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BEGIN:VEVENT
SUMMARY:Derek Harland (University of Leeds)
DTSTART:20210201T150000Z
DTEND:20210201T160000Z
DTSTAMP:20260404T041620Z
UID:BIRS_21w5002/1
DESCRIPTION:Title: (Survey) Monopoles: Construction\, Dynamics\, and Transforms\nby Derek Harland (University of Leeds) as part of BIRS workshop: Geome
try\, Analysis\, and Quantum Physics of Monopoles\n\n\nAbstract\nThis talk
will be part pedagogical introduction and part survey. I will review som
e of the foundational tools used to construct and study monopoles\, includ
ing the Nahm transform\, spectral curves\, and rational maps. I will go o
n to survey recent progress on the problems of explicitly constructing mon
opoles and classifying their dynamics\, both on Euclidean R^3 and on other
geometries.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5002/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roger Bielawski (University of Hannover)
DTSTART:20210201T160000Z
DTEND:20210201T170000Z
DTSTAMP:20260404T041620Z
UID:BIRS_21w5002/2
DESCRIPTION:Title: Monopoles and Hyper-Poisson Bivectors\nby Roger Bielawski
(University of Hannover) as part of BIRS workshop: Geometry\, Analysis\, a
nd Quantum Physics of Monopoles\n\n\nAbstract\nIt is well-known that the R
iemannian geometry of the moduli space of Euclidean SU(2)-monopoles of ch
arge $k$ is determined by spectral curves of monopoles. I had often wonde
red whether there is a purely differential-geometric explanation of this f
act\, i.e. whether there exists an infinitesimal object on the moduli spa
ce which makes it so. I shall show that the answer is yes\, and that the
object in question is what I call a hyper-Poisson bivector\, i.e. a bivec
tor which induces\, for each complex structure\, a Poisson structure on
holomorphic functions\, compatible with the respective complex-symplectic
form.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5002/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Goncalo Oliveira (Universidade Federal Fluminense)
DTSTART:20210201T183000Z
DTEND:20210201T193000Z
DTSTAMP:20260404T041620Z
UID:BIRS_21w5002/3
DESCRIPTION:Title: (Survey) Monopoles in Higher Dimensions\nby Goncalo Olivei
ra (Universidade Federal Fluminense) as part of BIRS workshop: Geometry\,
Analysis\, and Quantum Physics of Monopoles\n\n\nAbstract\nI will review t
he basics of what is known about monopoles in higher dimensions. Time perm
itting\, I will mention a few possible future directions regarding the use
of monopoles in special holonomy.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5002/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siqi He (Stony Brook)
DTSTART:20210201T193000Z
DTEND:20210201T203000Z
DTSTAMP:20260404T041620Z
UID:BIRS_21w5002/4
DESCRIPTION:Title: The Compactness Problem for the Hitchin-Simpson Equations\
nby Siqi He (Stony Brook) as part of BIRS workshop: Geometry\, Analysis\,
and Quantum Physics of Monopoles\n\n\nAbstract\nThe Hitchin-Simpson equati
ons defined over a Kähler manifold are first order\, non-linear equations
for a pair of a connection on a Hermitian vector bundle and a 1-form with
values in the endomorphism bundle. We will describe the behavior of solut
ions to the Hitchin–Simpson equations with norms of these 1-forms unboun
ded. We will also discuss the deformation problem of Taubes' Z2 harmonic 1
-form.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5002/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Braverman (University of Toronto)
DTSTART:20210202T150000Z
DTEND:20210202T160000Z
DTSTAMP:20260404T041620Z
UID:BIRS_21w5002/5
DESCRIPTION:Title: Monopoles and quasimaps in representation theory (Survey)\
nby Alexander Braverman (University of Toronto) as part of BIRS workshop:
