# Hodge Club

The Hodge Club is the seminar for Hodge Institute graduate students and postdocs. That means we're interested in Algebra, Geometry, Topology, Number Theory, and all possible combinations and derivations of the four. Before the 2016/17 academic year, the Hodge Club was known as the Geometry Club.

We meet every Friday at 1:45pm in JCMB 4312 where we take it in turn to present a topic of interest to the rest of the group. Talks tend to be fairly informal and provide excellent practice for conference talks in front of a friendly audience. You can find our current schedule and a historical list of talks below.

Future events are circulated on our mailing list and advertised on the Graduate School calendar. See instructions below on how to join our mailing list.

The Hodge Club is organised by Ruth Reynolds and Matt Booth.

### Current schedule of talks for 2017/18:

##### Semester 1
 October 6, 1:45pm Matt Booth DGAs and A-infinity algebras Abstract: A differential graded algebra (dga) over a ring R is a chain complex of R-modules equipped with a multiplication. Examples include the tensor algebra or the endomorphism algebra of a dg-R-module, the de Rham complex of a smooth manifold, and any graded R-algebra. Over a field of characteristic 0, commutative dgas are the affine derived schemes. Unfortunately, dgas can behave badly with respect to homotopy: if R is a field, any chain complex C is quasi-isomorphic to its homology HC, and if C is a dga then so is HC, but they will generally not be quasi-isomorphic as dgas. A-infinity algebras extend dgas by providing a notion of 'dgas up to homotopy', and have better behaviour. In particular, Kadeishvili's Theorem says that if A is an A-infinity algebra, then HA admits an A-infinity algebra structure such that the natural map from A to HA is an A-infinity quasi-isomorphism. October 13, 1:45pm Graham Manuell Is the closed interval compact? Abstract: The closed real interval is one of the most familiar examples of a compact topological space. However, there are systems of mathematics in which it isn't compact at all. In particular, compactness fails in situations where every function is Turing-computable. We will explore the conditions under which compactness holds and fails to hold and consider a way to salvage compactness in the bad case. October 20, 1:45pm Carlos Zapata-Carratala Generalisations of Symplectic Geometry and Symplectic Reduction Abstract: In this talk I will present a collection of geometric structures that generalise symplectic structures (classical phase spaces) and we will discuss the notion of morphisms and reductions between them. The material will be presented from an introductory level and we will cover popular topics like Lie Algebroids, Poisson manifolds and discussions around the symplectic "category". October 27, 1:45pm Ruth Reynolds TBA Abstract: November 3, 1:45pm Jenny August TBA Abstract: November 10, 1:45pm Juliet Cooke TBA Abstract: November 17, 1:45pm Simon Crawford TBA Abstract: November 24, 1:45pm Fatemeh Rezazee TBA Abstract:

### Historical schedules

Hodge Club 2016/17
Geometry club 2015/16
Geometry club 2014/15
Geometry club 2013/14
Geometry club 2012/13
You can also visit the old Geometry club website for more historical schedules

### Mailing list

Announcements are handled by the mailing list hodgeclub. To subscribe, send a message to sympa at mlist.is.ed.ac.uk with the following content:

SUBSCRIBE hodgeclub
QUIT