Topological quantum field theories (TQFTs) are an extensively studied scheme for constructing invariants of manifolds, inspired by physics. In this talk, we will discuss a particular flavour of TQFT, where we equip our manifolds with principal bundles for some finite group. After introducing TQFTs and this particular flavour, I will discuss games one can play with these TQFTs, and a possible strategy for classifying equivariant TQFTs in three dimensions. 

A cohomology class on the diffeomorphism group Diff(M) of a manifold M

can be thought of as a characteristic class for smooth M-bundles.
I will survey a technique for producing examples of such classes,
and then explain how the signature (of 4-manifolds) provides an
obstruction to this technique in dimension 3.

I will define Miller-Morita-Mumford classes and explain how we can
think of them as coming from classes on the cobordism category.
Madsen and Weiss showed that for a surface S of genus g all cohomology
classes
of the mapping class group MCG(S) (of degree < 2(g-2)/3) are MMM-classes.
This technique has been successfully ported to higher even dimensions d= 2n,
but it cannot possibly work in odd dimensions:
a theorem of Ebert says that for d=3 all MMM-classes are trivial.
In the second part of my talk I will sketch a new proof of (a part of)
Ebert's theorem.
I first recall the definition of the signature sign(W) of a 4 manifold W,
and some of its properties, such as additivity with respect to gluing.
Using the signature and an idea from the world of 1-2-3-TQFTs,
I then go on to define a 'central extension' of the three dimensional
cobordism category.
This central extension corresponds to a 2-cocycle on the 3d cobordism
category,
and we will see that the construction implies that the associated MMM-class
has to vanish on all 3-dimensional manifold bundles.

Commuting concerns people’s spatial behaviour resulting from the geographic separation of home and workplace and is connected with their willingness to seek economic opportunities outside their place of residence (Rouwendal J., Nijkamp P., 2004). Such opportunities are usually found in the urban areas, so this phenomenon is often a subject of urban studies or research focusing on city centres (Drejerska N., Chrzanowska M., 2014). In literature, commuting patterns are used to determine the boundaries of local and regional labour markets. Furthermore, labour market is one of the most important features for the delimitation of functional regions, as commuting involves not only working outside one’s place of residence but also, among other things, using various services offered there, from shopping to health or cultural services. Taking this into account, it can be stated that commuting is an important characteristic of relations between territories, and these relations form complex networks.

People decide to commute to work for various reasons. Most commuters travel from a small town, village or rural area to a city or town where they have a wider range of employment opportunities. However, people differ in their attitudes toward commuting. While some people find it troublesome, others enjoy their daily travel. There are also people who regard commuting as the necessary condition for supporting themselves and their families. Therefore, commuting is an important factor that should be taken into account in the research on the quality of life and quality of work.

The main goals of this presentation is to identify and analyse relations between communities (municipalities) from the perspective of labour market, especially commuting in the vicinity of Warsaw, Data on the number of commuters come from the Central Statistical Office of Poland and cover the year 2011.

 Bibliography

Drejerska N., Chrzanowska M., 2014: Commuting in the Warsaw suburban area from a spatial perspective – an example of empirical research, Acta Universitatis Lodziensis. Folia Oeconomica 2014, Vol. 6, no 309, pp. 87-96.

Rouwendal J., Nijkamp P., 2004: Living in Two Worlds: A Review of Home-to-Work Decisions, Growth and Change, Volume 35, Issue 3, p. 287.

One of the key unsolved challenges at the interface of physical and life sciences is to formulate comprehensive computational modeling of cells of higher organisms that is based on microscopic molecular principles of chemistry and physics. Towards addressing this problem, we have developed a unique reactive mechanochemical force-field and software, called MEDYAN (Mechanochemical Dynamics of Active Networks: http://medyan.org).  MEDYAN integrates dynamics of multiple mutually interacting phases: 1) a spatially resolved solution phase is treated using a reaction-diffusion master equation; 2) a polymeric gel phase is both chemically reactive and also undergoes complex mechanical deformations; 3) flexible membrane boundaries interact mechanically and chemically with both solution and gel phases.  In this talk, I will first outline our recent progress in simulating multi-micron scale cytosolic/cytoskeletal dynamics at 1000 seconds timescale, and also highlight the outstanding challenges in bringing about the capability for routine molecular modeling of eukaryotic cells. I will also report on MEDYAN’s applications, in particular, on developing a theory of contractility of actomyosin networks and also characterizing dissipation in cytoskeletal dynamics. With regard to the latter, we devised a new algorithm for quantifying dissipation in cytoskeletal dynamics, finding that simulation trajectories of entropy production provide deep insights into structural evolution and self-organization of actin networks, uncovering earthquake-like processes of gradual stress accumulation followed by sudden rupture and subsequent network remodeling.
 

