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**Discrete Geometry and Combinatorics Seminar**- Previous Discrete Geometry and Combinatorics Seminars
- Discrete Geometry and Combinatorics Seminar Summer 2015
- Discrete Geometry and Combinatorics Seminar Spring 2015
- Discrete Geometry and Combinatorics Seminar Autumn 2014
- Discrete Geometry and Combinatorics Seminar Summer 2014
- Discrete Geometry and Combinatorics Seminar Spring 2014
- Discrete Geometry and Combinatorics Seminar Autumn 2013
- Discrete Geometry and Combinatorics Seminar Spring 2013
- Discrete Geometry and Combinatorics Seminar Autumn 2012
- Discrete Geometry and Combinatorics Seminar Spring 2012
- Discrete Geometry and Combinatorics Seminar Autumn 2011
- Discrete Geometry and Combinatorics Seminar Spring 2011
- Discrete Geometry and Combinatorics Seminar Autumn 2010
- Discrete Geometry and Combinatorics Seminar Spring 2010
- Discrete Geometry and Combinatorics Seminar Autumn 2009
- Discrete Geometry and Combinatorics Seminar Spring 2009

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*EPSRC award offers new PhD opportunities in pure mathematics* - PhD Open Afternoon, Wednesday 2 December 2015 - Registration
- Helen Wilson and Adam Townsend publish a paper on 'The Physics of Chocolate Fountains'

## Discrete Geometry and Combinatorics Seminar

### Autumn 2015

All seminars (unless otherwise stated) will take place on **Tuesdays at 5.00pm in Room 707 in the Mathematics Department **(25 Gordon Street). There will be tea afterwards in Room 606 in the
Mathematics Department (25 Gordon Street) - see how to find us for further details. If
you require any more information on the Discrete Geometry and Combinatorics seminars please
contact Dr John Talbot e-mail: j.talbot AT ucl.ac.uk or
tel:
020-7679-4102.

### 20 October 2015

#### Jan Foniok, Manchester Metropolitan University

###### Title: Hedetniemi's graph-colouring conjecture and adjoint functors

Abstract:

Hedetniemi's conjecture links
the chromatic number of the product of two graphs to the chromatic numbers of
the two factors: namely, that \chi(G \times H) = \min\{\chi(G),\chi(H)\}.

Simple to formulate, yet the conjecture seems hard to solve, having been open for almost 50 years now. I will present an approach using adjunction in the categories of graphs or digraphs and homomorphisms (but no prior knowledge of category theory is assumed). My objective is mainly to stimulate interest in the topic that may lead to new, productive ideas.

### 3 November 2015

#### Ewan Davies, LSE

###### Title: Independent Sets, Matchings, and Occupancy Fractions

Abstract:

We use a new
technique to prove a strengthening of Jeff Kahn's theorem that disjoint unions
of K_{d,d}'s maximise the number of independent sets in a bipartite d-regular
graph. In probabilistic language, we show that for bipartite d-regular graphs
and all λ, the occupancy fraction of the hard-core model with fugacity λ is
maximised by K_{d,d}. The method can be extended to non-bipartite graphs,
applied to matchings where the analogue of Kahn's result was not previously
known, and used to provide lower bounds. For this talk the focus is on the
background and the key idea: defining and solving an optimisation problem over
distributions of local random variables that use the model directly.

### 17 November 2015

#### Laszlo Vegh, LSE

###### Title: A strong polynomial algorithm for generalised flow maximisation

Abstract:

TBC

### 24 November 2015

#### David Ellis, QMUL

###### Title: Stability results for some geometric inequalities, via entropy

Abstract:

TBC

### 8 December 2015

#### Prof Peter Keevash University of Oxford

###### Title: TBC

Abstract:

TBC

Previous discrete geometry and combinatorics seminars

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