# Fall 2017 Seminars

**Time:** Monday, October 23. (SC 1312, 4:10 p.m.)

**Speaker: **Andrew Moorhead

**Title: **Abelianness in Universal Algebra I

**Time:** Monday, October 30. (SC 1312, 4:10 p.m.)

**Speaker: **Andrew Moorhead

**Title: **Abelianness in Universal Algebra II

**Time:** Monday, November 6. (SC 1312, 4:10 p.m.)

**Speaker: **Andrew Moorhead

**Title: **Abelianness in Universal Algebra III

**Time:** Monday, November 13. (SC 1312, 4:10 p.m.)

**Speaker: **Andrew Moorhead

**Title: **Abelianness in Universal Algebra IV

**Time:** Tuesday, November 28. (SC TBA, 4:10 p.m.)

**Speaker: **Stephen G. Simpson

**Title: **Linear Lattices

**Abstract: **Let Eq(X) denote the lattice of all equivalence relations on a fixed set X. Let o denote relational composition. Two equivalence relations e1 and e2 on X are said to commute if e1 o e2 = e2 o e1. By a linear lattice we mean a sublattice of Eq(X) consisting of commuting equivalence relations. A standard example of a linear lattice is a projective geometry, i.e., the lattice of finite dimensional subspaces of a fixed vector space X. Linear lattices have been studied for well over a century. Some of the names here are Dedekind, Birkhoff, Malcev, Jónsson, Rota, Haiman, and Yan. We discuss some of this history, and we present a new result and a current research problem.

**Time:** Monday, December 4. (SC 1312, 4:10 p.m.)

**Speaker: **Stephen G. Simpson

**Title: **Linear Lattices II

**Abstract: **Let Eq(X) denote the lattice of all equivalence relations on a fixed set X. Let o denote relational composition. Two equivalence relations e1 and e2 on X are said to commute if e1 o e2 = e2 o e1. By a linear lattice we mean a sublattice of Eq(X) consisting of commuting equivalence relations. A standard example of a linear lattice is a projective geometry, i.e., the lattice of finite dimensional subspaces of a fixed vector space X. Linear lattices have been studied for well over a century. Some of the names here are Dedekind, Birkhoff, Malcev, Jónsson, Rota, Haiman, and Yan. We discuss some of this history, and we present a new result and a current research problem.

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