Past

We consider the pricing of American put options in a model-independent setting: that is, we do not assume that asset prices behave according to a given model, but aim to draw conclusions that hold in any model. We incorporate market information by supposing that the prices of European options are known. In this setting, we are able to provide conditions on the American Put prices which are necessary for the absence of arbitrage. Moreover, if we further assume that there are finitely many European and American options traded, then we are able to show that these conditions are also sufficient. To show sufficiency, we construct a model under which both American and European options are correctly priced at all strikes simultaneously. In particular, we need to carefully consider the optimal stopping strategy in the construction of our process. (Joint with Christoph Hoeggerl).

A pseudofinite group is an infinite model of the theory of finite groups. I will discuss what can be said about pseudofinite groups under various tameness assumptions on the theory (e.g. NIP, supersimplicity), structural results on pseudofinite permutation groups, and connections to word maps and generalisations.

Ricci solitons were introduced by Richard Hamilton in the 80's and they are a generalization of the better know Einstein metrics. During this talk we will define the notion of Ricci soliton and I will try to convince you that these metrics arise "naturally" in a number of different settings. I will also present various examples and talk a bit about some symmetry properties that Ricci solitons have.

Note: This talk is meant to be introductory and no prior knowledge about Einstein metrics will be assumed (or necessary).

After a short survey of the notion of level of distribution for
arithmetic functions, and its importance in analytic number theory, we
will explain how our recent studies of twists of Fourier coefficients of
modular forms (and especially Eisenstein series) by "trace functions"
lead to an improvement of the results of Friedlander-Iwaniec and
Heath-Brown for the ternary divisor function in arithmetic progressions
to prime moduli.

This is joint work with É. Fouvry and Ph. Michel.

Many real-life complex systems arise as a network of simple interconnected individual agents. A central question is to determine how network topology and individual agent dynamics combine to create the global dynamics.

In this talk we focus on the case of continuous-time random walks on networks, with a waiting time of the walker on each node assuming arbitrary probability distributions. Such random walks are useful to model diffusion processes over complex temporal networks representing human interactions, often characterized by non-Poissonian contact patterns.

We find that the mixing time of the random walker, i.e. the relaxation time for the process to reach stationarity, is determined by a combination of three factors: the spectral gap, associated to bottlenecks in the underlying topology, burstiness, related to the second moment of the waiting time distribution, and the characteristic time of its exponential tail, which is an indicator of the tail `fatness'. We show

theoretically that a strong modular structure dampens the importance of burstiness, and empirically that either of the three factors may be dominant in real-life data.

These results are available in arXiv:1309.4155

TBA

The fundamental mechanisms of microorganism motility have been extensively studied in the past. Most previous work focused on cell locomotion in simple (Newtonian) fluids.
However, in many cases of biological importance (including mammalian reproduction and bacterial infections), the fluids that surround the organisms are strongly non-Newtonian (so-called complex fluids), either because they have shear-dependent viscosities, or because they display an elastic response. These non-Newtonian effects challenge the most fundamental intuition in fluid mechanics, resulting in our incapacity to predict its implications in biological cell locomotion. In this talk, our on-going experimental investigation to quantify the effect of non-Newtonian behavior on the locomotion and fluid transport of microorganisms will be described. Several types of magnetic micro-robots were designed and built. These devices were actuated to swim or move in a variety of fluids : Newtonian, elastic with constant viscosity (Boger fluids) or inelastic with shear-thinning viscosity. We have found that, depending on the details of locomotion, the swimming performance can either be increased, decreased or remain unaffected by the non Newtonian nature of the liquid. Some key elements to understand the general effect of viscoelasticity and shear-thinning viscosity of the motility of microorganisms will be discussed.

In this talk we will show the existence  of a regular "small" weak solution to the flow of the higher dimensional H-systems with initial-boundary conditions. We also analyze its time asymptotic bahavior and we give a stability result.

This talk aims to illustrate how graphical calculus can be used to reason about Hopf algebras and their modules. The talk will be aimed at a general audience requiring no previous knowledge of the topic.

