University of Crete
Department of Mathematics and Applied Mathematics
Κεντρικο Σεμιναριο Τμηματος

Academic Year 2016-17

Tue, 11 Oct 2016 14:15 A303 Christof Melcher RWTH Aachen University Chiral skyrmions near the conformal limit

Tue, 18 Oct 2016 13:15 A303 Javier Utreras Universidad de Concepción Undecidable first-order theories of $R[t]$ with addition and fragments of multiplication

Abstract: An undecidability result for the first-order theory of a ring structure leads to a "weakening" of the language in order to find at which point the theory changes from decidable to undecidable. The standard weakenings consist of replacing either or both operations by a fragment of it, i.e., an operation or relation that can be defined from it, but for which the converse is not (or at least not trivially) true. In this talk I will discuss two different fragments of multiplication: the set of images of a degree two polynomial and the relation of coprimeness. I will present my work on the undecidability of the first-order theories of certain polynomial rings for each language, and comment on possible further ideas in each case.

Academic Year 2015-16

Fri, 9 Oct 2015 12:15 A303 Werner Varnhorn Univ. Kassel Developments in Navier Stokes equations
Thu, 15 Oct 2015 17:00 A303 Aristides Kontogeorgis Univ. of Athens Arithmetic topology and the absolute Galois group

Θα δούμε μια σειρά από ομοιότητες ανάμεσα σε φαινόμενα των πολλαπλοτήτων διάστασης 3 και των σωμάτων αριθμών, όπως αυτά έχουν καθοριστεί στο λεξικό MKR. Θα δοθεί μια περιγραφή της απόλυτης ομάδας Galois ως mapping class group και θα δοθεί μια εξήγηση των η ομοιοτήτων ανάμεσα στις δύο θεωρίες βασισμένη στις αναπαραστάσεις ομάδων στους αυτομορφισμούς της ελεύθερης προπεπερασμένης ομάδας.

Tue, 12 Apr 2016 12:15 A303 Dimitris Bagkavos Accenture and Univ. of Crete Development of measures of asymmetry and a new test of symmetry for the probability density function of random variables

In statistical methodology, the techniques for assessing if a distribution is symmetrical or not are based on characteristic properties of symmetric distributions. These properties form the basis for developing measures and statistical tests through the skewness coefficient of the distribution. However the skewness coefficient is affected by the tail behavior of the distribution and naturally this affects the performance of the measures/tests. For this reason, here we follow a different path and based on a necessary and a necessary and sufficient condition for the symmetry of a probability density function we develop two measures of symmetry and a statistical test for symmetry. This is developed on the basis of calculus techniques. Apart from the properties of the measures, we study the distribution of the statistical test as well as the implementation details of the methods in practice.

Academic Year 2014-15

Mon, 22 Sep 2014 15:15 A303 Kevin Burrage Univ. of Oxford and Queensland Univ. of Technology From cells to tissue: modelling the electrophysiology of the human heart

This talk gives an overview on the use of non-local or fractional models for modelling the electrophysiology of the heart when taking into account the heterogeneous nature of cardiac tissue. Space fractional partial differential equations will be introduced along with some new computational approaches. We will then show how model parameters can be extracted from Diffusion Tensor Magnetic Resonance Images and using clinical data we will attempt to construct spatial biomarkers for understanding hypertrophic cardio-myopathy – disarray of the cardiac fibres.

Fri, 3 Oct 2014 12:15 A303 J.J.P. Veerman Portland State Univ. Synchronization of Large Linear Oscillator Arrays

Synchronization of a large collection of coupled, simple dynamical systems is a problem that has applications from neuroscience to traffic modeling to modeling of consensus formation.

Consider an array of identical linear oscillators, each coupled to its front and rear neighbor. The coupling may be asymmetric. If we kick the front oscillator (the leader), how does this signal propagate through the system? In some isolated cases, for certain values of the parameters, the answer is well-known, but until recently the only general results applicable to large were very qualitative.

We developed a theory that gives the correct quantitative description. The theory uses ideas from partial differential equations, but without taking a continuum limit. We will describe the theory and the conjectures it is based upon, as well as the quantitative results.

Fri, 10 Oct 2014 12:15 A303 Claus-Guenther Schmidt Karlsruhe Institute of Technology On special values of L-functions
Thu, 23 Oct 2014 18:15 A303 Aggelos Kiayias Univ. of Athens Cryptocurrencies: Bitcoin and Beyond
Abstract: Cryptocurrencies have emerged as a powerful new technology for financial transactions in a global scale. In this talk we review the cryptographic aspects of such systems and we discuss open questions both in terms of their realization as well as in terms of expanding the type of services they can offer. We will cover the basics behind proof of work cryptocurrencies such as bitcoin, as well as proof of stake type of cryptocurrencies and we will review various attacks that can be mounted against such systems.
Wed, 12 Nov 2014 13:15 A303 Filippo Santambrogio Univ. Paris--Sud Density-constrained evolution PDEs for crowds and fluids


I will present some models where a density $\rho$ of particles move, following a velocity field, but subject to a density constraint $\rho\leq 1$. When needed, they adapt their "spontaneous" velocity in order to preserve this density constraint. The model was originally introduced for crowd motion but is adapted to many kind of particle flows. Mathematically, the PDE solved by the density is easy to write, but it lacks regularity, and is difficult to study. It has been possible to study it thanks to optimal transport techniques, which also suggested efficient numerical methods. I will briefly introduce the main ingredients from optimal transport that we need to understand the method, and the talk will be essentially self-contained.