Abstract:  As is well known, every rational representation of a finite group $G$ can be realized over $\mathbb{Z}$, that is, the corresponding $\mathbb{Q}G$-module $V$ admits a $\mathbb{Z}$-form. Although $\mathbb{Z}$-forms are usually far from being unique, the famous Jordan--Zassenhaus Theorem shows that there are only finitely many $\mathbb{Z}$-forms of any given $\mathbb{Q}G$-module, up to isomorphism. Determining the precise number of these isomorphism classes or even explicit representatives is, however, a hard task in general. In this talk we shall be concerned with the case where $G$ is the symmetric group $\mathfrak{S}_n$ and $V$ is a simple $\mathbb{Q}\mathfrak{S}_n$-module labelled by a hook partition. Building on work of Plesken and Craig we shall present some results as well as open problems concerning the construction of the
integral forms of these modules. This is joint work with Tommy Hofmann from Kaiserslautern.

Deformation quantization modules or DQ-modules where introduced by M. Kontsevich to study the deformation quantization of complex Poisson varieties. It has been advocated that categories of DQ-modules should provide invariants of complex symplectic varieties and in particular a sort of complex analog of the Fukaya category. Hence, it is natural to aim at describing the functors between such categories and relate them with categories appearing naturally in algebraic geometry. Relying, on methods of homotopical algebra, we obtain an analog of Orlov representation theorem for functors between categories of DQ-modules and relate these categories to deformations of the category of quasi-coherent sheaves.
 

This meeting is being held in celebration of Prof Philip Maini's 60th birthday. Prof Maini has been an internationally leading researcher in mathematical biology for decades. He is currently the Director of the Wolfson Centre for Mathematical Biology, a position he has held since 1998. In the past 20 years he has grown the group significantly. He has established countless interdisciplinary collaborations, has over 400 publications in numerous areas of mathematical biology, with major contributions in mathematical modelling of tumours, wound healing and embryonic pattern formation. He has been elected Fellow of the Royal Society (FRS), Fellow of the Academy of Medical Sciences (FMedSci), and Foreign Fellow of the Indian National Science Academy (FNA). He has served or is serving on editorial board of a large number of journals, and was Editor-in-Chief of the Bulletin of Mathematical Biology [2002-15]. And yet his service to the community cannot be captured just by numbers and titles. Anyone who has met him and worked with him cannot but notice and be touched by his unfailing generosity and the many sacrifices he has made and continues to make day in and day out to help students, early career researchers, and fellow faculty alike.

This meeting provides an opportunity to celebrate Prof Maini's many accomplishments; to thank him for all of his sacrifices; and to bring together the large number of researchers – mathematicians, biologists, physiologists, and clinicians – that he has worked with and interacted with over the years. More broadly, the meeting provides a unique opportunity to reflect on mathematical biology, to provide perspectives on the trajectory of a field that was scarcely recognised and had very few dedicated researchers in the days of Prof Maini's own DPhil; yet a field that has grown tremendously since then. Much of this growth is attributable to the work of Prof Maini, so that today the value of mathematics in biology is increasingly recognized by biologists and clinicians, and with theoretical predictions of mathematical models having cemented a role in advancing biological understanding. 

Speakers

David Sumpter, Uppsala University (Public lecture), Derek Moulton, University of Oxford, Hans Othmer, Minnesota University, Jen Flegg, University of Melbourne, Jim Murray, University of Washington, Jonathan Sherratt, Heriot-Watt University, Kevin Painter, Heriot-Watt University, Linus Schumacher, University of Edinburgh, Lucy Hutchinson, Roche, Mark Chaplain, University of St Andrews, Mark Lewis, University of Alberta, Mary Myerscough, University of Sydney, Natasha Martin, University of Bristol, Noemi Picco, Swansea University, Paul Kulesa, Stowers Institute for Medical Research, Ruth Baker, University of Oxford, Santiago Schnell, University of Michigan, Tim Pedley, University of Cambridge

Organising committee

Ruth Baker (University of Oxford)

Derek Moulton (University of Oxford)

Helen Byrne (University of Oxford)

Santiago Schnell (University of Michigan)

Mark Chaplain (University of St Andrews)

We adapt convergent look-ahead and backward finite difference formulas to compute future eigenvectors and eigenvalues of piecewise smooth time-varying matrix flows $A(t)$. This is based on the Zhang Neural Network model for time-varying problems and uses the associated error function

$E(t) =A(t)V(t)−V(t)D(t)$

with the Zhang design stipulation

$\dot{E}(t) =−\eta E(t)$.

Here $E(t)$ decreased exponentially over time for $\eta >0$. It leads to a discrete-time differential equation of the form $P(t_k)\dot{z}(t_k) = q(t_k)$ for the eigendata vector $z(t_k)$ of $A(t_k)$. Convergent high order look-ahead difference formulas then allow us to express $z(t_k+1)$ in terms of earlier discrete $A$ and $z$ data. Numerical tests, comparisons and open questions follow.

I plan to present a brief introduction to optimal control theory (no background knowledge assumed), and discuss a fascinating and oft-forgotten family of problems where the optimal control behaves very strangely; it changes state infinitely often in finite time. This causes havoc in practice, and even more so in the literature.