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DTSTART;TZID=America/Toronto:20250428T113000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-gr
 aph-theory-sidhanth-mohanty
SUMMARY:Algebraic Graph Theory-Sidhanth Mohanty
CLASS:PUBLIC
DESCRIPTION:TITLE: Explicit Lossless Vertex Expanders\n\nSPEAKER:\n\nSidha
 nth Mohanty\n\nAFFILIATION:\n\nMassachusetts Institute of Technology\n\nLO
 CATION:\n Please contact Sabrina Lato for Zoom link.\n\nABSTRACT: We giv
 e the first construction of explicit constant-degree\nlossless vertex expa
 nders. Specifically\, for any ε>0 and sufficiently\nlarge d\, we give an 
 explicit construction of an infinite family of\nd-regular graphs where eve
 ry small set S of vertices has (1−ε)d|S|\nneighbors (which implies (1
 −2ε)d|S| unique-neighbors). Our results\nalso extend naturally to const
 ruct biregular bipartite graphs of any\nconstant imbalance\, where small s
 ets on each side have strong\nexpansion guarantees. The graphs we construc
 t admit a free group\naction\, and hence realize new families of quantum L
 DPC codes of Lin\nand M. Hsieh with a linear time decoding algorithm.\n\nO
 ur construction is based on taking an appropriate product of a\nconstant-s
 ized lossless expander with a base graph constructed from\nRamanujan Cayle
 y cubical complexes.\n\nBased on joint work with Jun-Ting Hsieh\, Alexande
 r Lubotzky\, Assaf\nReiner\, and Rachel Yun Zhang (https://arxiv.org/abs/2
 504.15087)
DTSTAMP:20260402T143451Z
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