Past

DNA double strand breaks (DSB) are the most deleterious type of DNA damage induced by ionizing radiation and cytotoxic agents used in the treatment of cancer. When DSBs are formed, the cell attempts to repair the DNA damage through activation of a variety of molecular repair pathways. One of the earliest events in response to the presence of DSBs is the phosphorylation of a histone protein, H2AX, to form γH2AX. Many hundreds of copies of γH2AX form, occupying several mega bases of DNA at the site of each DSB. These large collections of γH2AX can be visualized using a fluorescence microscopy technique and are called ‘γH2AX foci’. γH2AX serves as a scaffold to which other DNA damage repair proteins adhere and so facilitates repair. Following re-ligation of the DNA DSB, the γH2AX is dephosphorylated and the foci disappear.

We have developed a contrast agent, 111In-anti-γH2AX-Tat, for nuclear medicine (SPECT) imaging of γH2AX which is based on an anti-γH2AX monoclonal antibody. This agent allows us to image DNA DSB in vitro in cells, and in in vivo model systems of cancer. The ability to track the spatiotemporal distribution of DNA damage in vivo would have many potential clinical applications, including as an early read-out of tumour response or resistance to particular anticancer drugs or radiation therapy.

The imaging tracer principle states that a contrast agent should not interfere with the physiology of the process being imaged. Therefore, we have investigated the influence of the contrast agent itself on the kinetics of DSB formation, repair and on γH2AX foci formation and resolution and now wish to synthesise these data into a coherent kinetic-dynamic model.

Dualities of various types have been used by different authors to 
describe free and projective objects in a large
  number of classes of algebras. Particularly, natural dualities provide a 
general tool to describe free objects. In
  this talk we present two interesting applications of this fact. 
  We first provide a combinatorial classification of unification problems 
by their unification type for the
varieties of Bounded Distributive Lattices, Kleene algebras, De Morgan 
algebras. Finally we provide axiomatizations forsingle
and multiple conclusion admissible rules for the varieties of Kleene 
algebras, De Morgan algebras, Stone algebras.

Understanding the fatigue of metals under cyclic loads is crucial for some fields in mechanical engineering, such as the design of wheels of high speed trains and aero-plane engines. Experimentally it has been found that metal fatigue induced by cyclic loads is closely related to a ladder shape pattern of dislocations known as a persistent slip band (PSB). In this talk, a quantitative description for the formation of PSBs is proposed from two angles: 1. the motion of a single dislocation analised by using asymptotic expansions and numerical simulations; 2. the collective behaviour of a large number of dislocations analised by using a method of multiple scales.

De Concini-Kac-Procesi conjecture gives a good estimate for the dimensions of finite--dimensional non-restricted representations of quantum groups at m-th root of unity. According to De Concini, Kac and Procesi such representations can be split into families parametrized by conjugacy classes in an algebraic group G, and the dimensions of representations corresponding to a conjugacy class O are divisible by m^{dim O/2}. The talk will consist of two parts. In the first part I shall present an approach to the proof of De Concini-Kac-Procesi conjecture based on the use of q-W algebras and Bruhat decomposition in G. It turns out that properties of representations corresponding to a conjugacy class O depend on the properties of intersection of O with certain Bruhat cells. In the second part, which is more technical, I shall discuss q-W algebras and some related results in detail.

We present progress on an Interior Point based multi-step solution approach for stochastic programming problems. Our approach works with a series of scenario trees that can be seen as successively more accurate discretizations of an underlying probability distribution and employs IPM warmstarts to "lift" approximate solutions from one tree to the next larger tree.

In this talk we will discuss geometric quantization. First of all we will discuss what it is, but shall also see that it has relations to many other parts of mathematics. Especially shall we see how the Hitchin connection in geometric quantization can give us representations of a certain group associated to a surface, the mapping class group. If time permits we will discuss some recent results about these groups and their representations, results that are essentially obtained from geometrically quantizing a moduli space of flat connections on a surface."

In this seminar, we discuss three questions related to the finite difference computation of early exercise options, one of which has a useful answer, one an interesting one, and one is open.

We begin by showing that a simple iteration of the exercise strategy of a finite difference solution is efficient for practical applications and its convergence can be described very precisely. It is somewhat surprising that the method is largely unknown.

We move on to discuss properties of a so-called penalty method. Here we show by means of numerical experiments and matched asymptotic expansions that the approximation of the value function has a very intricate local structure, which is lost in functional analytic error estimates, which are also derived.

Finally, we describe a gap in the analysis of the grid convergence of finite difference approximations compared to empirical evidence.

This is joint work with Jan Witte and Sam Howison.

Pseudo-differential operators (PDO's) are primarily defined in the familiar setting of the Euclidean space. For four decades, they have been standard tools in the study of PDE's and it is natural to attempt defining PDO's in other settings. In this talk, after discussing the concept of PDO's on the Euclidean space and on the torus, I will present some recent results and outline future work regarding PDO's on Lie groups as well as some of the applications to PDE's

The lamplighter groups, solvable Baumslag-Solitar groups and lattices in SOL all share a nice kind of geometry. We'll see how the Cayley graph of a lamplighter group is a Diestel-Leader graph, that is a horocyclic product of two trees. The geometry of the solvable Baumslag-Solitar groups has been studied by Farb and Mosher and they showed that these groups are quasi-isometric to spaces which are essentially the horocyclic product of a tree and the hyperbolic plane. Finally, lattices in the Lie groups SOL can be seen to act on the horocyclic product of two hyperbolic planes. We use these spaces to measure the length of short conjugators in each type of group.

