Geometry Seminar

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Polycubes with small perimeter defect

Speaker: Gill Barequet, Technion, Haifa

Location: Online On Zoom only

Date: Tuesday, November 3, 2026, 2 p.m.

Synopsis:

Lattice animals are finite connected sets of cells on a lattice.  For example, polyominoes are connected sets of cells on the planar square lattice, where connectivity is defined by shared sides.

Similarly, \(d\)-dimensional polycubes are connected sets of cubes on the \(d\)-dimensional cubical lattice, where connectivity is defined by shared \((d-1)\)-dimensional faces.

One of the main problems in this area is to find formulae for the number of animals with a specified number of cells.

The perimeter of a lattice animal is the number of empty lattice cells that are adjacent to the animal.

In this talk, I will explore methods for obtaining formulae for the number of animals on the \(d\)-dimensional cubical lattice, whose perimeter deviates from the maximum possible value by a fixed constant.

Notes:

Only on Zoom.  Please contact Boris Aronov to be put on the email announcement list and obtain Zoom details.