Category: Málstofa í stærðfræði

Þorsteinn Jónsson (02/07/18)

Anders Claesson, júní 29, 2018

Málstofa í stærðfræði

Fyrirlesari: Þorsteinn Jónsson, University of Guelph

Titill: Hnikaaðferðir til að læra dreififöll gagna

Staðsetning: V-147 (VR-II)
Tími: Mánudagur 2. júlí kl. 10:30

Ágrip:

Á þessari málstofu mun ég kynna safn aðferða sem að leyfir okkur að skilgreina tölfræðileg líkön sem lýsa líkindadreifingum sem búa til gögn.
Til þessa kynnum við tauganet sem hraða, en ótrúlega áhrifaríka leið til að leysa hnikaverkefni fyrir vel valið kostnaðarfall.
Ég mun ræða tvær mismunandi aðferðir til þess að skilgreina þetta kostnaðarfall ásamt því að sýna áhugaverðar niðurstöður.

Thomas Selig (27/6/18)

Sigurður Örn Stefánsson, júní 25, 2018

Málstofa í stærðfræði

Fyrirlesari: Thomas Selig, University of Strathclyde

Titill: EW-tableaux, permutations and recurrent configurations of the sandpile model on Ferrers graphs.

Staðsetning: VRII, V-147
Tími: Miðvikudagur 27. júní kl. 10:30

Ágrip:

The Abelian sandpile model (ASM) is a dynamic process on a graph. More specifically, it is a Markov chain on the set of configurations on that graph. Of particular interest are the recurrent configurations, i.e. those that appear infinitely often in the long-time running of the model. We study the ASM on Ferrers graphs, a class of bipartite graphs in one-to-one correspondence with Ferrers diagrams. We show that minimal recurrent configurations are in one-to-one correspondence with a set of certain 0/1 fillings of the Ferrers diagrams introduced by Ehrenborg and van Willigensburg. We refer to these fillings as EW-tableaux, and establish a bijection between the set of EW-tableaux of a given Ferrers diagram and a set of permutations whose descent bottoms are given by the shape of the Ferrers diagram. This induces a bijection between these permutations and minimal recurrent configurations of the ASM. We enrich this bijection to encode all recurrent configurations, via a decoration of the corresponding permutation. We also show that the set of recurrent configurations over all Ferrers graphs of a given size are in bijection with the set of alternating trees of that size.

Delphin Sénizergues (11/06/18)

Sigurður Örn Stefánsson, júní 11, 2018

Málstofa í stærðfræði

Fyrirlesari: Delphin Sénizergues, Université Paris 13

Titill: Random metric spaces constructed using a gluing procedure

Staðsetning: VRII-V147
Tími: Mánudagur 18. júní kl. 10:50

Ágrip:

I will introduce a model of random trees which are constructed by iteratively gluing an infinite number of segments of given length onto each other. This model can be generalized to a gluing of „blocks“ that are more complex than segments. We are interested in the metric properties of the limiting metric space, mainly its Hausdorff dimension. We will show that its Hausdorff dimension depends in a non-trivial (and surprising !) manner on the different scaling parameters of the model and the dimension of the blocks.

Tony Guttmann (28/05/18)

Anders Claesson, maí 25, 2018

Málstofa í stærðfræði

Fyrirlesari: Tony Guttmann, The University of Melbourne

Titill: On the number of Av(1324) permutations

Staðsetning: V-147 (VR-II)
Tími: Mánudagur 28. maí kl. 10:50

Ágrip:

We give an improved algorithm for counting the number of 1324-avoiding permutations, resulting in 14 further terms of the generating function, which is now known to length 50.
We re-analyse the generating function and find compelling evidence that unlike other classical length-4 pattern-avoiding permutations, the generating function does not have a simple power-law singularity, but rather, the number of 1324-avoiding permutations of length n behaves as \(B\cdot \mu^n \cdot \mu_1^{\sqrt{n}} \cdot n^g\).
We estimate \(\mu = 11.600 \pm 0.003.\) The presence of the stretched exponential term \(\mu_1^{\sqrt{n}}\) is an unexpected feature of the conjectured solution, but we show that such a term is present in a number of other combinatorial problems.
(A.J. Guttmann with A.R. Conway and P. Zinn-Justin)

Michael Melgaard (13/04/18)

Anders Claesson, apríl 10, 2018

Málstofa í stærðfræði

Fyrirlesari: Michael Melgaard, University of Sussex

Titill: Rigorous mathematical results on nonlinear PDEs arising in Quantum Chemistry

Staðsetning: V-147 (VR-II)
Tími: Föstudagur 13. apríl kl. 13:30

Ágrip:

An introduction to electronic structure models is given and rigorous results are discussed on the existence of solutions (ground states and excited states) to weakly coupled, semi-linear elliptic PDEs with nonlocal operators arising in Hartree-Fock, Kohn-Sham and multiconfigurative many-particle models in quantum chemistry, in particular for systems with relativistic effects and external magnetic fields.

