Directed Algebraic Topology: Models of Non-Reversible Worlds (New Mathematical Monographs)


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Description Table of Contents Product Details Click on the cover image above to read some pages of this book! Introduction p. Chain complexes p. All Rights Reserved. Differential Topology and Quantum Field Theory. Advances in Dynamic Equations on Time Scales. Catastrophe Theory To the Memory of M. Foliations I Graduate Studies in Mathematics. Geometry of Foliations Monographs in Mathematics.

New Mathematical Monographs

Measures and Probabilities Universitext. Knots and Surfaces Oxford Science Publications. Sign-Changing Critical Point Theory.

Ghil, and W. Tetsuharu Fuse, Planetary perturbations on the mean motion resonance with Neptune, Publ. Japan 54 , George Voyatzis and John D. Luz V. Vela-Arevalo and Jerrold E. Marsden, Time-frequency analysis of the restricted three-body problem: transport and resonance transitions, Class. Michael Berry, Chaos and the semiclassical limit of quantum mechanics is the moon there when somebody looks?

Hamburg 4 , Paris , Lawrence Breen, Theorie de Schreier superieure, Ann. Ecole Norm. Blanco, M. Bullejos and E. Faro, Categorical non abelian cohomology, and the Schreier theory of groupoids, available as arXiv:math. Also available as math. James Stasheff, Parallel transport in fibre spaces, Bol. Mexicana , James Stasheff, Associated fibre spaces, Michigan Math. Journal 15 , Pure Math. Ronald Brown and P. Higgins, Crossed complexes and non-abelian extensions, Category theory proceedings, Gummersbach, , ed. Kamps et al Lecture Notes in Math. Ronald Brown and O.

Mucuk, Covering groups of non-connected topological groups revisited, Math. Also available as arXiv:math. Ronald Brown and Ilhan Icen, Homotopies and automorphisms of crossed modules of groupoids, Applied Categorical Structures, 11 Higgins, The classifying space of a crossed complex, Math. Iakovos Androulidakis, Classification of extensions of principal bundles and transitive Lie groupoids with prescribed kernel and cokernel, J. Claudio Hermida, Descent on 2-fibrations and strongly 2-regular 2-categories, Applied Categorical Structures, 12 , Stephen W. William Rowan Hamilton, Second essay on a general method in dynamics, ed.

David R. Jakob Palmkvist, A realization of the Lie algebra associated to a Kantor triple system, available as arXiv:math. Bruce H. Bartlett, Categorical aspects of topological quantum field theories, M. Thesis, Utrecht University, Available as arXiv:math. Aaron D. Aaron Lauda, Frobenius algebras and ambidextrous adjunctions, available as arXiv:math. Aaron Lauda, Frobenius algebras and planar open string topological field theories, arXiv:math.

Hoffman, The computer-aided discovery of new embedded minimal surfaces, Mathematical Intelligencer 9 , Note No. D, Washington, DC, Garstecki and R. Holyst, Scattering patterns of self-assembled gyroid cubic phases in amphiphilic systems, J. Nelido Gonzalez-Segredo and Peter V. Press, Cambridge, Pseudorandomness and Cryptographic Applications. Razborov, Lower bounds for propositional proofs and independence results in bounded arithmetic, in Proceedings of ICALP , , pp. III, , pp. Buss, Bounded arithmetic and propositional proof complexity, in Logic of Computation, ed.

Schwictenberg, Springer-Verlag, , pp. Also available as cs. Calude, Springer, Singapore, , pp. John Baez, Recursivity in quantum mechanics, Trans. Klaus Weihrauch and Ning Zhong Is wave propagation computable or can wave computers beat the Turing machine? Press, , pp. Scott, Some aspects of categories in computer science, Handbook of Algebra, Vol. Hazewinkel, Elsevier, New York, Algebra Seely, Weak adjointness in proof theory, in Proc. Durham Conf. Seely, Modeling computations: a 2-categorical framework, in Proc. Freeman, New York, Schwaemmle and H.