Many swimming microorganisms inhabit heterogeneous environments consisting of solid particles immersed in viscous fluid. Such environments require the organisms attempting to move through them to negotiate both hydrodynamic forces and geometric constraints. Here, we study this kind of locomotion by first observing the kinematics of the small nematode and model organism Caenorhabditis elegans in fluid-filled, micro-pillar arrays. We then compare its dynamics with those given by numerical simulations of a purely mechanical worm model that accounts only for the hydrodynamic and contact interactions with the obstacles. We demonstrate that these interactions allow simple undulators to achieve speeds as much as an order of magnitude greater than their free-swimming values. More generally, what appears as behavior and sensing can sometimes be explained through simple mechanics.

This is a report on a joint work (in progress) with Pantev, Vaquie and Vezzosi. After some

reminders on derived algebraic geometry, I will present the notion of shifted symplectic structures, as well as several basic examples. I will state existence results: mapping spaces towards a symplectic targets, classifying spaces of reductive groups, Lagrangian intersections, and use them to construct many examples of (derived) moduli spaces endowed with shifted symplectic forms. In a second part, I will explain what "Quantization" means in the shifted context. The general theory will be illustrated by the particular examples of moduli of sheaves on oriented manifolds, in dimension 2, 3 and higher.

The phase transition deals with sudden global changes and is observed in many fundamental random discrete structures arising from statistical physics, mathematics and theoretical computer science, for example, Potts models, random graphs and random $k$-SAT. The phase transition in random graphs refers to the phenomenon that there is a critical edge density, to which adding a small amount results in a drastic change of the size and structure of the largest component. In the Erdős--R\'enyi random graph process, which begins with an empty graph on $n$ vertices and edges are added randomly one at a time to a graph, a phase transition takes place when the number of edges reaches $n/2$ and a giant component emerges. Since this seminal work of Erdős and R\'enyi, various random graph processes have been introduced and studied. In this talk we will discuss new approaches to study the size and structure of components near the critical point of random graph processes: key techniques are the classical ordinary differential equations method, a quasi-linear partial differential equation that tracks key statistics of the process, and singularity analysis.

This is a report on a joint work (in progress) with Pantev, Vaquie and Vezzosi. After some

reminders on derived algebraic geometry, I will present the notion of shifted symplectic structures, as well as several basic examples. I will state existence results: mapping spaces towards a symplectic targets, classifying spaces of reductive groups, Lagrangian intersections, and use them to construct many examples of (derived) moduli spaces endowed with shifted symplectic forms. In a second part, I will explain what "Quantization" means in the shifted context. The general theory will be illustrated by the particular examples

of moduli of sheaves on oriented manifolds, in dimension 2, 3 and higher.

Quantile forecasting of wind power using variability indices
Abstract: Wind power forecasting techniques have received substantial attention recently due to the increasing penetration of wind energy in national power systems.  While the initial focus has been on point forecasts, the need to quantify forecast uncertainty and communicate the risk of extreme ramp events has led to an interest in producing probabilistic forecasts. Using four years of wind power data from three wind farms in Denmark, we develop quantile regression models to generate short-term probabilistic forecasts from 15 minutes up to six hours ahead. More specifically, we investigate the potential of using various variability indices as explanatory variables in order to include the influence of changing weather regimes. These indices are extracted from the same  wind power series and optimized specifically for each quantile. The forecasting performance of this approach is compared with that of some benchmark models. Our results demonstrate that variability indices can increase the overall skill of the forecasts and that the level of improvement depends on the specific quantile.

We prove that the 3-D free-surface incompressible Euler equations with regular initial geometries and velocity fields have solutions which can form a finite-time ``splash'' singularity, wherein the evolving 2-D hypersurface intersects itself at a point. Our approach is based on the Lagrangian description of the free-boundary problem, combined with novel approximation scheme. We do not assume the fluid is irrotational, and as such, our method can be used for a number of other fluid interface problems. This is joint work with Daniel Coutand.

We consider the prime k-tuples conjecture, which predicts that a system of linear forms are simultaneously prime infinitely often, provided that there are no obvious obstructions. We discuss some motivations for this and some progress towards proving weakened forms of the conjecture.

I shall describe the construction of the four-brane giant graviton on $\mathrm{AdS}_4\times \mathbb{CP}^3$ (extended and moving in the complex projective space), which is dual to a subdeterminant operator in the ABJM model. This dynamically stable, BPS configuration factorizes at maximum size into two topologically stable four-branes (each wrapped on a different $\mathbb{CP}^2 \subset \mathbb{CP}^3$ cycle) dual to ABJM dibaryons. Our study of the spectrum of small fluctuations around this four-brane giant provides good evidence for a dependence in the spectrum on the size, $\alpha_0$, which is a direct result of the changing shape of the giant’s worldvolume as it grows in size. I shall finally comment upon the implications for operators in the non-BPS, holomorphic sector of the ABJM model.