BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Derek Harland (University of Leeds) DTSTART:20210201T150000Z DTEND:20210201T160000Z DTSTAMP:20260422T185228Z UID:BIRS_21w5002/1 DESCRIPTION:Title: (Survey) Monopoles: Construction\, Dynamics\, and Transforms\nby Derek Harland (University of Leeds) as part of BIRS workshop: Geometry\, A nalysis\, and Quantum Physics of Monopoles\n\n\nAbstract\nThis talk will b e part pedagogical introduction and part survey. I will review some of th e foundational tools used to construct and study monopoles\, including the Nahm transform\, spectral curves\, and rational maps. I will go on to su rvey recent progress on the problems of explicitly constructing monopoles and classifying their dynamics\, both on Euclidean R^3 and on other geomet ries.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5002/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Roger Bielawski (University of Hannover) DTSTART:20210201T160000Z DTEND:20210201T170000Z DTSTAMP:20260422T185228Z UID:BIRS_21w5002/2 DESCRIPTION:Title: Monopoles and Hyper-Poisson Bivectors\nby Roger Bielawski (Univer sity of Hannover) as part of BIRS workshop: Geometry\, Analysis\, and Quan tum Physics of Monopoles\n\n\nAbstract\nIt is well-known that the Riemanni an geometry of the moduli space of Euclidean SU(2)-monopoles of charge $k $ is determined by spectral curves of monopoles. I had often wondered whe ther there is a purely differential-geometric explanation of this fact\, i .e. whether there exists an infinitesimal object on the moduli space whic h 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 bivector whi ch induces\, for each complex structure\, a Poisson structure on holomor phic functions\, compatible with the respective complex-symplectic form.\ n LOCATION:https://researchseminars.org/talk/BIRS_21w5002/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Goncalo Oliveira (Universidade Federal Fluminense) DTSTART:20210201T183000Z DTEND:20210201T193000Z DTSTAMP:20260422T185228Z UID:BIRS_21w5002/3 DESCRIPTION:Title: (Survey) Monopoles in Higher Dimensions\nby Goncalo Oliveira (Uni versidade Federal Fluminense) as part of BIRS workshop: Geometry\, Analysi s\, and Quantum Physics of Monopoles\n\n\nAbstract\nI will review the basi cs of what is known about monopoles in higher dimensions. Time permitting\ , I will mention a few possible future directions regarding the use of mon opoles in special holonomy.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5002/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Siqi He (Stony Brook) DTSTART:20210201T193000Z DTEND:20210201T203000Z DTSTAMP:20260422T185228Z UID:BIRS_21w5002/4 DESCRIPTION:Title: The Compactness Problem for the Hitchin-Simpson Equations\nby Siq i He (Stony Brook) as part of BIRS workshop: Geometry\, Analysis\, and Qua ntum Physics of Monopoles\n\n\nAbstract\nThe Hitchin-Simpson equations def ined 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 solutions to the Hitchin–Simpson equations with norms of these 1-forms unbounded. We will also discuss the deformation problem of Taubes' Z2 harmonic 1-form.\ n LOCATION:https://researchseminars.org/talk/BIRS_21w5002/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Braverman (University of Toronto) DTSTART:20210202T150000Z DTEND:20210202T160000Z DTSTAMP:20260422T185228Z UID:BIRS_21w5002/5 DESCRIPTION:Title: Monopoles and quasimaps in representation theory (Survey)\nby Ale xander Braverman (University of Toronto) as part of BIRS workshop: Geometr y\, Analysis\, and Quantum Physics of Monopoles\n\nAbstract: TBA\n LOCATION:https://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:20260422T185228Z UID:BIRS_21w5002/6 DESCRIPTION:Title: Elliptic Zastava\nby Michael Finkelberg (National Research Univer sity Higher School of Economics) as part of BIRS workshop: Geometry\, Anal ysis\, and Quantum Physics of Monopoles\n\n\nAbstract\nFor a semisimple gr oup G and a smooth curve C\, open zastava space Z(G\,C) is a smooth variet y\, affine over a configuration space of C. In case C is the additive or m ultiplicative group\, Z(G\,C) is isomorphic to a moduli space of euclidean or periodic monopoles. It carries a natural symplectic form\, and the pro jection to the configuration space is an integrable system (open Toda latt ice 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 Polishchuk.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5002/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Norbury (University of Melbourne) DTSTART:20210202T183000Z DTEND:20210202T193000Z DTSTAMP:20260422T185228Z UID:BIRS_21w5002/7 DESCRIPTION:Title: Spectral Curves in Surfaces\nby Paul Norbury (University of Melbo urne) as part of BIRS workshop: Geometry\, Analysis\, and Quantum Physics of Monopoles\n\n\nAbstract\nAn embedded curve in a Poisson surface $\\Sigm a\\subset X$ defines a smooth deformation space $\\mathcal{B}$ of nearby e mbedded curves. In this talk we will describe a key idea of Kontsevich an d Soibelman to equip the Poisson surface $X$ with a foliation in order 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 foliation\, to gether with a vector space $V_\\Sigma$ of meromorphic differentials on $\\ Sigma$\, endows an embedded curve $\\Sigma$ with the structure of the init ial data of topological recursion\, which defines a collection of symmetri c tensors on $V_\\Sigma$. These tensors produce a formal series\, which t urns out to be a formal Seiberg-Witten differential\, that descends under a quotient to an analytic series.