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DTSTART:20240310T070000
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TZOFFSETFROM:-0400
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DTSTART:20231105T060000
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BEGIN:VEVENT
UID:69b114f16b747
DTSTART;TZID=America/Toronto:20240328T143000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240328T153000
URL:https://uwaterloo.ca/pure-mathematics-geometry-topology/events/paraboli
 c-gap-theorems-yang-mills-functional
SUMMARY:Parabolic gap theorems for the Yang-Mills functional
CLASS:PUBLIC
DESCRIPTION:ALEX WALDRON\, UNIVERSITY OF WISCONSIN-MADISON\n\nGiven a princ
 ipal bundle over a compact Riemannian 4-manifold or\nspecial-holonomy mani
 fold\, it is natural to ask whether a uniform gap\nexists between the inst
 anton energy and that of any non-minimal\nYang-Mills connection. This ques
 tion is quite open in general\,\nalthough positive results exist in the li
 terature. We'll review\nseveral of these gap theorems and strengthen them 
 to statements of the\nfollowing type: the space of all connections below a
  certain energy\ndeformation retracts (under Yang-Mills flow) onto the spa
 ce of\ninstantons. As applications\, we recover a theorem of Taubes on\npa
 th-connectedness of instanton moduli spaces on the 4-sphere\, and\nobtain 
 a method to construct instantons on quaternion-Kähler\nmanifolds with pos
 itive scalar curvature.\n\nMC 5417
DTSTAMP:20260311T070833Z
END:VEVENT
BEGIN:VEVENT
UID:69b114f175e3a
DTSTART;TZID=America/Toronto:20240321T143000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240321T153000
URL:https://uwaterloo.ca/pure-mathematics-geometry-topology/events/finitene
 ss-monodromy-fibered-calabi-yau-threefolds
SUMMARY:Finiteness of monodromy for fibered Calabi-Yau threefolds
CLASS:PUBLIC
DESCRIPTION:FRANÇOIS GREER\, MICHIGAN STATE UNIVERSITY\n\nAn old question 
 going back to S.T. Yau asks whether there are finitely\nmany diffeomorphis
 m types for smooth projective Calabi-Yau manifolds\nof a given dimension. 
 The answer is affirmative for dimensions one and\ntwo (elliptic curves and
  K3 surfaces). It has recently been settled\nfor Calabi-Yau threefolds adm
 itting elliptic fibrations. We discuss\nthe case of CY3’s admitting abel
 ian surface or K3 fibrations. \n\nMC 5417
DTSTAMP:20260311T070833Z
END:VEVENT
BEGIN:VEVENT
UID:69b114f176caf
DTSTART;TZID=America/Toronto:20240314T143000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240314T153000
URL:https://uwaterloo.ca/pure-mathematics-geometry-topology/events/steady-g
 radient-kahler-ricci-solitons-and-calabi-yau-metrics
SUMMARY:Steady gradient Kähler-Ricci solitons and Calabi-Yau metrics on C^
 n
CLASS:PUBLIC
DESCRIPTION:CHARLES CIFARELLI\, CIRGET & STONY BROOK\n\nI will present rece
 nt joint work with V. Apostolov on a new\nconstruction of complete stead
 y gradient Kähler-Ricci solitons on\nC^n\, using the theory of hamiltonia
 n 2 forms\, introduced by\nApostolov-Calderbank-Gauduchon-Tønnesen-Friedm
 an\, as an Ansatz. The\nmetrics come in families of two types with distinc
 t geometric\nbehavior\, which we call Cao type and Taub-NUT type. In parti
 cular\, the\nCao type and Taub-NUT type families have a volume growth rate
  of r^n\nand r^{2n-1}\, respectively. Moreover\, each Taub-NUT type family
 \ncontains a codimension 1 subfamily of complete Ricci-flat metrics.\n\nMC
  5417
DTSTAMP:20260311T070833Z
END:VEVENT
BEGIN:VEVENT
UID:69b114f177963
DTSTART;TZID=America/Toronto:20240307T143000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240307T153000
URL:https://uwaterloo.ca/pure-mathematics-geometry-topology/events/solitons
 -and-extended-bogomolny-equations-jumping-data
SUMMARY:Solitons and the Extended Bogomolny Equations with Jumping Data
CLASS:PUBLIC
DESCRIPTION:ANDY ROYSTON\, PENN STATE UNIVERSITY\n\nThe extended Bogomolny 
 equations are a system of PDE's for a\nconnection and a triplet of Higgs f
