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DTSTART;TZID=America/New_York:20260417T120000
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DTSTAMP:20260417T225230
CREATED:20260409T170535Z
LAST-MODIFIED:20260409T170535Z
UID:10003134-1776427200-1776430800@www.math.harvard.edu
SUMMARY:Higgs and Coulomb branches: Geometry and Representation Theory
DESCRIPTION:Higgs and Coulomb branches of quiver gauge theories form two important families of Poisson varieties that are expected to be exchanged under so-called 3D mirror symmetry. Quantized Coulomb branches are associative algebras deforming the algebras of functions on Coulomb branches. They are closely related to many important representation-theoretic structures\, such as Yangians\, quantum groups\, and Hecke algebras. In this talk\, I will discuss how 3D mirror symmetry\, together with other insights motivated by physics\, yields very explicit answers to purely representation-theoretic questions about representations of some of these quantum groups. Talk is based on joint works with Dinkins\, Karpov\, Klyuev\, and Lance. \n 
URL:https://www.math.harvard.edu/event/higgs-and-coulomb-branches-geometry-and-representation-theory/
LOCATION:CMSA\, 20 Garden St\, Common Room\, 20 Garden Street\, Cambridge\, 02138\, United States
CATEGORIES:CMSA MEMBER SEMINAR
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DTSTART;TZID=UTC:20260417T141500
DTEND;TZID=UTC:20260417T163000
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CREATED:20260409T132335Z
LAST-MODIFIED:20260409T132400Z
UID:10003132-1776435300-1776443400@www.math.harvard.edu
SUMMARY:How to Pick Out the Slicing Degree of Knots Using a Spork
DESCRIPTION:The slicing degree of a knot K is the smallest integer k such that K is k-slice (i.e.\, bounds a disk with self-intersection number –k) in #n(-CP)^2 for some n. In this talk\, we establish bounds on the slicing degrees of knots using Rasmussen’s s-invariant\, knot Floer homology\, and singular instanton homology. \nWe also introduce sporks\, defined as pairs (W\, f) consisting of a contractible 4-manifold W and a boundary diffeomorphism f that extends smoothly inside. Sporks appear naturally in certain k-RBG links and produce knots with the same k-trace; although too blunt to produce exotic smooth structures\, they are effective in detecting slicing degree in the examples we consider. \n 
URL:https://www.math.harvard.edu/event/how-to-pick-out-the-slicing-degree-of-knots-using-a-spork/
LOCATION:Science Center 507\, 1 Oxford Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:GAUGE THEORY AND TOPOLOGY
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