A Steiner Triple System on a set X is a collection T of 3-element subsets of X such that every pair of elements of X is contained in exactly one of the triples in T. An example considered by Plücker in 1835 is the affine plane of order three, which consists of 12 triples on a set of 9 points. Plücker observed that a necessary condition for the existence of a Steiner Triple System on a set with n elements is that n be congruent to 1 or 3 mod 6. In 1846, Kirkman showed that this necessary condition is also sufficient.

In 1853, Steiner posed the natural generalisation of the question: given integers q and r, for which n is it possible to choose a collection Q of q-element subsets of an n-element set X such that any r elements of X are contained in exactly one of the sets in Q? There are some natural necessary divisibility conditions generalising the necessary conditions for Steiner Triple Systems. The Existence Conjecture states that for all but finitely many n these divisibility conditions are also sufficient for the existence of general Steiner systems (and more generally designs).

We prove the Existence Conjecture, and more generally, we show that the natural divisibility conditions are sufficient for clique decompositions of simplicial complexes that satisfy a certain pseudorandomness condition.

Convolution is widely-used and fundamental mathematical operation
in signal processing, statistics, and PDE theory.

Unfortunately the CONV() method in Chebfun for convolving two chebfun 
objects has long been one of the most disappointingly slow features of 
the project. In this talk we will present a new algorithm, which shows 
performance gains on the order of a factor 100.

The key components of the new algorithm are:
* a convolution theorem for Legendre polynomials 
* recurrence relations satisfied by spherical Bessel functions
* recent developments in fast Chebyshev-Legendre transforms [1]

Time-permitting, we shall end with an application from statistics,
using the fact that the probability distribution of the sum of two 
independent random variables is the convolution of their individual 
distributions.

[1] N. Hale and A. Townsend, "A fast, simple, and stable Chebyshev-
Legendre transform using an asymptotic formula”, SISC (to appear).

The accurate and efficient solution of linear systems $Ax=b$ is very important in many engineering and technological applications, and systems of this form also arise as subproblems within other algorithms. In particular, this is true for interior point methods (IPM), where the Newton system must be solved to find the search direction at each iteration. Solving this system is a computational bottleneck of an IPM, and in this talk I will explain how preconditioning and deflation techniques can be used, to lessen this computational burden.  This work is joint with Jacek Gondzio.

The finance literature documents a relation between labor income and

the cross-section of stock returns. One possible explanation for this

is the hedging decisions of investors with relative wealth concerns.

This implies a negative risk premium associated with stock returns

correlated with local undiversifiable wealth, since investors are

willing to pay more for stocks that help their hedging goals. We find

evidence that is consistent with these regularities. In addition, we

show that the effect varies across geographic areas depending on the

size and variability of undiversifiable wealth, proxied by labor income.

This is another opportunity to hear the 2013 LMS Presidential Address:

Abstract: The idea of space is central to the way we think.  It is the technology we have evolved for interpreting our experience of the world.  But space is presumably a human creation, and even inside mathematics it plays a variety of different roles, some modelling our intuition very closely and some seeming almost magical.  I shall point out how the homotopy category in particular breaks away from its own roots.  Then I shall describe how quantum theory leads us beyond the well-established notion of a topological space into the realm of noncommutative geometry.  One might think that noncommutative spaces are not very space-like, and yet it is noncommutativity that makes the world look as it does to us, as a collection of point particles.

In the first part of the talk we are going to build up some intuition about limit-periodic functions and I will explain why they are the 'simplest' class of arithmetic functions appearing in analytic number theory. In the second part, I will give an equivalent description of 'limit-periodicity' by using exponential sums and explain how this property allows us to solve 'twin-prime'-like problems by the circle method.