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5002/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Singer (University College London) DTSTART:20210203T150000Z DTEND:20210203T160000Z DTSTAMP:20260422T185228Z UID:BIRS_21w5002/8 DESCRIPTION:Title: Asymptotics of Monopole Moduli Spaces (Survey)\nby Michael Singer (University College London) as part of BIRS workshop: Geometry\, Analysis \, and Quantum Physics of Monopoles\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/BIRS_21w5002/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Kottke (New College of Florida) DTSTART:20210203T160000Z DTEND:20210203T170000Z DTSTAMP:20260422T185228Z 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 BIRS works hop: Geometry\, Analysis\, and Quantum Physics of Monopoles\n\n\nAbstract\ nThe moduli spaces $M_k$ of $SU(2)$ monopoles on $R^3$ of charge $k$ are a mong the oldest studied objects in gauge theory\, yet open questions still remain\, such as Sen's conjecture for their $L^2$ cohomology. I will disc uss compactifications of these moduli spaces as manifolds with corners\, w ith respect to which their hyperKahler metrics are of "quasi fibered bound ary" (QFB) type\, a metric structure which generalizes the quasi asymptoti cally locally euclidean (QALE) and quasi asymptotically conic (QAC) struct ures introduced by Joyce and others. This geometric structure\, which is b est understood by comparison to the simpler moduli space of point clusters on $R^3$\, systematically organizes the various asymptotic regions of the moduli space in which charge $k$ monopoles decompose into widely separate d monopoles of charges summing to $k$. This is joint work with M. Singer a nd K. Fritzsch.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5002/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Andy Royston (Penn State Fayette) DTSTART:20210203T183000Z DTEND:20210203T193000Z DTSTAMP:20260422T185228Z UID:BIRS_21w5002/10 DESCRIPTION:Title: Monopoles and Quantum Field Theory (Survey)\nby Andy Royston (Pe nn State Fayette) as part of BIRS workshop: Geometry\, Analysis\, and Quan tum Physics of Monopoles\n\n\nAbstract\nMagnetic monopoles and quantum the ory have been joined at the hip from the beginning. Over the years monopo les have motivated\, or at least had front row seats at\, many of the most fundamental advances in quantum field theory. In recent times\, monopole s have become a primary conduit through which quantum field theory directl y impacts mathematics and vice versa. In this talk I will highlight some of these developments and connections\n LOCATION:https://researchseminars.org/talk/BIRS_21w5002/10/ END:VEVENT BEGIN:VEVENT SUMMARY:T. Daniel Brennan (University of Chicago) DTSTART:20210203T193000Z DTEND:20210203T203000Z DTSTAMP:20260422T185228Z UID:BIRS_21w5002/11 DESCRIPTION:Title: Monopoles and Fermions\nby T. Daniel Brennan (University of Chic ago) as part of BIRS workshop: Geometry\, Analysis\, and Quantum Physics o f Monopoles\n\n\nAbstract\nIn this talk we will discuss some of the featur es of monopole-fermion interactions. In the low energy limit of SUSY gauge theories\, monopole interactions can be described by dynamics on monopole moduli space. Coupling these theories to fermionic matter the theory on t he moduli space M to a hyperholomorphic bundle on M. We will discuss how t his bundle arises and how it can be understood in the rational map formula tion of monopole moduli space.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5002/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Takuro Mochizuki (Kyoto University) DTSTART:20210204T150000Z DTEND:20210204T160000Z DTSTAMP:20260422T185228Z UID:BIRS_21w5002/12 DESCRIPTION:Title: Monopoles and Difference Modules\nby Takuro Mochizuki (Kyoto Uni versity) as part of BIRS workshop: Geometry\, Analysis\, and Quantum Physi cs of Monopoles\n\n\nAbstract\nWe shall discuss equivalences between vario us types of monopoles and difference modules. They are variants of Kobayas hi-Hitchin correspondences between algebro-geometric objects and different ial geometric objects. We may also regard them as equivalences between mon opoles and their underlying scattering data\, which have been pursued in v arious contexts. Though it is difficult to construct monopoles explicitly\ , we would like to explain that some asymptotic properties can be easily u nderstood through the corresponding difference modules.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5002/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Laura Fredrickson (Stanford University) DTSTART:20210204T160000Z DTEND:20210204T170000Z DTSTAMP:20260422T185228Z UID:BIRS_21w5002/13 DESCRIPTION:Title: ALG Gravitational Instantons and Hitchin Moduli Spaces\nby Laura Fredrickson (Stanford University) as part of BIRS workshop: Geometry\, An alysis\, and Quantum Physics of Monopoles\n\n\nAbstract\nFour-dimensional complete hyperkaehler manifolds can be classified into ALE\, ALF\, ALG\, A LG*\, 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 hy perkaehler metrics on Hitchin moduli spaces are of independent interest\, as the physicists Gaiotto—Moore—Neitzke give an intricate conjectural description of their asymptotic geometry.