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DTSTART:20240310T070000
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TZOFFSETFROM:-0400
TZOFFSETTO:-0500
DTSTART:20231105T060000
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BEGIN:VEVENT
UID:6825f02b87ee8
DTSTART;TZID=America/Toronto:20240328T143000
SEQUENCE:0
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DTEND;TZID=America/Toronto:20240328T153000
URL:/pure-mathematics-geometry-topology/events/paraboli
 c-gap-theorems-yang-mills-functional
SUMMARY:Parabolic gap theorems for the Yang-Mills functional
CLASS:PUBLIC
DESCRIPTION:Summary \n\nALEX WALDRON\, UNIVERSITY OF WISCONSIN-MADISON\n\nG
 iven a principal bundle over a compact Riemannian 4-manifold or\nspecial-h
 olonomy manifold\, it is natural to ask whether a uniform gap\nexists betw
 een the instanton energy and that of any non-minimal\nYang-Mills connectio
 n. This question is quite open in general\,\nalthough positive results exi
 st in the literature. We'll review\nseveral of these gap theorems and stre
 ngthen them to statements of the\nfollowing type: the space of all connect
 ions below a certain energy\ndeformation retracts (under Yang-Mills flow) 
 onto the space of\ninstantons. As applications\, we recover a theorem of T
 aubes on\npath-connectedness of instanton moduli spaces on the 4-sphere\, 
 and\nobtain a method to construct instantons on quaternion-Kähler\nmanifo
 lds with positive scalar curvature.\n\nMC 5417\n 
DTSTAMP:20250515T134619Z
END:VEVENT
BEGIN:VEVENT
UID:6825f02b8aed5
DTSTART;TZID=America/Toronto:20240321T143000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240321T153000
URL:/pure-mathematics-geometry-topology/events/finitene
 ss-monodromy-fibered-calabi-yau-threefolds
SUMMARY:Finiteness of monodromy for fibered Calabi-Yau threefolds
CLASS:PUBLIC
DESCRIPTION:Summary \n\nFRANÇOIS GREER\, MICHIGAN STATE UNIVERSITY\n\nAn o
 ld question going back to S.T. Yau asks whether there are finitely\nmany d
 iffeomorphism types for smooth projective Calabi-Yau manifolds\nof a given
  dimension. The answer is affirmative for dimensions one and\ntwo (ellipti
 c curves and K3 surfaces). It has recently been settled\nfor Calabi-Yau th
 reefolds admitting elliptic fibrations. We discuss\nthe case of CY3’s ad
 mitting abelian surface or K3 fibrations. \n\nMC 5417\n 
DTSTAMP:20250515T134619Z
END:VEVENT
BEGIN:VEVENT
UID:6825f02b8b7d8
DTSTART;TZID=America/Toronto:20240314T143000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240314T153000
URL:/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:Summary \n\nCHARLES CIFARELLI\, CIRGET & STONY BROOK\n\nI will 
 present recent joint work with V. Apostolov on a new\nconstruction of co
 mplete steady gradient Kähler-Ricci solitons on\nC^n\, using the theory o
 f hamiltonian 2 forms\, introduced by\nApostolov-Calderbank-Gauduchon-Tøn
 nesen-Friedman\, as an Ansatz. The\nmetrics come in families of two types 
 with distinct geometric\nbehavior\, which we call Cao type and Taub-NUT ty
 pe. In particular\, 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 me
 trics.\n\nMC 5417\n 
DTSTAMP:20250515T134619Z
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BEGIN:VEVENT
UID:6825f02b8c07a
DTSTART;TZID=America/Toronto:20240307T143000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240307T153000
URL:/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:Summary \n\nANDY ROYSTON\, PENN STATE UNIVERSITY\n\nThe extende
 d Bogomolny equations are a system of PDE's for a\nconnection and a triple
 t of Higgs fields on a three-dimensional space.\nThey are a hybrid of the 
 Bogomolny equations and the Nahm equations.\nAfter reviewing how these lat
 ter systems arise in the study of\nmagnetic monopoles\, I will present an 
 energy functional for which\nsolutions of the extended Bogomolny equations
  are minimizers in a\nfixed topological class. In this construction\, the 
 connection and\nHiggs triplet are defined on all of R^3 and couple to addi
 tional\ndynamical fields localized on a two-plane that are analogous to\nj
 umping data in the Nahm equations. Solutions can therefore be\ninterpreted