Herrmann, Solitary wave behaviour of sand dunes, Nature Dec. Hermann, Minimal model for sand dunes, Phys. Elbelrhiti, P. Claudin, and B. Andreotti, Field evidence for surface-wave-induced instability of sand dunes, Nature Sep. Goldman and Louis H. Kauffman, Rational tangles, Advances in Applied Mathematics 18 , Kauffman and Sofia Lambropoulou, On the classification of rational tangles, available as arXiv:math.

Carr and J. Calude and M. Monthly , Gonzalez-Springberg and J. Verdier, Construction geometrique de la correspondance de McKay, Ann. ENS 16 , Mikhail Kapranov and Eric Vasserot, Kleinian singularities, derived categories and Hall algebras, available as arXiv:math.

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Dynkin with Commentary, eds. Yushkevich, G. Seitz and A. Onishchik, AMS, Hazewinkel, W. Hesselink, D.

Siermsa, and F. Michael R. John Milnor, Singular points of complex hypersurfaces, Ann. Studies 61, Princeton U. Press, Princeton, Coxeter, The evolution of Coxeter-Dynkin diagrams, in: T. Bisztriczky, P. McMullen, R. Schneider, A. Ivic Weiss, eds. Witt, Spiegelungsgruppen und Aufzahlung halbeinfacher Liescher Ringe.

Figure 4. Cavazzoni, G. Chiarotti, S. Scandolo, E. Tosatti, M. Bernasconi and M. Parrinello, Superionic and metallic states of water and ammonia at giant planet conditions, Science January , Celliers et al, Electronic conduction in shock-compressed water, Plasmas 11 , LL Knopf, New York, Press, Cambridge Gabriel and A. Aaron Bergman, Moduli spaces for Bondal quivers, available as arXiv:math. Ferrario and S.

Terracini, On the existence of collisionless equivariant minimizers for the classical n-body problem. D69 Sundance O. Terry Gannon, The algebraic meaning of genus-zero, available as arXiv:math. Yongchang Zhu, Modular invariance of characters of vertex operator algebras, J. Soc 9 , Voituriez, Random walks on the braid group B 3 and magnetic translations in hyperbolic geometry, Nucl. Studies 72, Princeton U. Press, Princeton, New Jersey, Thomas M. Adrian P. Conway, Noam D. Elkies, Jeremy L. Havel and David G. Cory, Solid-state NMR three-qubit homonuclear system for quantum information processing: control and characterization, Phys.

A 73 , Nielsen and Isaac L.

John Preskill, Quantum computation - lecture notes, references etc. Lo, S. Popescu, and T. Barbara M. Terhal and Guido Burkard, Fault-tolerant quantum computation for local non-markovian noise, Phys. A 71, Leff and Andrew F. Aristide Baratin and Laurent Freidel, Hidden quantum gravity in 4d Feynman diagrams: emergence of spin foams. John Baez and Urs Schreiber, Higher gauge theory, to appear in the volume honoring Ross Street's 60th birthday, available as arXiv:math. Ralph C. Merkle, Two types of mechanical reversible logic, Nanotechnology 4 , Translated as "The consistency of arithmetic" in M.

Szabo ed. Goodstein, On the restricted ordinal theorem, Journal of Symbolic Logic, 9 , Kirby and J. Paris, Accessible independence results for Peano arithmetic, Bull. Alan M. Turing, Systems of logic defined by ordinals, Proc. London Math. Jeremy Avigad and Erich H. Hendricks et al, Kluwer, Dordrecht , pp. Peters, Ltd. Benno Artmann, About the cover: the mathematical conquest of the third dimension, Bulletin of the AMS, 43 , Heath, editor, Euclid's Elements, chap. V: the text, Cambridge U.

VI: the scholia, Cambridge U. DMV 13 , Here the drawing of the icosahedron in Euclid's elements is analysed in detail. This discusses traditions concerning Theaetetus and Platonic solids. Justin T. In an asexually reproducing population where slightly deleterious mutations accumulate along the individual lineages and the individual selection disadvantage is assumed to be proportional to the number of accumulated mutations, the current best class will eventually disappear from the population, a phenomenon known as Muller's ratchet.

