LMS General Meeting & LMS Lecture 2021
The lectures are aimed at a general mathematical audience. All interested, whether LMS members or not, are most welcome to attend this event.
Programme (all timings are in BST)
3.30 pm Opening of the meeting and LMS Business (open to all)
Election of the LMS Honorary Members in 2021
Announcement of the 2021 LMS Prize winners
4.00 pm LMS Lecture 2021: Emily Riehl (Johns Hopkins University)
Elements of ∞-Category Theory
Confusingly for the uninitiated, experts in weak infinite-dimensional category theory make use of different definitions of an ∞-category, and theorems in the ∞-categorical literature are often proven "analytically", in reference to the combinatorial specifications of a particular model. In this talk, we present a new point of view on the foundations of ∞-category theory, which allows us to develop the basic theory of ∞-categories --- adjunctions, limits and colimits, co/cartesian fibrations, and pointwise Kan extensions --- "synthetically" starting from axioms that describe an ∞-cosmos, the infinite-dimensional category in which ∞-categories live as objects. We demonstrate that the theorems proven in this manner are "model-independent", i.e., invariant under change of model. Moreover, there is a formal language with the feature that any statement about ∞-categories that is expressible in that language is also invariant under change of model, regardless of whether it is proven through synthetic or analytic techniques. This is joint work with Dominic Verity.
Please Register here
Graduate Student Meeting
The Programme was as follows - all timings are in BST.
13.00 Opening of Meeting
Markus Land (Copenhagen)– Infinity-categories in Algebra and Topology
Abstract: I will begin by recalling the notion of a category and their use in various aspects of mathematics. I will then indicate why categories do not capture all phenomena that one encounters in practice, and use this to give an informal picture of what an infinity category is and what sort of problems they allow to treat in an efficient way. I will make no precise definitions and rather focus on ideas and examples.
14.00 Graduate Student Talks (Breakout Rooms)
Room 1 – Algebras:
- 2.00 pm Alice Dell'Arciprete (UEA) Blocks of Ariki-Koike algebras.
- 2.15 pm Davide Morigi (UEA) A brief introduction to preprojective algebras.
- 2.30 pm Michael Rosbotham (QUB) Cohomological dimension for C*-algebras
Room 2 - Graphs:
- 2.00pm Sam Mutter (Newcastle) k-dimensional dominoes and k-rank graphs
- 2.15pm Carl-Fredrik Nyberg Brodda (UEA) Context-free Graphs in Context.
- 2.30pm Davide Leonessi (Oxford) Transfinite Game Values in Infinite Games
Room 3 – Polytopes/Groups:
- 2.00pm Monika Kudlinska (Oxford) Fibering of 3-manifolds and free-by-cyclic groups via polytopes
- 2.15pm Aura-Cristiana Radu (Newcastle) The extensions between simple modules for the Ree groups of type F4
- 2.30pm Nicholas Williams (Leicester) The higher Stasheff-Tamari orders on triangulations of cyclic polytopes
Room 4 - Number Theory / Algebraic Geometry:
- 2.00pm Pedro-Jose Carzola Garcia (Manchester) What's left after Fermat's Last Theorem?
- 2.15pm Tarun Dalal (Indian Institute of Technology, Hyderabad) The structure of Drinfeld modular forms of level $\Gamma_0(T)$ and applications.
- 2.30pm Andrew Pearce-Crump (York) A Discrete Mean-Value Theorem for the Higher Derivatives of the Riemann Zeta Function.
- 2.45pm Abhiram Natarajan (University of Colorado-Boulder) Topological Questions in Random Real Algebraic Geometry
Prizes were awarded.
15.10 Introductions to the Early Career Research Committee and its work.
15.20 Break out rooms to discuss the LMS activities for Early Career Researchers.
15.45 Break out rooms close and all return to the main room. Questions from the floor.
16.00 Meeting ends and thanks.