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A striking example of dimensional reduction established by Brydges and Imbrie is an exact relation between the hard sphere gas in $d$ dimensions and branched polymers in $d+2$ dimensions. I will introduce this topic and discuss a new proof, which also establishes dimensional reduction formulas for generalized models of polymers associated to central hyperplane arrangements. The new proof is essentially combinatorial, in contrast to the original proof which uses supersymmetry.

Note change in room.