A question which is simple to ask but hard to answer is: 'How fast is the best type lost'? This is joint work with Alison Etheridge and Peter Pfaffelhuber. Let a n be the sequence of integers defined by the recurrence. There are several ways to prove that the sequence is periodic for all initial values. In this talk, we prove this by using the self-inducing structure of a piecewise isometry emerging from the discretized pentagonal rotation.

PageRank is a popularity measure designed by Google to rank Web pages according to their importance. It has been noticed in empirical studies that PageRank and in-degree in the Web graph follow similar power law distributions. This work is an attempt to explain this phenomenon. We model the relation between PageRank and other Web parameters through a stochastic equation inspired by the original definition of PageRank. Further, we use the theory of regular variation to prove that in our model, PageRank and in-degree follow power laws with the same exponent.

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The difference between these two power laws is in a multiplicative constant, which depends mainly on the settings of the PageRank algorithm. Our theoretical results are in good agreement with experimental data. Wavelets have proven to be a powerful tool in nonlinear approximation data compression and nonlinear estimation data smoothing. The nonlinearity is essential in applications with data that are not smooth but piecewise smooth. The key motivation behind the nonlinear estimation is the fact that a wavelet transform is a multiscale or multiresolution analysis of the data, leading to a sparse representation.

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Data are well approximated by reconstruction from a few, large coefficients in this representation. This talk starts with a summary of the most essential properties and results. Next, we introduce the concepts of lifting and second generation wavelets. Lifting is both a technique for implementing wavelet transforms and a philosophy for the design of new wavelet transforms, the second generation wavelets. Giving up the equidistancy leads to new theoretical issues with respect to convergence, numerical stability and smoothness of the approximation or estimation.

We conclude with a discussion on adaptive and nonlinear lifting schemes and a few examples. What is in common between the Clairvoyant Demon scheduling problem, the Riemann hypothesis and quasi-isometries of large objects? All these questions can be represented and studied as critical or near-critical percolative systems. Can we handle it by stochastic methods? Quantum systems under repeated or continuous observation can be considered as Markov chains on the space of quantum states. The gain of information by the observer is reflected by a tendency towards pure states on the part of the system.

In certain subspaces of the Hilbert space the quantum system may be shielded off from observation. We study such spaces and relate them to the problem of protecting information against decoherence in some future quantum computing device. Hecke algebras arise in a surprisingly wide variety of situations in algebra, geometry, number theory, and mathematical physics.

An affine Hecke algebra has a natural harmonic analysis attached to it, depending on a set of continuous parameters. In recent joint work with Maarten Solleveld the spectra of the affine Hecke algebras were completely determined. We will discuss some basic aspects of these results. Mijn nieuwsgierigheid werd gewekt door twee verwijzingen hiernaar in de wiskundige literatuur. In deze voordracht zal ik aan de hand van een flink aantal plaatjes en citaten verslag doen van mijn speurtocht naar Eigen Haard, naar P. Schoute, en naar de context waarin deze soms verrassend moderne rubriek verscheen.

December 6 Prof. Multi-fluid flows are found in many applications: flows of air and fuel droplets in combustion chambers, flows of air and exhaust gases at engine outlets, gas and petrolea flows in pipes of oil rigs, water-air flows around ship hulls, etc. To gain better insight in the behavior of multi-fluid flows, especially two-fluid flows, numerical simulations are needed. We assume that the fluids do not mix, but remain separated by a sharp interface. With this assumption a model is developed for unsteady, compressible two-fluid flow, with pressures and velocities that are equal on both sides of the two-fluid interface.

The model describes the behavior of a numerical mixture of the two-fluids not a physical mixture. This type of interface modeling is called interface capturing. Numerically, the interface becomes a transition layer between both fluids. The model consists of five equations: the mass, momentum and energy equation for the mixture the standard Euler equations , the mass equation for one of the two fluids and an energy equation for the same fluid.

