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DTSTART:20240310T070000
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DTSTART;TZID=America/Toronto:20240731T170000
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URL:https://uwaterloo.ca/pure-mathematics/events/phd-thesis-defence-34
SUMMARY:PhD Thesis Defence
CLASS:PUBLIC
DESCRIPTION:AIDEN SUTER\, DEPARTMENT OF PURE MATHEMATICS\, UNIVERSITY OF WA
 TERLOO \n\n“Mathematical aspects of Higgs and Coulomb branches” \n\n
 3d mirror symmetry is a duality between topological twists of 3\ndimension
 al quantum field theories (QFTs) with N=4 supersymmetry. One\nof the most 
 salient features of this duality is the symplectic duality\nbetween the br
 anches of the moduli space of vacua of the full physical\ntheory know as t
 he “Higgs” and “Coulomb” branches. These\nbranches are singular hy
 perkahler varieties that are interchanged\nunder the duality. In this talk
 \, I will primarily discuss two results\nregarding these varieties:\n\nThe
  first utilises a construction due to Costello and Gaiotto allowing\none t
 o associate a vertex operator algebra (VOA) to certain boundary\ncondition
 s of these twisted QFTs and it has been conjectured that the\nassociated v
 ariety of this VOA is the Higgs branch of the theory. In\nthis talk I will
  outline a proof of this conjecture in the case of\nU(1) gauge theory acti
 ng on n>3 hypermultiplets\, building on prior\nwork of Beam and Ferrari wh
 o conjectured that the boundary VOA is the\nsimple quotient of the psl(n|n
 ) affine VOA.\n\nIn the second part of this talk I will outline a construc
 tion of a\ntilting generator for the derived category of sheaves on T*Gr(2
 \,4).\nThis space is the Coulomb branch for a certain quiver gauge theory 
 and\nthe construction is a realisation of a result due to Webster who\npro
 ved the existence of such a tilting generator. In the case of\nquiver gaug
 e theories such as this\, the Coulomb branch algebra can be\ndescribed in 
 terms of a cyldrinical KLRW algebra\, a type of\ndiagrammatic algebra. Usi
 ng these diagrammatic methods we explicitly\ndescribe the tilting generato
 r and find that it differs to those\npreviously known in the literature.\n
 \nRemote - contact Ben Webster for the Zoom link. 
DTSTAMP:20260505T000554Z
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