  as finite-energy BPS solitons in a three-dimensional\ntheory with a plana
 r defect. This talk is based on work done in\ncollaboration with Sophia Do
 mokos.\n\nMC 5417\n 
DTSTAMP:20250515T134619Z
END:VEVENT
BEGIN:VEVENT
UID:6825f02b8c882
DTSTART;TZID=America/Toronto:20240305T143000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240305T153000
URL:/pure-mathematics-geometry-topology/events/multipli
 cative-higgs-bundles-monopoles-and-involutions
SUMMARY:Multiplicative Higgs bundles\, monopoles and involutions
CLASS:PUBLIC
DESCRIPTION:Summary \n\nGUILLERMO GALLEGO\, UNIVERSIDAD COMPLUTENSE DE MAD
 RID\n\nMultiplicative Higgs bundles are a natural analogue of Higgs bundle
 s\non Riemann surfaces\, where the Higgs field now takes values on the\nad
 joint group bundle\, instead of the adjoint Lie algebra bundle. In\nthe wo
 rk of Charbonneau and Hurtubise\, they have been related to\nsingular mono
 poles over the product of a circle with the Riemann\nsurface.\n\nIn this t
 alk we study the natural action of an involution of the group\non the modu
 li space of multiplicative Higgs bundles\, also from the\npoint of view of
  monopoles. This provides a \"multiplicative analogue\"\nof the theory of 
 Higgs bundles for real groups.\n\nMC 5403\n 
DTSTAMP:20250515T134619Z
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BEGIN:VEVENT
UID:6825f02b8d065
DTSTART;TZID=America/Toronto:20240215T143000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240215T153000
URL:/pure-mathematics-geometry-topology/events/calderon
 -problem-connections-coupled-spinors
SUMMARY:The Calderón problem for U(N)-connections coupled to spinors
CLASS:PUBLIC
DESCRIPTION:Summary \n\nCARLOS VALERO\, MCGILL UNIVERSITY\n\nThe Calderón 
 problem refers to the question of whether one can\ndetermine the Riemannia
 n metric on a manifold with boundary from its\n\"Dirichlet-to-Neumann (DN)
  map\"\, which maps a function on the boundary\nto the normal derivative o
 f its harmonic extension. In this talk\, we\ndefine the analogue of the DN
  map for the spinor Laplacian twisted by\na unitary connection and show th
 at it is a pseudodifferential operator\nof order 1\, whose symbol determin
 es the Taylor series of the metric\nand connection at the boundary. We go 
 on to show that if all the data\nare real-analytic\, then the spinor DN ma
 p determines the connection\nmodulo gauge.\n\nMC 5417\n 
DTSTAMP:20250515T134619Z
END:VEVENT
BEGIN:VEVENT
UID:6825f02b8d890
DTSTART;TZID=America/Toronto:20240229T143000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240229T153000
URL:/pure-mathematics-geometry-topology/events/hyperbol
 ic-bloch-transform
SUMMARY:On the hyperbolic Bloch transform
CLASS:PUBLIC
DESCRIPTION:Summary \n\nÁKOS NAGY\, BEIT CANADA\n\nMotivated by recent the
 oretical and experimental developments in the\nphysics of hyperbolic cryst
 als\, I will introduce the noncommutative\nBloch transform for Fuchsian gr
 oups which I will call the hyperbolic\nBloch transform (HBT). The HBT tran
 sforms wave functions on the\nhyperbolic plane to sections of irreducible\
 , flat\, Hermitian vector\nbundles over the orbit space and transforms the
  hyperbolic Laplacian\ninto the covariant Laplacian. I will prove that the
  HBT is injective\nand “asymptotically unitary”. If time permits\, I w
 ill talk about\npotential applications to hyperbolic band theory. This is 
 a joint work\nwith Steve Rayan (arXiv:2208.02749).\n\nMC 5417\n 
DTSTAMP:20250515T134619Z
END:VEVENT
BEGIN:VEVENT
UID:6825f02b8e0cd
DTSTART;TZID=America/Toronto:20240208T143000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240208T153000
URL:/pure-mathematics-geometry-topology/events/bois-sin
 gularities-rational-singularities-and-beyond
SUMMARY:Du Bois singularities\, rational singularities\, and beyond
CLASS:PUBLIC
DESCRIPTION:Summary \n\nWANCHUN ROSIE SHEN\, HARVARD UNIVERSITY\n\nWe surve
 y some extensions of the classical notions of Du Bois and\nrational singul
 arities\, known as the k-Du Bois and k-rational\nsingularities. By now\, t
 hese notions are well-understood for local\ncomplete intersections (lci). 