In the latter, a novel model for the energy exchange between both fluids is introduced. The energy-exchange model forms a source term. The spatial discretization of the model uses a monotone, higher-order accurate finite-volume approximation, the temporal discretization a three-stage Runge-Kutta scheme. For the flux evaluation a Riemann solver is constructed. The source term is evaluated using the wave pattern found with the Riemann solver. The two-fluid model is validated on several shock-tube problems and on two standard shock-bubble interaction problems. A recent theorem of Bhargava shows that a positive definite quadratic form of a certain type will generate every positive integer if and only if it generates the integers 1,2,3,5,6,7,10,14 and We shall find that an equally simple result holds for sums of triangular numbers.

The question will be addressed how fast one can compute the number of ways in which an integer m can be written as a sum of n squares. At the moment the answer is not know. I will explain why I think that if n is even and m is given with its factorisation into primes, this counting can be done in time polynomial in n. The proposed method uses a generalisation of the main results of joint work with J-M.

Couveignes, R. Merkl on the complexity of the computation of coefficients of modular forms. A Dedekind zeta function doesn't always encode the isomorphism class of a number field. The dynamical Laplace operator zeta function doesn't always encode the isometry type of a manifold e. We look at such problems using tools from noncommutative geometry: to a compact Riemann surface of genus at least two, I will associate a finite-dimensional noncommutative Riemannian manifold a.

The encoding lies in the zeta functions of the spectral triple: the spectra of various operators in the spectral triple reconstruct the Riemann surface, via application of an ergodic rigidity theorem a la Mostow. Joint work with Matilde Marcolli. Invasion percolation is a random spatial growth model with very simple rules but surprisingly rich and complex behaviour.

It was introduced around by reserachers related to the oil industry but soon drew attention from many others, including theoretical physicists and mathematicians. After defining the model, I will concentrate on an object called a 'pond', and explain that this object has indeed a natural 'hydrologic' interpretation.

Although there is no special tuning of a parameter in this model, it turns out that these ponds are, in a sense which will be explained, critical. Such 'self-organized critical behaviour' seems to be quite common in nature, but this is one of the very few 'natural' models where it can be rigorously proved. Fourier analysis of real-valued functions on the Boolean hypercube has been an extremely versatile tool in theoretical computer science in the last decades.

Applications include the analysis of the behavior of Boolean functions with noisy inputs, machine learning theory, design of probabilistically checkable proofs, threshold phenomena in random graphs, etc. The Bonami-Beckner hypercontractive inequality is an important result in this context. Time permitting, I will also describe an application of this new inequality to a problem in quantum information theory.

This talk will focus on a number of open problems from the field of Diophantine equations, and related areas. I will attempt to indicate where these questions arise, why they turn out to be so difficult, and whether modern methods can provide, if not their complete resolution, at least a certain amount of insight. Michael Bennett was the Kloosterman Professor His research focuses on proving results for Diophantine equations by combining various theoretical and computational techniques. Bennett was visiting our institute during April and May Non-equilibrium statistical mechanics aims at describing the macroscopic properties of systems which are in contacts with two thermal baths starting from simple microscopic models made of interacting particle systems.

We will give an introduction to this largely open problem by considering models in one spatial dimension, i. We will present both Hamiltonian and stochastic dynamics. The role of conservation law energy, momentum,etc. Japanese puzzles, also known as "nonograms", are a form of logical drawing. Initially, the puzzle consists of a grid of small, empty squares, along with certain logical descriptions for every row and column in the grid. The puzzler gradually fills the grid by colouring the squares, using either black or white, based on the row and column descriptions.

Although Japanese puzzles have never reached the level of popularity of the more recent Sudoku puzzles, they are still highly ranked on the favourite puzzle list of many people in The Netherlands and around the world. All of the Japanese puzzles in regular puzzle magazines can be solved by repeatedly applying a relatively small set of logical rules. All such puzzles have a unique solution. However, the general Japanese puzzle problem is NP-hard. It is possible to construct puzzles that cannot be solved using simple rules and that have many different solutions.

In this talk, I will present an approach to solving Japanese puzzles which is far more powerful compared to the simple logical rules used by most human puzzlers. The approach is based completely on logical reasoning and can be used to find, with proof, all solutions of a puzzle. I explain quantum nonlocality experiments and discuss how to optimize them. Statistical tools from missing data maximum likelihood are crucial.

