Springer theory is an important branch of geometric representation theory. It is a beautiful interplay between combinatorics, geometry and representation theory.
It started with Springer correspondence, which yields geometric construction of irreducible representations of symmetric groups, and Ginzburg's construction of universal enveloping algebra U(sl_n).

Here I will present a view of two-row Springer theory of type A (thus looking at nilpotent elements with two Jordan blocks) from a scope of a symplectic topologist (hence the title), that yields connections between symplectic-topological invariants and link invariants (Floer homology and Khovanov homology) and connections to representation theory (Fukaya category and parabolic category O), thus summarising results by Abouzaid,
Seidel, Smith and Mak on the subject.

I will present Pila's Modular Zilber-Pink with Derivatives (MZPD) conjecture, which is a Zilber-Pink type statement for the j-function and its derivatives, and discuss some weak and functional/differential analogues. In particular, I will define special varieties in each setting and explain the relationship between them. I will then show how one can prove the aforementioned weak/functional/differential MZPD statements using the Ax-Schanuel theorem for the j-function and its derivatives and some basic complex analytic geometry. Note that I gave a similar talk in Oxford last year (where I discussed a differential MZPD conjecture and proved it assuming an Existential Closedness conjecture for j), but this talk is going to be significantly different from that one (the approach presented in this talk will be mostly complex analytic rather than differential algebraic, and the results will be unconditional).

Would you like to meet some of your fellow students, and some graduate students and postdocs, in an informal and relaxed atmosphere, while building your communication skills?  In this Friday@2 session, you'll be able to play a selection of board games, meet new people, and practise working together.  What better way to spend the final Friday afternoon of term?!  We'll play the games in the south Mezzanine area of the Andrew Wiles Building, outside L3.

This session is particularly aimed at fourth-year and OMMS students who are completing a dissertation this year. The talk will be given by Dr Richard Earl who chairs Projects Committee. For many of you this will be the first time you have written such an extended piece on mathematics. The talk will include advice on planning a timetable, managing the  workload, presenting mathematics, structuring the dissertation and creating a narrative, providing references and avoiding plagiarism.

Outbreaks and epidemics from Ebola to influenza and measles are often in the news. Statistical analysis and modelling are frequently used to understand the transmission dynamics of epidemics as well as to inform and evaluate control measures, with real-time analysis being the most challenging but potentially most impactful. Examples will be drawn from diseases affecting both humans and animals.