 We explain the difficulties beyond the\nlci case\, and propose new definit
 ions in general to make further\nprogress in the theory. This is joint wor
 k (in progress) with Matthew\nSatriano\, Sridhar Venkatesh and Anh Duc Vo.
 \n\nMC 5417\n 
DTSTAMP:20250515T134619Z
END:VEVENT
BEGIN:VEVENT
UID:6825f02b8e90f
DTSTART;TZID=America/Toronto:20240201T143000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240201T153000
URL:/pure-mathematics-geometry-topology/events/local-no
 rmal-forms-complex-bk-geometry
SUMMARY:Local normal forms in complex b^k geometry
CLASS:PUBLIC
DESCRIPTION:Summary \n\nMICHAEL FRANCIS\, WESTERN UNIVERSITY\n\nThe b-tange
 nt bundle (terminology due to Melrose) is defined so that\nits sections ar
 e smooth vector fields on the base manifold tangent\nalong a given hypersu
 rface. Complex b-manifolds\, studied by Mendoza\,\nare defined just like o
 rdinary complex manifolds\, replacing the usual\ntangent bundle by the b-t
 angent bundle. Recently\, a\nNewlander-Nirenberg theorem for b-manifolds w
 as obtained by\nFrancis-Barron\, building on Mendoza's work. This talk wil
 l discuss the\nextension of the latter result to the setting of b^k-geomet
 ry for k>1.\nThe original approach to b^k-geometry is due to Scott. A slig
 htly\ndifferent approach that allows for global holonomy phenomena not\npr
 esent in Scott's framework was introduced by Francis and\,\nindependently\
 , by Bischoff-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\n\n 
DTSTAMP:20250515T134619Z
END:VEVENT
BEGIN:VEVENT
UID:6825f02b8f105
DTSTART;TZID=America/Toronto:20240125T143000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240125T153000
URL:/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:Summary \n\nPANAGIOTIS DIMAKIS\, UNIVERSITÉ DU QUÉBEC À MONT
 RÉAL\, CIRGET\n\nSince their introduction in 2006\, the Kapustin-Witten (
 KW) equations\nhave become the subject of a number of conjectures. Given a
  knot $K$\nembedded in a closed $3$-manifold $Y$\, the most prominent conj
 ecture\npredicts that the number of solutions to the KW equations on\n$Y\\
 times\\mathbb{R}_+$ with boundary conditions determined by the\nembedding 
 and with fixed topological charge\, is a topological\ninvariant of the kno
 t. A major obstacle with this conjecture is the\ndifficulty of constructin
 g solutions satisfying these boundary\nconditions. In this talk we assume 
 $Y\\cong \\Sigma\\times\\mathbb{R}_+$\nand study solutions to the dimensio
 nally reduced KW equations with the\nrequired boundary conditions. We prov
 e that the moduli spaces are\ndiffeomorphic to certain holomorphic lagrang
 ian sub-manifolds inside\nthe moduli of Higgs bundles associated to $\\Sig
 ma$. Time permitting\,\nwe explain how one could use this result to constr
 uct knot invariants.\n\nMC 5417\n 
DTSTAMP:20250515T134619Z
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