Liquid Crystals (LC), anisotropic fluids that combine many tensor properties of crystalline solids with the fluidity of liquids, have long been providing major challenges to theorists and molecular modelers. In the classical textbook picture a molecule giving rise to LC phases is represented by a uniaxial rod endowed with repulsive (Onsager) or attractive (Maier-Saupe) interactions or possibly with a combination of the two (van der Waals picture) [1]. While these models have proved able to reproduce at least qualitatively the most common LC phase, the nematic one, and its phase transition to a normal isotropic fluid, they have not been able to deal with quantitative aspects (e.g. the orientational order at the transition) and more seriously, with the variety of novel LC phases and of sophisticated experiments offering increasing detailed observations at the nanoscale. Classical Monte Carlo and molecular dynamics computer simulations that have been successfully used for some time on simple lattice or off-lattice generic models [2-5] have started to offer unprecedented, atomistic level, details of the molecular organization of LC in the bulk and close to surfaces [6,7]. In particular, atomistic simulations are now starting to offer predictive power, opening the possibility of closing the gap between molecular structure and phase organizations. The availability of detailed data from these virtual experiments requires to generalize LC models inserting molecular features like deviation from uniaxiality or rigidity, the inclusion of partial charges etc. Such more detailed descriptions should reflect also in the link between molecular and continuum theories, already developed for the simplest models [8,9], possibly opening the way to a molecular identification of the material and temperature dependent coefficients in Landau-deGennes type free energy functionals.

[1] see, e.g., G. R. Luckhurst and G. W. Gray, eds., The Molecular Physics of Liquid Crystals (Academic Press,, 1979).

[2] P. Pasini and C. Zannoni, eds., Advances in the computer simulations of liquid crystals (Kluwer, 1998)

[3] O. D. Lavrentovich, P. Pasini, C. Zannoni and S. Zumer, eds. Defects in Liquid Crystals: Computer Simulations, Theory and Experiments, (Kluwer, Dordrecht , 2001).

[4] C. Zannoni, Molecular design and computer simulations of novel mesophases, J. Mat. Chem. 11, 2637 (2001).

[5] R.Berardi, L.Muccioli, S.Orlandi, M.Ricci, C.Zannoni, Computer simulations of biaxial nematics, J. Phys. Cond. Matter 20, 1 (2008).

[6] G. Tiberio, L. Muccioli, R. Berardi and C. Zannoni , Towards “in silico” liquid crystals. Realistic Transition temperatures and physical properties for n-cyanobiphenyls via molecular dynamics simulations, ChemPhysChem 10, 125 (2009).

[7] O. Roscioni, L. Muccioli, R. Della Valle, A. Pizzirusso, M. Ricci and C. Zannoni, Predicting the anchoring of liquid crystals at a solid surface: 5-cyanobiphenyl on cristobalite and glassy silica surfaces of increasing roughness, Langmuir 29, 8950 (2013).

[8] 1. J. Katriel, G. F. Kventsel, G. R. Luckhurst and T. J. Sluckin, Free-energies in the Landau and Molecular-field approaches, Liq. Cryst. 1, 337 (1986).

[9] J. M. Ball and A. Majumdar, Nematic liquid crystals: From Maier-Saupe to a Continuum Theory, Mol. Cryst. Liq. Cryst. 525, 1 (2010).

Computational structures---from simple objects like bits and qubits,

to complex procedures like encryption and quantum teleportation---can

be defined using algebraic structures in a symmetric monoidal

2-category. I will show how this works, and demonstrate how the

representation theory of these structures allows us to recover the

ordinary computational concepts. The structures are topological in

nature, reflecting a close relationship between topology and

computation, and allowing a completely graphical proof style that

makes computations easy to understand. The formalism also gives

insight into contentious issues in the foundations of quantum

computing. No prior knowledge of computer science or category theory

will be required to understand this talk.

Noncommutative projective geometry is the study of quantum versions of projective space and other projective varieties.  Starting with the celebrated work of Artin, Tate and Van den Bergh on noncommutative projective planes, a substantial theory of noncommutative curves and surfaces has been developed, but the classification of noncommutative versions of projective three-space remains unknown.  I will explain how a portion of this classification can be obtained, via deformation quantization, from a corresponding classification of holomorphic foliations due to Cerveau and Lins Neto.  In algebraic terms, the result is an explicit description of the deformations of the polynomial ring in four variables as a graded Calabi--Yau algebra.