This seminar has now finished.
The Lunch Seminar is a weekly seminar organised to encourage discussion between first year LSGNT students and potential supervisors from UCL, KCL, and Imperial. Each week there are going to be two talks (one from a geometer and one from a number theorist), in which each speaker will discuss their research and potential projects. We encourage students to ask questions and discuss ideas between and after the talks.
The seminar will take place in person on Tuesday 12-2pm. The first two weeks will be online, and after that in King's room S4.29, Strand building. Food will be provided.
For questions please contact one of the organisers: Jamie Bell (james.bell.20@ucl.ac.uk) and Sara Veneziale (s.veneziale21@imperial.ac.uk).
Taut foliations of 3-manifolds
Abstract. A foliation of a 3-dimensional manifold is a decomposition of it into disjoint surfaces that locally fit together like a stack of papers. Examples of singular foliations in one dimension lower are marbleised papers and tree rings. A particular class of foliations, called taut, has been instrumental in resolving several major problems in low-dimensional topology. I will explain what taut foliations are and discuss some of the open questions in the area.
Teaching modern mathematics to computers
Abstract. A computer proof checker is a computer program which knows the axioms of mathematics and is capable of checking that a mathematical proof is complete and correct. However most mathematicians operate at a level way "above" the axioms of mathematics and do not want to spend their time changing one line of maths in a pdf to 100 lines of axiom applications. I am an algebraic number theorist and over the past few years I've been investigating whether it is possible in practice to use a modern computer proof checker to check modern number theory. Turns out that it is. I will talk about a case study (recent work of Clausen and Scholze, formalised in the Lean theorem prover) and, more importantly, I will also talk about why this is important and what the future might hold as computers begin to learn more about modern mathematics.