrows. It was solved by Ginzburg and Kazhdan using an ad hoc te
chnique which can be thought of as a kind of "symplectic reduction by a gr
oup scheme." We clarify their construction by introducing a general notion
of "symplectic reduction by a groupoid along a submanifold\," which gener
alizes many constructions at once\, such as standard symplectic reduction\
, preimages of Slodowy slices\, the Mikami-Weinstein reduction\, and the G
inzburg-Kazhdan examples. This is joint work with Peter Crooks.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Svetlana Makarova (University of Pennsylvania)
DTSTART;VALUE=DATE-TIME:20200910T185000Z
DTEND;VALUE=DATE-TIME:20200910T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034607Z
UID:GPRTatNU/2
DESCRIPTION:Title: Moduli spaces of stable sheaves over quasipolarized K3
surfaces and Strange Duality\nby Svetlana Makarova (University of Pennsylv
ania) as part of Geometry\, Physics\, and Representation Theory Seminar\n\
n\nAbstract\nIn this talk\, I will show a construction of relative moduli
spaces of stable sheaves over the stack of quasipolarized K3 surfaces of d
egree two. For this\, we use the theory of good moduli spaces\, whose stud
y was initiated by Alper. As a corollary\, we obtain the generic Strange D
uality for K3 surfaces of degree two\, extending the results of Marian and
Oprea on the generic Strange Duality for K3 surfaces.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Jeffrey (University of Toronto)
DTSTART;VALUE=DATE-TIME:20200917T185000Z
DTEND;VALUE=DATE-TIME:20200917T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034607Z
UID:GPRTatNU/3
DESCRIPTION:Title: Flat connections and the $SU(2)$ commutator map\nby Lis
a Jeffrey (University of Toronto) as part of Geometry\, Physics\, and Repr
esentation Theory Seminar\n\n\nAbstract\nThis talk is joint work with Nan-
Kuo Ho\, Paul Selick and Eugene Xia. We describe the space of conjugacy cl
asses of representations of the fundamental group of a genus 2 oriented 2-
manifold into $G := SU(2)$.\n\nWe identify the cohomology ring and a cell
decomposition of a\; space homotopy equivalent to the space of commuting p
airs in $SU(2)$.\n\nWe compute the cohomology of the space $M:= \\mu^{-1}(
-I)$\, where $\\mu:G^4 \\to G$ is the product of commutators.\n\nWe give a
new proof of the cohomology of $A:= M/G$\, both as a group and as a ring.
The group structure is due to Atiyah and Bott in their landmark 1983 pape
r. The ring structure is due to Michael Thaddeus 1992.\n\nWe compute the c
ohomology of the total space of the prequantum line bundle over $A$.\n\nWe
identify the transition functions of the induced $SO(3)$ bundle $M\\to A$
.\n\nTo appear in QJM (Atiyah memorial special issue). arXiv:2005.07390\n\
nReferences:\n\n[1] M.F. Atiyah\, R. Bott\, The Yang-Mills equations over
Riemann surfaces\, Phil. Trans. Roy. Soc. Lond. A308 (1983) 523-615.\n\n[2
] T. Baird\, L. Jeffrey\, P. Selick\, The space of commuting n-tuples in $
SU(2)$\, Illinois J. Math. 55 (2011)\, no. 3\, 805–813.\n\n[3] M. Crabb\
, Spaces of commuting elements in $SU(2)$\, Proc. Edin. Math. Soc. 54 (201
1)\, no. 1\, 67–75.\n\n[4] N. Ho\, L. Jeffrey\, K. Nguyen\, E. Xia\, The
$SU(2)$-character variety of the closed surface of genus 2. Geom. Dedicat
a 192 (2018)\, 171–187.\n\n[5] N. Ho\, L. Jeffrey\, P. Selick\, E. Xia\,
Flat connections and the commutator map for $SU(2)$\, Oxford Quart. J. Ma
th.\, to appear (in the Atiyah memorial special issue).\n\n[6] L. Jeffrey\
, A. Lindberg\, S. Rayan\, Explicit Poincar´e duality in the cohomology r
ing of the $SU(2)$ character variety of a surface. Expos. Math.\, to appea
r.\n\n[7] M.S. Narasimhan and C.S. Seshadri\, Stable and unitary vector bu
ndles on a compact Riemann surface. Ann. of Math. 82 (1965) 540–567.\n\n
[8] P. Newstead\, Topological properties of some spaces of stable bundles\
, Topology 6 (1967)\, 241–262.\n\n[9] C.T.C Wall\, Classification proble
ms in differential topology. V. On certain 6-manifolds. Invent. Math. 1 (1
966)\, 355–374\; corrigendum\, ibid.\, 2 (1966) 306.\n\n[10] M. Thaddeus
\, Conformal field theory and the cohomology of the moduli space of stable
bundles. J. Differential Geom. 35 (1992) 131–149.\n\n[11] E. Witten\, T
wo dimensional gauge theories revisited\, J. Geom. Phys. 9 (1992) 303-368.
