The study of knots is an important field within topology. For example, one can use knots to draw blueprints for 4-dimensional manifolds. Hence understanding particular properties of knots (and collections of knots called links) allows us to better understand 4-dimensional objects. During the summer, students will: explore a particular geometric property of knots called sliceness; learn how linear algebra (in the form of lattices) can be used as a tool to understand this geometric property; and see how slice knots can be used to construct special 4-dimensional manifolds called rational homology 4-balls. Throughout the summer, students will also work on an original project related to these ideas.