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DTSTART:20240310T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20240731T170000
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URL:https://uwaterloo.ca/pure-mathematics/events/phd-thesis
SUMMARY:PhD Thesis
CLASS:PUBLIC
DESCRIPTION:AIDEN SUTER\n\nMathematical aspects of Higgs and Coulomb branch
 es\n\n3d mirror symmetry is a duality between topological twists of 3\ndim
 ensional quantum field theories (QFTs) with N=4 supersymmetry. One\nof the
  most salient features of this duality is the symplectic duality\nbetween 
 the branches of the moduli space of vacua of the full physical\ntheory kno
 w as the “Higgs” and “Coulomb” branches. These\nbranches are singu
 lar hyperkahler varieties that are interchanged\nunder the duality. In thi
 s talk\, I will primarily discuss two results\nregarding these varieties:\
 n\nThe first utilises a construction due to Costello and Gaiotto allowing\
 none to associate a vertex operator algebra (VOA) to certain boundary\ncon
 ditions of these twisted QFTs and it has been conjectured that the\nassoci
 ated variety 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 theor
 y acting on n>3 hypermultiplets\, building on prior\nwork of Beam and Ferr
 ari who conjectured that the boundary VOA is the\nsimple quotient of the p
 sl(n|n) affine VOA.\n\nIn the second part of this talk I will outline a co
 nstruction 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 t
 heory and\nthe construction is a realisation of a result due to Webster wh
 o\nproved the existence of such a tilting generator. In the case of\nquive
 r gauge theories such as this\, the Coulomb branch algebra can be\ndescrib
 ed in terms of a cyldrinical KLRW algebra\, a type of\ndiagrammatic algebr
 a. Using these diagrammatic methods we explicitly\ndescribe the tilting ge
 nerator and find that it differs to those\npreviously known in the literat
 ure.\n\nJoin online at: https://pitp.zoom.us/j/97622507197
DTSTAMP:20260506T034010Z
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