Fri, 20 Feb 2015 12:15 A303 Mariusz Lemanczyk Nicolaus Copernicus University Moebius disjointness, ergodic theory and the Chowla conjecture


In 2010, P. Sarnak formulated the following Moebius disjointness conjecture: $\frac1N\sum_{n\leq N} \mu(n)f(T^nx)\to 0$ as $N\to \infty$, for an arbitrary zero entropy homeomorphism $T$ of a compact metric space $X$, arbitrary $f\in C(X)$ and $x\in X$. Here, $\mu(\cdot):{\mathbb N}\to\{-1,0,1\}$ denotes the classical arithmetic Moebius function. I will show how this conjecture is connected on one hand with ergodic theory and on the other hand with other problems in number theory, concentrating on the Chowla conjecture from 1960 on the multiple correlations of the Moebius function.

Fri, 27 Feb 2015 12:30 A303 J.J.P. Veerman Portland State Univ. Mediatrices and Minimal Separating Sets

For distinct points $p$ and $q$ in a two-dimensional connected Riemannian manifold $M$, we define their mediatrix $L_{pq}$ as the set of points equidistant to $p$ and $q$. It is known that mediatrices have a cell decomposition consisting of a finite number of branch points connected by Lipschitz curve. We show additional geometric regularity properties of mediatrices: at each point they have the radial linearizability property, which means that they are tangent to a finite collection of lines meeting in the origin. In the case of mediatrices on the sphere, where mediatrices are simple closed Lipschitz curves, we show these curves have at most countable singularities, and the total angular deficiency has a finite upper bound related to the total curvature of the metric on the sphere.

On the other hand mediatrices have the topological property that they separate the manifold $M$ into two parts and that non proper subset of them does. This allows for their topological classification. This classification is in some sense a generalization of the Jordan Brouwer Theorem. We will briefly discuss the classification of minimal separating sets in the orientable surfaces of genus 0, 1, and 2

Just last year, mediatrices found an application in a territorial conflict between Peru and Chile. We'll show the opinion of the International Court of Justice in The Hague.

Fri, 3 Apr 2015 11:05 A303 Rom Pinchasi Technion The odd area of an odd number of parallel translates of a fixed set

Let $F$ be a family that consists of an odd number of parallel translates of a given (compact and with positive measure) set $F$ in the plane. We are interested in the area of those points in the plane that belong to an odd number of sets in $F$. What is the minimum possible such area in terms of the area of $F$? This depends a lot on the set $F$. We will resolve completely the cases of triangles, parallelograms, and trapezoids. We will also prove the existence and construct a set $F$ such that this area may be arbitrarily small. Many beautiful questions still remain open. This is an on-going project based on works with Assaf Oren and Igor Pak and with Uri Rabinovich.

Fri, 17 Apr 2015 12:15 A303 Agelos Georgakopoulos Univ. of Warwick Discrete Riemann mapping and the Poisson boundary

Answering a question of Benjamini & Schramm, we show that the Poisson boundary of any planar, uniquely absorbing (e.g. one-ended and transient) graph with bounded degrees can be realised geometrically as a circle, which circle arises from a discrete version of Riemann's mapping theorem. When the graph is hyperbolic, the aforementioned circle coincides with the usual boundary.

Fri, 10 Jul 2015 11:15 A303 Bernard Host Universite Paris-Est Marne-la-Vallee Partition regularity and higher order uniformity of multiplicative functions

Partition regularity is a classical notion in combinatorics: A collection of subsets of the integer is partition regular if for every finite partition of the integers at least one atom contains an element of the collection. On the other hand, multiplicative functions are a standard topic in number theory. In this talk we explain how a question of partition regularity led us to an unusual problem involving multiplicative functions, and we plan to say a few words about the methods needed to solve it.This is a joint work with Nikos Frantzikinakis.

Fri, 10 Jul 2015 12:15 A303 Assaf Naor Princeton University Discretization and quantitative differentiation

Geometric questions for discrete objects are often easier to understand by first considering an appropriate continuous analogue, using additional structure that is available in the continuous setting to prove the desired theorem, and then passing back to a discrete object via an appropriate "discretization" procedure. This last discretization step often relies on ad hoc arguments that are quite involved but technical, yet sometimes it requires conceptually new ideas, and there are instances in which it remains an open problem. In this talk we will discuss results that systematize the discretization step in certain important situations. We will present both older and recent theorems along these lines, and describe several basic open questions.