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5002/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Lara Anderson (Virginia Tech) DTSTART:20210204T183000Z DTEND:20210204T193000Z DTSTAMP:20260422T185228Z UID:BIRS_21w5002/14 DESCRIPTION:Title: String Compactifications and Hitchin Systems\nby Lara Anderson ( Virginia Tech) as part of BIRS workshop: Geometry\, Analysis\, and Quantum Physics of Monopoles\n\n\nAbstract\nIn this talk I will describe recent a pplications of Higgs bundles (including wild/irregular Higgs bundles) whic h arise within a wide range of applications in string compactifications ov er special holonomy manifolds --- including Calabi-Yau and G2 holonomy geo metries. In string theory\, much recent work has exploited links between C alabi-Yau and Hitchin Integrable systems. In particular\, the work of Diac onescu\, Donagi and Pantev brought to light a remarkable isomorphism betwe en (non-compact) Calabi-Yau integrable systems and those of Hitchin. Exte nsions of this correspondence to compact Calabi-Yau geometry have recently been found in the context of string compactifications but many open quest ions remain. In particular\, links between Hitchin and Calabi-Yau moduli s paces have the potential to shed light on a number of important physical q uestions regarding string vacuum spaces.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5002/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Nikita Nekrasov (Simons Center for Geometry and Physics) DTSTART:20210205T150000Z DTEND:20210205T160000Z DTSTAMP:20260422T185228Z UID:BIRS_21w5002/15 DESCRIPTION:Title: From Instanton Counting to Hyperkahler Geometry of Monopole Moduli\nby Nikita Nekrasov (Simons Center for Geometry and Physics) as part of BIRS workshop: Geometry\, Analysis\, and Quantum Physics of Monopoles\n\n \nAbstract\nThe advances of the last 20 years of nonperturbative supersymm etric gauge theory led to the double deformation of complex geometry of Hi tchin systems and moduli spaces of periodic monopoles. I will review these results and sketch a speculative path towards construction of hyperkahler metrics on these moduli spaces.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5002/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Stern (Duke University) DTSTART:20210205T160000Z DTEND:20210205T170000Z DTSTAMP:20260422T185228Z UID:BIRS_21w5002/16 DESCRIPTION:Title: Bubbling Threshholds for Yang Mills and Harmonic Maps in Fat Negativ ely Curved Spaces\nby Mark Stern (Duke University) as part of BIRS wor kshop: Geometry\, Analysis\, and Quantum Physics of Monopoles\n\n\nAbstrac t\nI will discuss the effect of negative curvature and girth on singularit y formation in Yang Mills and harmonic maps. This work is joint with Luca DiCerbo.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5002/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Yang Li (MIT) DTSTART:20210205T183000Z DTEND:20210205T193000Z DTSTAMP:20260422T185228Z UID:BIRS_21w5002/17 DESCRIPTION:Title: High Codimension Phenomena for Hermitian Yang-Mills Connections\ nby Yang Li (MIT) as part of BIRS workshop: Geometry\, Analysis\, and Quan tum Physics of Monopoles\n\n\nAbstract\nI will discuss my recent work cons tructing a non-conical singular Hermitian Yang-Mills connection on a homog eneous reflexive sheaf over $\\mathbb{C}^3$\, which is supposed to model t he generic situation of bubbling phenomenon when the Fueter section has a zero. This example in particular shows that the uniqueness part of the Hit chin-Kobayashi correspondence does not extend naively to noncompact manifo lds. A variant of this construction gives a sequence of HYM connections on the unit ball in $\\mathbb{C}^3$ with uniformly bounded $L^2$ curvature\, but the number of codimension 6 singularities tends to infinity along the sequence. This illustrates the substantial difficulty of the compactifica tion problem in higher dimensional gauge theory.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5002/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Weifeng Sun (Harvard University) DTSTART:20210205T193000Z DTEND:20210205T203000Z DTSTAMP:20260422T185228Z UID:BIRS_21w5002/18 DESCRIPTION:Title: Bogomolny Equations on R3 with a Knot Singularity\nby Weifeng Su n (Harvard University) as part of BIRS workshop: Geometry\, Analysis\, and Quantum Physics of Monopoles\n\n\nAbstract\nThe moduli space of the Bogom olny Equations on R3 with certain asymptotic conditions has been fully stu died by S.Donaldson\, based on an algebraic geometry approach developed by N.Hitchin. An alternative analytical approach towards studying the moduli space was established by C.Taubes. An adaption of C.Taubes' method can al so 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 is possi ble to study the equations with a knot singularity by algebraic geometry m ethod? If this is possible\, then it may have the potential to bring knot theory into algebraic geometry.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5002/18/ END:VEVENT END:VCALENDAR