Geometry\, Analysis\, and Quantum Physics of Monopoles\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5002/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Finkelberg (National Research University Higher School of
Economics)
DTSTART:20210202T160000Z
DTEND:20210202T170000Z
DTSTAMP:20260404T041620Z
UID:BIRS_21w5002/6
DESCRIPTION:Title: Elliptic Zastava\nby Michael Finkelberg (National Research
University Higher School of Economics) as part of BIRS workshop: Geometry
\, Analysis\, and Quantum Physics of Monopoles\n\n\nAbstract\nFor a semisi
mple group G and a smooth curve C\, open zastava space Z(G\,C) is a smooth
variety\, affine over a configuration space of C. In case C is the additi
ve or multiplicative group\, Z(G\,C) is isomorphic to a moduli space of eu
clidean or periodic monopoles. It carries a natural symplectic form\, and
the projection to the configuration space is an integrable system (open To
da lattice for G=SL(2)). I will explain what happens when C is an elliptic
curve. This is a joint work with Mykola Matviichuk and Alexander Polishch
uk.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5002/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Norbury (University of Melbourne)
DTSTART:20210202T183000Z
DTEND:20210202T193000Z
DTSTAMP:20260404T041620Z
UID:BIRS_21w5002/7
DESCRIPTION:Title: Spectral Curves in Surfaces\nby Paul Norbury (University o
f Melbourne) as part of BIRS workshop: Geometry\, Analysis\, and Quantum P
hysics of Monopoles\n\n\nAbstract\nAn embedded curve in a Poisson surface
$\\Sigma\\subset X$ defines a smooth deformation space $\\mathcal{B}$ of n
earby embedded curves. In this talk we will describe a key idea of Kontse
vich and Soibelman to equip the Poisson surface $X$ with a foliation in or
der to study the deformation space $\\mathcal{B}$. For example\, $X=TP^1\
\to P^1$ is a Poisson surface surface foliated by its fibres. The foliati
on\, together with a vector space $V_\\Sigma$ of meromorphic differentials
on $\\Sigma$\, endows an embedded curve $\\Sigma$ with the structure of t
he initial data of topological recursion\, which defines a collection of s
ymmetric tensors on $V_\\Sigma$. These tensors produce a formal series\,
which turns out to be a formal Seiberg-Witten differential\, that descends
under a quotient to an analytic series.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5002/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Singer (University College London)
DTSTART:20210203T150000Z
DTEND:20210203T160000Z
DTSTAMP:20260404T041620Z
UID:BIRS_21w5002/8
DESCRIPTION:Title: Asymptotics of Monopole Moduli Spaces (Survey)\nby Michael
Singer (University College London) as part of BIRS workshop: Geometry\, A
nalysis\, and Quantum Physics of Monopoles\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5002/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Kottke (New College of Florida)
DTSTART:20210203T160000Z
DTEND:20210203T170000Z
DTSTAMP:20260404T041620Z
UID:BIRS_21w5002/9
DESCRIPTION:Title: The Quasi Fibered Boundary (QFB) Compactification of Monopole
Moduli Spaces\nby Chris Kottke (New College of Florida) as part of BIR
S workshop: Geometry\, Analysis\, and Quantum Physics of Monopoles\n\n\nAb
stract\nThe moduli spaces $M_k$ of $SU(2)$ monopoles on $R^3$ of charge $k
$ are among the oldest studied objects in gauge theory\, yet open question
s still remain\, such as Sen's conjecture for their $L^2$ cohomology. I wi
ll discuss compactifications of these moduli spaces as manifolds with corn
ers\, with respect to which their hyperKahler metrics are of "quasi fibere
d boundary" (QFB) type\, a metric structure which generalizes the quasi as
ymptotically locally euclidean (QALE) and quasi asymptotically conic (QAC)
structures introduced by Joyce and others. This geometric structure\, whi
ch is best understood by comparison to the simpler moduli space of point c