 ields on a three-dimensional space.\nThey are a hybrid of the Bogomolny eq
 uations and the Nahm equations.\nAfter reviewing how these latter systems 
 arise in the study of\nmagnetic monopoles\, I will present an energy funct
 ional for which\nsolutions of the extended Bogomolny equations are minimiz
 ers in a\nfixed topological class. In this construction\, the connection a
 nd\nHiggs triplet are defined on all of R^3 and couple to additional\ndyna
 mical fields localized on a two-plane that are analogous to\njumping data 
 in the Nahm equations. Solutions can therefore be\ninterpreted as finite-e
 nergy BPS solitons in a three-dimensional\ntheory with a planar defect. Th
 is talk is based on work done in\ncollaboration with Sophia Domokos.\n\nMC
  5417
DTSTAMP:20260311T070833Z
END:VEVENT
BEGIN:VEVENT
UID:69b114f1785b5
DTSTART;TZID=America/Toronto:20240305T143000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240305T153000
URL:https://uwaterloo.ca/pure-mathematics-geometry-topology/events/multipli
 cative-higgs-bundles-monopoles-and-involutions
SUMMARY:Multiplicative Higgs bundles\, monopoles and involutions
CLASS:PUBLIC
DESCRIPTION:GUILLERMO GALLEGO\, UNIVERSIDAD COMPLUTENSE DE MADRID\n\nMulti
 plicative Higgs bundles are a natural analogue of Higgs bundles\non Rieman
 n surfaces\, where the Higgs field now takes values on the\nadjoint group 
 bundle\, instead of the adjoint Lie algebra bundle. In\nthe work of Charbo
 nneau and Hurtubise\, they have been related to\nsingular monopoles over t
 he product of a circle with the Riemann\nsurface.\n\nIn this talk we study
  the natural action of an involution of the group\non the moduli space of 
 multiplicative Higgs bundles\, also from the\npoint of view of monopoles. 
 This provides a \"multiplicative analogue\"\nof the theory of Higgs bundle
 s for real groups.\n\nMC 5403
DTSTAMP:20260311T070833Z
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BEGIN:VEVENT
UID:69b114f1791bb
DTSTART;TZID=America/Toronto:20240215T143000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240215T153000
URL:https://uwaterloo.ca/pure-mathematics-geometry-topology/events/calderon
 -problem-connections-coupled-spinors
SUMMARY:The Calderón problem for U(N)-connections coupled to spinors
CLASS:PUBLIC
DESCRIPTION:CARLOS VALERO\, MCGILL UNIVERSITY\n\nThe Calderón problem refe
 rs to the question of whether one can\ndetermine the Riemannian metric on 
 a manifold with boundary from its\n\"Dirichlet-to-Neumann (DN) map\"\, whi
 ch maps a function on the boundary\nto the normal derivative of its harmon
 ic extension. In this talk\, we\ndefine the analogue of the DN map for the
  spinor Laplacian twisted by\na unitary connection and show that it is a p
 seudodifferential operator\nof order 1\, whose symbol determines the Taylo
 r series of the metric\nand connection at the boundary. We go on to show t
 hat if all the data\nare real-analytic\, then the spinor DN map determines
  the connection\nmodulo gauge.\n\nMC 5417
DTSTAMP:20260311T070833Z
END:VEVENT
BEGIN:VEVENT
UID:69b114f179d6c
DTSTART;TZID=America/Toronto:20240229T143000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240229T153000
URL:https://uwaterloo.ca/pure-mathematics-geometry-topology/events/hyperbol
 ic-bloch-transform
SUMMARY:On the hyperbolic Bloch transform
CLASS:PUBLIC
DESCRIPTION:ÁKOS NAGY\, BEIT CANADA\n\nMotivated by recent theoretical and
  experimental developments in the\nphysics of hyperbolic crystals\, I will
  introduce the noncommutative\nBloch transform for Fuchsian groups which I
  will call the hyperbolic\nBloch transform (HBT). The HBT transforms wave 
 functions on the\nhyperbolic plane to sections of irreducible\, flat\, Her
 mitian vector\nbundles over the orbit space and transforms the hyperbolic 
 Laplacian\ninto the covariant Laplacian. I will prove that the HBT is inje
 ctive\nand “asymptotically unitary”. If time permits\, I will talk abo
 ut\npotential applications to hyperbolic band theory. This is a joint work