\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Smirnov (University of North Carolina at Chapel Hill)
DTSTART;VALUE=DATE-TIME:20201001T185000Z
DTEND;VALUE=DATE-TIME:20201001T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034607Z
UID:GPRTatNU/4
DESCRIPTION:Title: Quantum difference equations\, monodromies and mirror s
ymmetry\nby Andrey Smirnov (University of North Carolina at Chapel Hill) a
s part of Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbst
ract\nAn important enumerative invariant of a symplectic variety $X$ is it
s vertex function. The vertex function is the analog of J-function in Grom
ov-Witten theory: it is the generating function for the numbers of rationa
l curves in $X$.\n\nIn representation theory these functions feature as so
lutions of various $q$-difference and differential equations associated wi
th $X$\, with examples including qKZ and quantum dynamical equations for q
uantum loop groups\, Casimir connections for Yangians and other objects.\n
\nIn this talk I explain how these equations can be extracted from algebra
ic topology of symplectic dual variety $X^!$\, also known as $3D$-mirror o
f $X$. This can be summarized as "identity"\n$$\n\\text{Enumerative geomet
ry of }X = \\text{algebraic topology of }X^!\n$$\nThe talk is based on wor
k in progress with Y.Kononov arXiv:2004.07862\; arXiv:2008.06309.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soheyla Feyzbakhsh (Imperial College)
DTSTART;VALUE=DATE-TIME:20201015T185000Z
DTEND;VALUE=DATE-TIME:20201015T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034607Z
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DESCRIPTION:Title: An application of Bogomolov-Gieseker type inequality to
counting invariants\nby Soheyla Feyzbakhsh (Imperial College) as part of
Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nIn t
his talk\, I will work on a smooth projective threefold $X$ which satisfie
s the Bogomolov-Gieseker conjecture of Bayer-Macrì-Toda\, such as the pro
jective space $\\mathbb{P}^3$ or the quintic threefold. I will show certai
n moduli spaces of 2-dimensional torsion sheaves on $X$ are smooth bundles
over Hilbert schemes of ideal sheaves of curves and points in $X$. When $
X$ is Calabi-Yau this gives a simple wall crossing formula expressing curv
e counts (and so ultimately Gromov-Witten invariants) in terms of counts o
f D4-D2-D0 branes. This is joint work with Richard Thomas\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Alekseev (University of Geneva)
DTSTART;VALUE=DATE-TIME:20201022T185000Z
DTEND;VALUE=DATE-TIME:20201022T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034607Z
UID:GPRTatNU/6
DESCRIPTION:Title: Poisson-Lie groups\, integrable systems and the Berenst
ein-Kazhdan potential\nby Anton Alekseev (University of Geneva) as part of
Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nInt
egrable systems and Poisson-Lie groups are closely related topics. In this
talk\, we will explain how integrability helps in understanding Poisson g
eometry of the dual Poisson-Lie group $K^*$ of a compact Lie group $K$. On
e of our main tools will be the Berenstein-Kazhdan potential from the theo
ry of canonical bases.\n\nThe talk is based on joint works with A. Berenst
ein\, I. Davidenkova\, B. Hoffman\, J. Lane and Y. Li.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Balázs Elek (Cornell University)
DTSTART;VALUE=DATE-TIME:20200924T185000Z
DTEND;VALUE=DATE-TIME:20200924T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034607Z
UID:GPRTatNU/7
DESCRIPTION:Title: Heaps\, Crystals and Preprojective algebra modules\nby
Balázs Elek (Cornell University) as part of Geometry\, Physics\, and Repr
esentation Theory Seminar\n\n\nAbstract\nKashiwara crystals are combinator
ial gadgets associated to a representation of a reductive algebraic group
that enable us to understand the structure of the representation in purely
combinatorial terms. We will describe a type-independent construction of
crystals of certain representations\, using the heap associated to a fully
commutative element in the Weyl group. Then we will discuss how these hea
ps also lead us to the construction of modules for the preprojective algeb
ra of the Dynkin quiver. Using the rank-nullity theorem\, we will see how
the Kashiwara operators have a surprisingly nice description in terms of t