lusters on $R^3$\, systematically organizes the various asymptotic regions
of the moduli space in which charge $k$ monopoles decompose into widely s
eparated monopoles of charges summing to $k$. This is joint work with M. S
inger and K. Fritzsch.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5002/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andy Royston (Penn State Fayette)
DTSTART:20210203T183000Z
DTEND:20210203T193000Z
DTSTAMP:20260404T041620Z
UID:BIRS_21w5002/10
DESCRIPTION:Title: Monopoles and Quantum Field Theory (Survey)\nby Andy Roys
ton (Penn State Fayette) as part of BIRS workshop: Geometry\, Analysis\, a
nd Quantum Physics of Monopoles\n\n\nAbstract\nMagnetic monopoles and quan
tum theory have been joined at the hip from the beginning. Over the years
monopoles have motivated\, or at least had front row seats at\, many of t
he most fundamental advances in quantum field theory. In recent times\, m
onopoles have become a primary conduit through which quantum field theory
directly impacts mathematics and vice versa. In this talk I will highligh
t some of these developments and connections\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5002/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:T. Daniel Brennan (University of Chicago)
DTSTART:20210203T193000Z
DTEND:20210203T203000Z
DTSTAMP:20260404T041620Z
UID:BIRS_21w5002/11
DESCRIPTION:Title: Monopoles and Fermions\nby T. Daniel Brennan (University
of Chicago) as part of BIRS workshop: Geometry\, Analysis\, and Quantum Ph
ysics of Monopoles\n\n\nAbstract\nIn this talk we will discuss some of the
features of monopole-fermion interactions. In the low energy limit of SUS
Y gauge theories\, monopole interactions can be described by dynamics on m
onopole moduli space. Coupling these theories to fermionic matter the theo
ry on the moduli space M to a hyperholomorphic bundle on M. We will discus
s how this bundle arises and how it can be understood in the rational map
formulation of monopole moduli space.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5002/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takuro Mochizuki (Kyoto University)
DTSTART:20210204T150000Z
DTEND:20210204T160000Z
DTSTAMP:20260404T041620Z
UID:BIRS_21w5002/12
DESCRIPTION:Title: Monopoles and Difference Modules\nby Takuro Mochizuki (Ky
oto University) as part of BIRS workshop: Geometry\, Analysis\, and Quantu
m Physics of Monopoles\n\n\nAbstract\nWe shall discuss equivalences betwee
n various types of monopoles and difference modules. They are variants of
Kobayashi-Hitchin correspondences between algebro-geometric objects and di
fferential geometric objects. We may also regard them as equivalences betw
een monopoles and their underlying scattering data\, which have been pursu
ed in various contexts. Though it is difficult to construct monopoles expl
icitly\, we would like to explain that some asymptotic properties can be e
asily understood through the corresponding difference modules.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5002/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Fredrickson (Stanford University)
DTSTART:20210204T160000Z
DTEND:20210204T170000Z
DTSTAMP:20260404T041620Z
UID:BIRS_21w5002/13
DESCRIPTION:Title: ALG Gravitational Instantons and Hitchin Moduli Spaces\nb
y Laura Fredrickson (Stanford University) as part of BIRS workshop: Geomet
ry\, Analysis\, and Quantum Physics of Monopoles\n\n\nAbstract\nFour-dimen
sional complete hyperkaehler manifolds can be classified into ALE\, ALF\,
ALG\, ALG*\, ALH\, ALH* families. It has been conjectured that every ALG
or ALG* hyperkaehler metric can be realized as a 4d Hitchin moduli space.
I will describe ongoing work with Rafe Mazzeo\, Jan Swoboda\, and Hartmut
Weiss to prove a special case of the conjecture\, and some consequences.