Open problems - there are indeed many! Prior knowledge of quantum theory or indeed physics is not needed to follow the talk; indeed its lack could be an advantage ;- It will be difficult to resist discussion of the metaphysical implications of Bell's inequality. December 7 Dr. When modeling or analyzing atmospheric flow, a major question is how to deal with the wide range of spatio-temporal scales that are active in the atmosphere. Stochastic methods have become increasingly important for dealing with this problem, and are used for topics such as analyzing atmospheric low-frequency variability, development of reduced models, the study of atmosphere-ocean interaction and improvement of parameterization schemes in models for weather and climate prediction.

I will discuss several approaches that use stochastic methods for studying atmospheric dynamics; among them are inverse modeling for stochastic differential equations SDEs , elimination of fast variables in stochastic systems, and the use of Hidden Markov Models. Define the mapping S d on the set of ordered d-tuples x of positive reals as follows: keep the smallest number, subtract it from the others and reorder the result in a non-decreasing way.

Later, Meester and K. In this lecture, the proof of this results is outlined, and some applications and generalizations will be given. One of the highlights of 19th century mathematics is the identification of the invariants of cubic forms in three variables with the classical modular forms in one variable as algebras.

This correspondence comes about by means of what we might now call the period mapping for polarized elliptic curves. After a review of this classical fact, we discuss some of its higher dimensional generalizations, among which are the recently settled cases of cubic forms in four and five variables. The last case leads us to consider a natural class of automorphic forms with poles. Metastability is an ubiquitous phenomenon of the dynamical behaviour of complex systems.

In this talk, I describe recent attempts towards a model-independent approach to metastability in the context of reversible Markov processes. I will present an outline of a general theory, based on careful use of potential theoretic ideas and indicate a number of concrete examples where this theory was used very successfully.

I will also indicate some challenges for future work. I will give a short introduction to the abelian sandpile model and discuss recent results on its infinite volume limit. Next, I'll discuss applications to a model of interacting sleepy, and sometimes activated random walkers in which we can show a phase transition as a function of the initial density of walkers.

This is an example of rigorous connection between self-organized and ordinary criticality, conjectured before by physicists. A well-known theorem of Minkowski gives a sharp multiplicative upper bound for the order of a finite subgroup of GL n, Q. We shall see how this result can be extended to other ground fields and to other reductive groups. We give a characterization of those tensor algebras that are invariant rings of a subgroup of the unitary group.

The theorem has as consequences several "First Fundamental Theorems" in the sense of Weyl in invariant theory. Moreover, the theorem gives a bridge between invariant theory and combinatorics. It is well known that the factorization of polynomials over the integers is in polynomial time. Unfortunately this algorithm was not useful in practice. Recently, Mark van Hoeij found a new factorization algorithm which works very well in practice.

We present the ideas of his algorithm and extend this algorithm to an algorithm for factoring polynomials in F[t][x], where F is a finite field. Surprisingly the algorithm is much simpler and more efficient in this setting. We prove in the rational and the bivariate case that the new algorithm runs theoretically in polynomial time.

We will explain why the expected running times should be heuristically much better than the given worst case estimates. The porous medium equation is a nonlinear degenerate version of the heat equation. It appears in many physical applications such as flows in porous media and thin film viscous flow. Compacly supported solutions of this equation have expanding supports.

Holes in the support are filled in finite time. I will discuss radially symmetric hole-filling solutions and their stability properties under radially and non-radially symmetric perturbations. Abstract: After a general introduction to nonparametric statistical estimation we discuss recent work [joint with Harry van Zanten] on Bayesian estimation using Gaussian prior distributions. As a concrete example consider estimating a probability density p using a random sample X 1, Brownian motion, indexed by the set in which the observations take their values.

The Bayesian machine Bayes, then mechanically produces a "posterior distribution", which is a random measure on the set of probability densities, can be used to infer the "true" value of p, and anno is computable. We investigate the conditions under which this Bayesian approach gives equally good results as other methods. A benchmark is whether it works well if the unknown p is known to belong to a given regularity class, such as the functions in a Holder or Sobolev space of a given regularity. This depends of course on the Gaussian process used.