Academic Year 2013-14

Fri, 20 Dec 2013 13:15 A303 M. Doxastakis University of Houston Mathematical and Computational modeling in interfacial systems: protein association in lipid membranes, adsorption on surfaces and reaction-diffusion in polymer films
Fri, 4 Apr 2014 12:15 Α 303 Apostolos Giannopoulos University of Athens Established and conjectured facts about the distribution of volume in high dimensions
Fri, 11 Apr 2014 12:15 Α 303 Jorge Ramirez Univ. Politecnica de Madrid Block copolymers for organic photovoltaic applications
Solar photovoltaic technology is one of the most promising renewable sources of energy, but its cost remain high compared to its efficiency. Organic photovoltaic (OPV) solar cells have a huge potential and have been a focus of interest during the last few years. Organic cells bring the promise of low cost photovoltaic devices, because they can be produced at low temperatures, processed in solution and they allow the production of flexible and attractive devices. In order to improve the efficiency of OPV devices, all the steps involved in the conversion of the sun's light into electricity must be optimized (absorption of a photon, transport of the exciton, separation and transport of free charges are among the most important steps in the process). For an efficient absorption of photons, the materials must have a small band gap. In organic molecules, this is achieved by using aromatic compounds. Efficient transport of excitons requires that the donor and acceptor materials phase separate, and that the dimensions of phases is of the order of 10nm. In addition, both phases must be continuous so that the free charges can be transported to the electrodes. So far, this complex morphology problem has been worked out by using mixtures of different solvents and annealing processes, in methods that are usually based on trial and error. I believe that statistical mechanics and polymer physics can help to improve the process of designing the right morphology.

Block copolymers are a classical example of self-assembling materials. By carefully selecting the monomers of each block and the composition of the copolymer, a rich collection of morphologies can be obtained. The theoretical approach to understand the phase separation of polymers is the well-established self-consistent field theory (SCFT), first proposed by Helfand and fully developed by Matsen and Fredrickson. However, this theory is not directly applicable to the rather stiff aromatic polymers used in photovoltaic applications. In this presentation, we investigate a recently proposed numerical approach for the solution of the SCFT for wormlike chains, and its potential application to the design of OPV cells.

Fri, 2 May 2014 12:15 Α 303 Zoltán Balogh Univ. Bern Horizontal convexity in the Heisenberg group
In this talk I will discuss the notion of horizontal convexity in the Sub-Riemannian context of Heisenberg groups as compared to the classical Euclidean convexity. Aleksandrov-type comparison and maximum principles will be proven for continuous horizontally convex functions on Heisenberg groups. This is joint work with Andrea Calogero and Alexandru Kristaly.
Fri, 9 May 2014 12:15 Α 303 Dimitris Betsakos University of Thessaloniki Symmetrization and variations of Schwarz's Lemma
Fri, 16 May 2014 12:15 Α 303 Apostolos Hadjidimos University of Crete Brauer-Ostrowski and Brualdi sets
Abstract (in Greek)
Fri, 30 May 2014 12:15 Α 303 Christos Athanasiadis University of Athens Combinatorics of subdivisions and local $h$-vectors
The enumerative theory of simplicial subdivisions (triangulations) of simplicial complexes was developed by Stanley in order to understand the effect of such subdivisions on an important enumerative invariant of a simplicial complex, namely the $h$-vector. A key role in the theory is played by the concept of a local $h$-vector. After explaining the basics of this theory, this talk will briefly survey some recent applications and extensions to subdivisions of flag simplicial spheres and will then focus on combinatorial aspects by discussing examples for which the computation of the local $h$-vector leads to interesting enumerative problems on objects such as words, colored permutations and noncrossing partitions.
Fri, 13 June 2014 12:15 Α 303 Ioannis Kamarianakis Arizona State University Statistical models for space-time data: applications to forecasting of network flows
This talk will focus on selected statistical models that I have developed while working on the prototype of IBM's Traffic Prediction Tool. The models are parametric piecewise-linear and use information from hundreds of potentially useful predictors (related to upstream and downstream locations in the network). Significant predictors are chosen via a 2-step, penalized estimation scheme, namely adaptive LAD-LASSO. The talk will start with an extended summary of my previous applied statistical works while working at FORTH, Cornell and ASU.
Wed, 16 July 2014 11:15 Α 303 George Androulakis University of South Carolina Generators of Quantum Markov Semigroups
Quantum Markov Semigroups (QMSs) originally arose in the study of the evolutions of irreversible open quantum systems. Mathematically, they are a generalization of classical Markov semigroups where the underlying function space is replaced by a non-commutative operator algebra. In the case when the QMS is uniformly continuous, theorems due to Lindblad Stinespring, and Kraus imply that the generator of the semigroup has the form $$L(A)=\sum_{n=1}^{\infty}V_n^*AV_n +GA+AG^*$$ where $V_n$ and $G$ are elements of the underlying operator algebra. The characterization of the generator of general QMSs acting on the bounded operators of a Hilbert space, remained open since 1976. In a recent work with Matthew Ziemke we proved that the generator of general QMSs (not necessarily uniformly continuous) must also satisfy the form given by Lindblad and Stinespring. We also made some progress towards forms reflecting Kraus' result. I will explain these results and I will present some examples in order to clarify these findings and to examine the domains of the unbounded operators that will be involved. The talk will be accessible to graduate students and general mathematics audience.

All seminars

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