Let L be a lattice in R^n and let Z in R^(m+n) a parameterized family of subsets Z_T of R^n. Starting from an old result of Davenport and using O-minimal structures, together with Martin Widmer, we proved for fairly general families Z an estimate for the number of points of L in Z_T, which is essentially best possible. 
After introducing the problem and stating the result, we will present applications to counting algebraic integers of bounded height and to Manin’s Conjecture.

For a nonlinear elliptic system coming from a nonlinear Schroedinger system, the interaction between components is represented by a symmetric matrix. The construction of possibly lower energy nontrivial solutions and the complete description of dependence of the solutions on the matrix are quite challenging tasks. Especially, we are interested in the case that intra-species interaction forces are fixed and inter-species forces are very large, that is, the diagonal part of the symmetric matric is fixed and the non-diagonal entries are very large. In this case, depending on the network between components by repulsive or attractive forces, several different types of patterns may appear. I would like to explain our recent studies on the problem with three components and touch a possible exploration on the general n-components problem.

Online discussions are the essence of many social platforms on the Internet. Discussion platforms are receiving increasing interest because of their potential to become deliberative spaces. Although previous studies have proposed approaches to measure online deliberation using the complexity of discussion networks as a proxy, little research has focused on how these networks are affected by changes of platform features.

In this talk, we will focus on how interfaces might influence the network structures of discussions using techniques like interrupted time series analysis and regression discontinuity design. Futhermore, we will review and extend state-of-the-art generative models of discussion threads to explain better the structure and growth of online discussions.
 

Starting from the seminal paper of Caporaso-Harris-Mazur, it has been proved that if Lang's Conjecture holds in arbitrary dimension, then it implies a uniform bound for the number of rational points in a curve of general type and analogue results in higher dimensions. In joint work with Kenny Ascher we prove analogue statements for integral points (or more specifically stably-integral points) on curves of log general type and we extend these to higher dimensions. The techniques rely on very recent developments in the theory of moduli spaces for stable pairs, a higher dimensional analogue of pointed stable curves.
If time permits we will discuss how very interesting problems arise in dimension 2 that are related to the geometry of the log-cotangent bundle.

Following Grothendieck's vision that many cohomological invariants of of an algebraic variety should be captured by a common motive, Voevodsky introduced a triangulated category of mixed motives which partially realises this idea. After describing this category, I will explain how to define the motive of certain algebraic stacks in this context. I will then report on joint work in progress with Victoria Hoskins, in which we study the motive of the moduli stack of vector bundles on a smooth projective curve and show that this motive can be described in terms of the motive of this curve and its symmetric powers.
 

Assortative mixing in networks is the tendency for nodes with the same attributes, or metadata, to link to each other. It is a property often found in social networks manifesting as a higher tendency of links occurring between people with the same age, race, or political belief. Quantifying the level of assortativity or disassortativity (the preference of linking to nodes with different attributes) can shed light on the factors involved in the formation of links and contagion processes in complex networks. It is common practice to measure the level of assortativity according to the assortativity coefficient, or modularity in the case of discrete-valued metadata. This global value is the average level of assortativity across the network and may not be a representative statistic when mixing patterns are heterogeneous. For example, a social network spanning the globe may exhibit local differences in mixing patterns as a consequence of differences in cultural norms. Here, we introduce an approach to localise this global measure so that we can describe the assortativity, across multiple scales, at the node level. Consequently we are able to capture and qualitatively evaluate the distribution of mixing patterns in the network. We find that for many real-world networks the distribution of assortativity is skewed, overdispersed and multimodal. Our method provides a clearer lens through which we can more closely examine mixing patterns in networks.

Link to arxiv paper:  https://arxiv.org/abs/1708.01236

The BSHM meeting on “The history of computing beyond the computer” looks at the people and the science underpinning modern software and programming, from Charles Babbage’s design notation to forgotten female pioneers.

Registration will be £32.50 for standard tickets, £22.00 for BSHM members and Oxford University staff, and £6.50 for students. This will include tea/coffee and biscuits at break times, but not lunch, as we wanted to keep the registration fee to a minimum. A sandwich lunch or a vegetarian sandwich lunch can be ordered separately on the Eventbrite page. If you have other dietary requirements, please use the contact button at the bottom of this page. There is also a café in the Mathematical Institute that sells hot food at lunchtime, alongside sandwiches and snacks, and there are numerous places to eat within easy walking distance.

https://www.eventbrite.co.uk/e/the-history-of-computing-beyond-the-comp…

Programme

21 March 2018

17:00 Andrew Hodges, University of Oxford, author of "Alan Turing: The Enigma” on 'Alan Turing: soft machine in a hard world.’
http://www.turing.org.uk/index.html

22 March 2018

9:00 Registration

9:30 Adrian Johnstone, Royal Holloway University of London, on Charles Babbage's design notation
http://blog.plan28.org/2014/11/babbages-language-of-thought.html

10:15 Reinhard Siegmund-Schultze, Universitetet i Agder, on early numerical methods in the analysis of the Northern Lights
https://www.uia.no/kk/profil/reinhars

11:00 Tea/Coffee

11:30 Julianne Nyhan, University College London, on Father Busa and humanities data
https://archelogos.hypotheses.org/135

12:15 Cliff Jones, University of Newcastle, on the history of programming language semantics
http://homepages.cs.ncl.ac.uk/cliff.jones/

13:00 Lunch

14:00 Mark Priestley, author of "ENIAC in Action, Making and Remaking the Modern Computer"
http://www.markpriestley.net

14:45 Marie Hicks, University of Wisconsin-Madison, author of "Programmed Inequality: How Britain Discarded Women Technologists and Lost Its Edge In Computing"
http://mariehicks.net

15:30 Tea/Coffee

16:00 Panel discussion to include Martin Campbell-Kelly (Warwick), Andrew Herbert (TNMOC), and Ursula Martin (Oxford)

17:00 End of conference

Co-located event

23 March, in Mathematical Institute, University of Oxford, Symposium for the History and Philosophy of Programming, HaPoP 2018, Call for extended abstracts
http://www.hapoc.org/node/241

Andrew Hodges, University of Oxford, author of "Alan Turing: The Enigma” on 'Alan Turing: soft machine in a hard world.’

http://www.turing.org.uk/index.html

This event is free but you need to register:

https://www.eventbrite.co.uk/e/the-history-of-computing-beyond-the-comp… 2018