The hyperkaehler metrics on Hitchin moduli spaces are of independent inte
rest\, as the physicists Gaiotto—Moore—Neitzke give an intricate conje
ctural description of their asymptotic geometry.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5002/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lara Anderson (Virginia Tech)
DTSTART:20210204T183000Z
DTEND:20210204T193000Z
DTSTAMP:20260404T041620Z
UID:BIRS_21w5002/14
DESCRIPTION:Title: String Compactifications and Hitchin Systems\nby Lara And
erson (Virginia Tech) as part of BIRS workshop: Geometry\, Analysis\, and
Quantum Physics of Monopoles\n\n\nAbstract\nIn this talk I will describe r
ecent applications of Higgs bundles (including wild/irregular Higgs bundle
s) which arise within a wide range of applications in string compactificat
ions over special holonomy manifolds --- including Calabi-Yau and G2 holon
omy geometries. In string theory\, much recent work has exploited links be
tween Calabi-Yau and Hitchin Integrable systems. In particular\, the work
of Diaconescu\, Donagi and Pantev brought to light a remarkable isomorphis
m between (non-compact) Calabi-Yau integrable systems and those of Hitchin
. Extensions of this correspondence to compact Calabi-Yau geometry have r
ecently been found in the context of string compactifications but many ope
n questions remain. In particular\, links between Hitchin and Calabi-Yau m
oduli spaces have the potential to shed light on a number of important phy
sical questions regarding string vacuum spaces.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5002/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Nekrasov (Simons Center for Geometry and Physics)
DTSTART:20210205T150000Z
DTEND:20210205T160000Z
DTSTAMP:20260404T041620Z
UID:BIRS_21w5002/15
DESCRIPTION:Title: From Instanton Counting to Hyperkahler Geometry of Monopole M
oduli\nby Nikita Nekrasov (Simons Center for Geometry and Physics) as
part of BIRS workshop: Geometry\, Analysis\, and Quantum Physics of Monopo
les\n\n\nAbstract\nThe advances of the last 20 years of nonperturbative su
persymmetric gauge theory led to the double deformation of complex geometr
y of Hitchin systems and moduli spaces of periodic monopoles. I will revie
w these results and sketch a speculative path towards construction of hype
rkahler metrics on these moduli spaces.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5002/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Stern (Duke University)
DTSTART:20210205T160000Z
DTEND:20210205T170000Z
DTSTAMP:20260404T041620Z
UID:BIRS_21w5002/16
DESCRIPTION:Title: Bubbling Threshholds for Yang Mills and Harmonic Maps in Fat
Negatively Curved Spaces\nby Mark Stern (Duke University) as part of B
IRS workshop: Geometry\, Analysis\, and Quantum Physics of Monopoles\n\n\n
Abstract\nI will discuss the effect of negative curvature and girth on sin
gularity formation in Yang Mills and harmonic maps. This work is joint wit
h Luca DiCerbo.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5002/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang Li (MIT)
DTSTART:20210205T183000Z
DTEND:20210205T193000Z
DTSTAMP:20260404T041620Z
UID:BIRS_21w5002/17
DESCRIPTION:Title: High Codimension Phenomena for Hermitian Yang-Mills Connectio
ns\nby Yang Li (MIT) as part of BIRS workshop: Geometry\, Analysis\, a
nd Quantum Physics of Monopoles\n\n\nAbstract\nI will discuss my recent wo
rk constructing a non-conical singular Hermitian Yang-Mills connection on
a homogeneous reflexive sheaf over $\\mathbb{C}^3$\, which is supposed to
model the generic situation of bubbling phenomenon when the Fueter section
has a zero. This example in particular shows that the uniqueness part of
the Hitchin-Kobayashi correspondence does not extend naively to noncompact
manifolds. A variant of this construction gives a sequence of HYM connect
ions on the unit ball in $\\mathbb{C}^3$ with uniformly bounded $L^2$ curv
ature\, but the number of codimension 6 singularities tends to infinity al
ong the sequence. This illustrates the substantial difficulty of the compa
ctification problem in higher dimensional gauge theory.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5002/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weifeng Sun (Harvard University)
DTSTART:20210205T193000Z
DTEND:20210205T203000Z
DTSTAMP:20260404T041620Z
UID:BIRS_21w5002/18
DESCRIPTION:Title: Bogomolny Equations on R3 with a Knot Singularity\nby Wei
feng Sun (Harvard University) as part of BIRS workshop: Geometry\, Analysi
s\, and Quantum Physics of Monopoles\n\n\nAbstract\nThe moduli space of th
e Bogomolny Equations on R3 with certain asymptotic conditions has been fu
lly studied by S.Donaldson\, based on an algebraic geometry approach devel
oped by N.Hitchin. An alternative analytical approach towards studying the
moduli space was established by C.Taubes. An adaption of C.Taubes' method
can also be used to study the moduli space of the Bogomolny equations on
R3 with a knot singularity. Moreover\, it is natural to ask\, whether it i
s possible to study the equations with a knot singularity by algebraic geo
metry method? If this is possible\, then it may have the potential to brin
g knot theory into algebraic geometry.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5002/18/
END:VEVENT
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