Jennifer Hyndman and JB Nation have worked together for over 20 years on questions involving lattices and quasivarieties. Dr. Nation is Professor Emeritus at the University of Hawaii where he worked from 1979 to 2014 in the Department of Mathematics. He has over 100 publications. Dr. Hyndman is Professor in the Department of Mathematics and Statistics at the University of Northern British Columbia. She joined as Founding Faculty Member in 1994 and has won several mentorship and teaching awards. Together they coauthored Lattices of Subquasivarieties of Locally Finite Quasivarieties of Finite Type in 2018. Then in 2022 with K. Adaricheva and J. Nishida, they published A Primer of Subquasivariety Lattices.

• Overview and background.- A glossary of subsemilattice representations.- Examples of longstyle representations.- Necessary conditions for a longstyle representation.- Direct products and gluing.- Finite distributive lattices.- Strong shortstyle representations.- Covers of the pentagon.- Some open questions.

Jennifer Hyndman and JB Nation have worked together for over 20 years on questions involving lattices and quasivarieties. Dr. Nation is Professor Emeritus at the University of Hawaii where he worked from 1979 to 2014 in the Department of Mathematics. He has over 100 publications. Dr. Hyndman is Professor in the Department of Mathematics and Statistics at the University of Northern British Columbia. She joined as Founding Faculty Member in 1994 and has won several mentorship and teaching awards. Together they coauthored Lattices of Subquasivarieties of Locally Finite Quasivarieties of Finite Type in 2018. Then in 2022 with K. Adaricheva and J. Nishida, they published A Primer of Subquasivariety Lattices.

• Overview and background.- A glossary of subsemilattice representations.- Examples of longstyle representations.- Necessary conditions for a longstyle representation.- Direct products and gluing.- Finite distributive lattices.- Strong shortstyle representations.- Covers of the pentagon.- Some open questions.

Jennifer Hyndman and JB Nation have worked together for over 20 years on questions involving lattices and quasivarieties. Dr. Nation is Professor Emeritus at the University of Hawaii where he worked from 1979 to 2014 in the Department of Mathematics. He has over 100 publications. Dr. Hyndman is Professor in the Department of Mathematics and Statistics at the University of Northern British Columbia. She joined as Founding Faculty Member in 1994 and has won several mentorship and teaching awards. Together they coauthored Lattices of Subquasivarieties of Locally Finite Quasivarieties of Finite Type in 2018. Then in 2022 with K. Adaricheva and J. Nishida, they published A Primer of Subquasivariety Lattices.

• Overview and background.- A glossary of subsemilattice representations.- Examples of longstyle representations.- Necessary conditions for a longstyle representation.- Direct products and gluing.- Finite distributive lattices.- Strong shortstyle representations.- Covers of the pentagon.- Some open questions.