Anthony Thomas Lyons (26/03/18)

Anders Claesson, mars 22, 2018

Málstofa í stærðfræði

Fyrirlesari: Anthony Thomas Lyons, Waterford Institute of Technology

Titill: The dressing method for the Camassa-Holm equation

Staðsetning: HB-5 (Háskólabíó)
Tími: Mánudagur 26. mars kl. 10:50

Ágrip:

The Camassa-Holm equation is a nonlinear shallow water model which has been the focus of a great deal of mathematical research in hydrodynamics for the past two decades. This interest is in part due to the versatility of the system, being relevant as a fluid model possessing solutions which display wave-breaking along with global solutions in the form of soliton, peakon and cuspon solutions.
The inverse scattering transform has been successfully implemented to construct numerous global solutions of this system, and in this talk we present a recently developed variation of this method for the Camassa-Holm equation, known as the dressing method. This efficient implementation allows one to integrate several nonlinear hydrodynamical models, and in particular we shall outline the details of this new dressing method and use it to construct the one and two-soliton solutions of the Camassa-Holm equation.

Phillip Wesolek (05/03/18)

Anders Claesson, mars 1, 2018

Málstofa í stærðfræði

Fyrirlesari: Phillip Wesolek, Binghamton University

Titill: Totally disconnected locally compact groups: from examples to general theory

Staðsetning: HB-5 (Háskólabíó)
Tími: Mánudagur 5. mars kl. 10:50

Ágrip:

Locally compact groups arise in many areas of mathematics as well as in physics. The study of locally compact groups splits into two cases: the connected groups and the totally disconnected groups. There is a rich and deep theory for the connected groups, which was developed over the last century. On the other hand, the study of totally disconnected locally compact groups groups only seriously began in the last 30 years, and moreover, these groups today appear to admit an equally rich and deep theory. In this talk, we will explore in details a wide variety of examples of totally disconnected locally compact groups. In particular, we discuss Lie groups over over the p-adic numbers, Galois groups, and automorphism groups of locally finite trees. We will then survey some recent results in the theory of totally disconnected locally compact groups.

Málstofa í stærðfræði

Anders Claesson, febrúar 15, 2018

Fyrirlesari: Alexander Wendland, University of Warwick

Titill: Facially restricted graph colouring’s

Staðsetning: HB-5 (Háskólabíó)
Tími: Mánudagur 19. febrúar kl. 10:50

Ágrip:

Arguably one of the best known theorems from combinatorics is the four colour theorem, stating that every planar graph can be coloured using at most four colours such that no edge connects two vertices of the same colour. In this talk I will discus variants on this theorem in particular list colouring’s and facial restriction’s on the colouring. In this, I present the method of discharging in Graph Theory, used to finally prove the four colour theorem nearly 140 years after it was first stated, which has been used to prove theorems elsewhere in Mathematics.

Hjörtur Björnsson (27/11/17)

Anders Claesson, nóvember 23, 2017

Málstofa í stærðfræði

Fyrirlesari: Hjörtur Björnsson, University of Iceland

Titill: Lyapunov functions for almost sure exponential stability

Staðsetning: VRII-158
Tími: Mánudagur 27. nóvember kl. 15:00

Ágrip:

We present a generalization of results obtained by X. Mao in his book „Stochastic Differential Equations and Applications“ (2008). When studying what Mao calls „almost sure exponential stability“, essentially a negative upper bound on the almost sure Lyapunov exponents, he works with Lyapunov functions that are twice continuously differentiable in the spatial variable and continuously differentiable in time. Mao gives sufficient conditions in terms of such a Lyapunov function for a solution of a stochastic differential equation to be almost surely exponentially stable. Further, he gives sufficient conditions of a similar kind for the solution to be almost surely exponentially unstable. Unfortunately this class of Lyapunov functions is too restrictive. Indeed, R. Khasminskii showed in his book „Stochastic Stability of Differential Equations“ (1979/2012) that even for an autonomous stochastic differential equation with constant coefficients, of which the solution is stochastically stable and such that the deterministic part has an unstable equilibrium, there cannot exists a Lyapunov function that is differentiable at the origin. These restrictions are inherited by Mao’s Lyapunov functions. We therefore consider Lyapunov functions that are not necessarily differentiable at the origin and we show that the sufficiency conditions Mao proves can be generalized to Lyapunov functions of this form.

Sigurður Freyr Hafstein (13/11/17)

Anders Claesson, nóvember 9, 2017

Málstofa í stærðfræði

Fyrirlesari: Sigurður Freyr Hafstein, University of Iceland

Titill: Dynamical Systems and Lyapunov functions

Staðsetning: VRII-158
Tími: Mánudagur 13. nóvember kl. 15:00

Ágrip:

We discuss dynamical systems and the theory of Lyapunov functions and complete Lyapunov functions. Further, we discuss several different numerical methods for the computation of Lyapunov functions and the corresponding estimation of basins of attraction.