 \nwith Steve Rayan (arXiv:2208.02749).\n\nMC 5417
DTSTAMP:20260311T070833Z
END:VEVENT
BEGIN:VEVENT
UID:69b114f17a8bf
DTSTART;TZID=America/Toronto:20240208T143000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240208T153000
URL:https://uwaterloo.ca/pure-mathematics-geometry-topology/events/bois-sin
 gularities-rational-singularities-and-beyond
SUMMARY:Du Bois singularities\, rational singularities\, and beyond
CLASS:PUBLIC
DESCRIPTION:WANCHUN ROSIE SHEN\, HARVARD UNIVERSITY\n\nWe survey some exten
 sions of the classical notions of Du Bois and\nrational singularities\, kn
 own as the k-Du Bois and k-rational\nsingularities. By now\, these notions
  are well-understood for local\ncomplete intersections (lci). We explain t
 he difficulties beyond the\nlci case\, and propose new definitions in gene
 ral to make further\nprogress in the theory. This is joint work (in progre
 ss) with Matthew\nSatriano\, Sridhar Venkatesh and Anh Duc Vo.\n\nMC 5417
DTSTAMP:20260311T070833Z
END:VEVENT
BEGIN:VEVENT
UID:69b114f17b4a3
DTSTART;TZID=America/Toronto:20240201T143000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240201T153000
URL:https://uwaterloo.ca/pure-mathematics-geometry-topology/events/local-no
 rmal-forms-complex-bk-geometry
SUMMARY:Local normal forms in complex b^k geometry
CLASS:PUBLIC
DESCRIPTION:MICHAEL FRANCIS\, WESTERN UNIVERSITY\n\nThe b-tangent bundle (t
 erminology due to Melrose) is defined so that\nits sections are smooth vec
 tor fields on the base manifold tangent\nalong a given hypersurface. Compl
 ex b-manifolds\, studied by Mendoza\,\nare defined just like ordinary comp
 lex manifolds\, replacing the usual\ntangent bundle by the b-tangent bundl
 e. Recently\, a\nNewlander-Nirenberg theorem for b-manifolds was obtained 
 by\nFrancis-Barron\, building on Mendoza's work. This talk will discuss th
 e\nextension of the latter result to the setting of b^k-geometry for k>1.\
 nThe original approach to b^k-geometry is due to Scott. A slightly\ndiffer
 ent approach that allows for global holonomy phenomena not\npresent in Sco
 tt's framework was introduced by Francis and\,\nindependently\, by Bischof
 f-del Pino-Witte.\n\nThis seminar will be held both online and in person:\
 n\n* Room: MC 5417\n * Zoom link:\nhttps://uwaterloo.zoom.us/j/94186354814
 ?pwd=NGpLM3B4eWNZckd1aTROcmRreW96QT09
DTSTAMP:20260311T070833Z
END:VEVENT
BEGIN:VEVENT
UID:69b114f17c040
DTSTART;TZID=America/Toronto:20240125T143000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240125T153000
URL:https://uwaterloo.ca/pure-mathematics-geometry-topology/events/moduli-s
 pace-solutions-dimensionally-reduced-kapustin-witten
SUMMARY:The moduli space of solutions to the dimensionally reduced\nKapusti
 n-Witten equations on $\\Sigma\\times\\mathbb{R}_+$
CLASS:PUBLIC
DESCRIPTION:PANAGIOTIS DIMAKIS\, UNIVERSITÉ DU QUÉBEC À MONTRÉAL\, CIRG
 ET\n\nSince their introduction in 2006\, the Kapustin-Witten (KW) equation
 s\nhave become the subject of a number of conjectures. Given a knot $K$\ne
 mbedded in a closed $3$-manifold $Y$\, the most prominent conjecture\npred
 icts that the number of solutions to the KW equations on\n$Y\\times\\mathb
 b{R}_+$ with boundary conditions determined by the\nembedding and with fix
 ed topological charge\, is a topological\ninvariant of the knot. A major o
 bstacle with this conjecture is the\ndifficulty of constructing solutions 
 satisfying these boundary\nconditions. In this talk we assume $Y\\cong \\S
 igma\\times\\mathbb{R}_+$\nand study solutions to the dimensionally reduce
 d KW equations with the\nrequired boundary conditions. We prove that the m
 oduli spaces are\ndiffeomorphic to certain holomorphic lagrangian sub-mani
 folds inside\nthe moduli of Higgs bundles associated to $\\Sigma$. Time pe
 rmitting\,\nwe explain how one could use this result to construct knot inv
 ariants.\n\nMC 5417
DTSTAMP:20260311T070833Z
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