It turns out to be neatly expressible in the reproducing Hilbert space of the process. Abstract: An algebraic curve determines an abelian variety, the Jacobian of the curve. For example, for a Riemann surface the Jacobian is a complex torus associated to the periods of integrals over the Riemann surface. Not every abelian variety is the Jacobian of a curve and the Schottky problem, due to Riemann, aks for a characterization of the Jacobians among all abelian varieties.

Various answers have been proposed. We shall discuss the problem, its history and some of the proposed answers to this problem. Abstract: If a deterministic system is perturbed by noise, it will not settle to a steady state. Instead, there may exist invariant measures. Existence of an invariant measure requires tightness of a solution, which is a compactness condition.

A solution of a finite dimensional stochastic differential equation is tight if it is bounded. Boundedness is not sufficient in the case of an infinite dimensional state space. We will discuss several conditions on infinite dimensional stochastic differential equations that provide existence of tight solutions and invariant measures. Milton Jara Profile cut-off for randomly perturbed dynamical systems Abstract.

Nederlands Mathematisch Congres Gorlaeusgebouw, Leiden; please register. Richard Gill Leiden : Einstein was wrong, probably Abstract. Rutherford was wrong too … References: a survey paper by myself on statistical issues in Bell-CHSH experiments debated on PubPeer , and slides of two recent talks. Remco van der Hofstad Eindhoven : The survival probability in high dimensions Abstract. Anthony Thornton Twente : Multi-scale modelling of segregating granular flows: From inclined planes to drums; via a volcano Abstract.

Arnoud den Boer Twente : Online learning in stochastic optimization problems Abstract. Daniel J. Peter Bruin Leiden : Heights in arithmetic and geometry Abstract. Martin Bright Leiden : Diophantine equations: geometry and the local-global approach Abstract. Walter van Suijlekom Nijmegen : Inner perturbations in noncommutative geometry Abstract. Gianne Derks Surrey : Existence and stability of stationary fronts in inhomogeneous wave equations Abstract. Daniele Sepe Utrecht : Integral affine geometry: from fundamentals to applications and back Abstract.

Marco Streng Leiden : Elliptic Curves: complex multiplication, application, and generalization Abstract. Xing Chaoping Nanyang Technological University : Algebraic curves over finite fields and applications Kloosterman lecture. Lectures in December 6, Snellius Filmvertoning: Late style - Yuri I. John F. Lectures in February 24, Oort building. Abel in Holland For details and registration click here. Jaap Top Groningen Schoute's discriminants Abstract. Tanja Eisner Amsterdam Arithmetic progressions via ergodic theory Abstract.

Directed Algebraic Topology

Lectures in December 16, Snellius, room Arjen Doelman Universiteit Leiden : Pulses in singularly perturbed reaction-diffusion equations Abstract. Lectures in December 17 Snellius, room Kloosterman lecture Prof. Ted Chinburg University of Pennsylvania : Two note number theory.

Directed Algebraic Topology: Models of Non-Reversible Worlds (New Mathematical Monographs) Directed Algebraic Topology: Models of Non-Reversible Worlds (New Mathematical Monographs)
Directed Algebraic Topology: Models of Non-Reversible Worlds (New Mathematical Monographs) Directed Algebraic Topology: Models of Non-Reversible Worlds (New Mathematical Monographs)
Directed Algebraic Topology: Models of Non-Reversible Worlds (New Mathematical Monographs) Directed Algebraic Topology: Models of Non-Reversible Worlds (New Mathematical Monographs)
Directed Algebraic Topology: Models of Non-Reversible Worlds (New Mathematical Monographs) Directed Algebraic Topology: Models of Non-Reversible Worlds (New Mathematical Monographs)
Directed Algebraic Topology: Models of Non-Reversible Worlds (New Mathematical Monographs) Directed Algebraic Topology: Models of Non-Reversible Worlds (New Mathematical Monographs)
Directed Algebraic Topology: Models of Non-Reversible Worlds (New Mathematical Monographs) Directed Algebraic Topology: Models of Non-Reversible Worlds (New Mathematical Monographs)

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