hese preprojective algebra modules. This is work in progress joint with An
ne Dranowski\, Joel Kamnitzer\, Tanny Libman and Calder Morton-Ferguson.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolle González (University of California at Los Angeles)
DTSTART;VALUE=DATE-TIME:20201008T185000Z
DTEND;VALUE=DATE-TIME:20201008T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034607Z
UID:GPRTatNU/8
DESCRIPTION:Title: A Skein theoretic Carlsson-Mellit algebra\nby Nicolle G
onzález (University of California at Los Angeles) as part of Geometry\, P
hysics\, and Representation Theory Seminar\n\n\nAbstract\nThe Carlsson-Mel
lit algebra arose for the first time in the proof of the shuffle conjectur
e\, which gives an explicit combinatorial formula for the Frobenius charac
ter of the space of diagonal harmonics in terms of parking functions. Its
polynomial representation\, given by certain complicated plethystic operat
ors over extensions of the ring of symmetric functions\, plays a particula
rly important role as it encodes much of the underlying combinatorial theo
ry. By various results of Gorsky\, Mellit and Carlsson it was shown that t
his algebra can be used to construct generators of the Elliptic Hall algeb
ra in addition to having deep connections to the homology of torus knots.
Thus\, a natural starting point in the search to categorify these structur
es is the categorification of the Carlsson-Mellit algebra and its polynomi
al representation. \n\nIn this talk I will explain joint work with Matt Ho
gancamp where we constructed a purely skein theoretic formulation of this
algebra and realized its generators as certain braid diagrams on a thicken
ed annulus. Consequently\, we used this framework to categorify the polyno
mial representation of the Carlsson-Mellit algebra as a family of functors
over the derived trace of the Soergel category.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Simental Rodríguez (University of California at Davis)
DTSTART;VALUE=DATE-TIME:20201029T185000Z
DTEND;VALUE=DATE-TIME:20201029T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034607Z
UID:GPRTatNU/9
DESCRIPTION:Title: Parabolic Hilbert schemes and representation theory\nby
José Simental Rodríguez (University of California at Davis) as part of
Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nWe e
xplicitly construct an action of type A rational Cherednik algebras and\,
more generally\, quantized Gieseker varieties\, on the equivariant homolog
y of the parabolic Hilbert scheme of points on the plane curve singularity
$C = \\{x^{m} = y^{n}\\}$ where $m$ and $n$ are coprime positive integers
. We show that the representation we get is a highest weight irreducible r
epresentation and explicitly identify its highest weight. We will also pla
ce these results in the recent context of Coulomb branches and BFN Springe
r theory. This is joint work with Eugene Gorsky and Monica Vazirani.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah White (Australian National University)
DTSTART;VALUE=DATE-TIME:20201105T195000Z
DTEND;VALUE=DATE-TIME:20201105T205000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034607Z
UID:GPRTatNU/10
DESCRIPTION:by Noah White (Australian National University) as part of Geom
etry\, Physics\, and Representation Theory Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ulrike Rieß (ETH Zürich)
DTSTART;VALUE=DATE-TIME:20201112T195000Z
DTEND;VALUE=DATE-TIME:20201112T205000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034607Z
UID:GPRTatNU/11
DESCRIPTION:by Ulrike Rieß (ETH Zürich) as part of Geometry\, Physics\,
and Representation Theory Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rekha Biswal (MPI Bonn)
DTSTART;VALUE=DATE-TIME:20201119T195000Z
DTEND;VALUE=DATE-TIME:20201119T205000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034607Z
UID:GPRTatNU/12
DESCRIPTION:by Rekha Biswal (MPI Bonn) as part of Geometry\, Physics\, and
Representation Theory Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Li Yu (University of Chicago)
DTSTART;VALUE=DATE-TIME:20201203T195000Z
DTEND;VALUE=DATE-TIME:20201203T205000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034607Z
UID:GPRTatNU/13
DESCRIPTION:by Li Yu (University of Chicago) as part of Geometry\, Physics
\, and Representation Theory Seminar\n\nAbstract: TBA\n
END:VEVENT
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