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### Fyrirlesari: Rögnvaldur Möller, University of Iceland

### Titill: Highly-arc-transitie digraphs of prime out-valency

Staðsetning: V-158, VRII

Tími: Mánudaginn 19. september kl. 15:00

### Ágrip:

Joint work with Primoz Potocnik, Ljubljana, and Norbert Seifter, Leoben.

The concept of a highly-arc-transitive digraph was defined by Cameron, Praeger and Wormald in a paper that appeared in 1993. Examples constructed by various people have shown that suggestions put forward in that paper are wrong. But if it assumed that the highly-arc-transitive digraph has prime out-valency then some of the suggestions of Cameron, Praeger and Wormald are correct. The second part of the talk is about a general method to construct k-arc-transitive digraphs that are not (k+1)-arc-transitive. This construction gives examples that limit the possibilities of extending the results in the first part and also give examples of digraphs with polynomial growth that are k-arc-transitive but not (k+1)-arc-transitive

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### Fyrirlesari: Daniel Friedan, Rutgers University and University of Iceland

Titill: Quasi Riemann Surfaces

Staðsetning: TG-227 (Tæknigarður, 2. hæð)

Tími: Föstudagur 26. ágúst kl. 13:20.

### Ágrip:

This will be a talk about some speculative mathematics (analysis) with

possible applications in quantum field theory. I will leave any mention

of quantum field theory to the end. I will try to define everything

from scratch, but it probably will help to have already seen the basics

of manifolds, differential forms, and Riemann surfaces.

The talk is taken from my recent paper

„Quantum field theories of extended objects“, arXiv:1605.03279 [hep-th]

which is a mixture of speculative quantum field theory and speculative

mathematics. In the talk, the speculative mathematics will be presented

on its own, without the motivations from quantum field theory.

Below is the abstract from a note I am presently writing to try to

interest mathematicians in looking at this structure:

Continue reading 'Daniel Friedan (26/08/16)'»

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### Fyrirlesari: Brittany A. Erickson

Titill: A Finite Difference Method for Plastic Response with an Application to the Earthquake Cycle

Staðsetning: V-157, VR-II.

Tími: Mánudagur 8. ágúst kl. 13:20.

### Ágrip:

We are developing an efficient, computational framework for simulating multiple earthquake cycles with off-fault plastic response. Both rate-independent and viscoplasticity are considered, where stresses are constrained by a Drucker-Prager yield condition. The constitutive theory furnishes a nonlinear elliptic partial differential equation which must be solved through an iterative procedure. A frictional fault lies at an interface in the domain. The off-fault volume is discretized using finite differences satisfying a summation-by-parts rule and interseismic loading is accounted for at the remote boundaries through weak enforcement of boundary conditions. Time-stepping is done through an incremental solution process which makes use of an elastoplastic tangent stiffness tensor and the return-mapping algorithm to obtain stresses consistent with the constitutive theory. Solutions are verified by convergence tests along with comparison to a finite element solution. I will conclude with some application problems related to earthquake cycle modeling.

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### Fyrirlesari: Anthony Bonato

Titill: Conjectures on Cops and Robbers Games on Graphs

Staðsetning: TG-227 (Tæknigarður, 2. hæð)

Tími: Fimmtudagur 30. júní kl. 13:20.

### Ágrip:

The game of Cops and Robbers gives rise to a rich set of conjectures, mainly associated with the cop number of a graph. Arguably the most important such conjecture is Meyniel’s, which posits a \(O(n^{1/2})\) upper bound on the cop number of a connected graph of order n. We discuss the state-of-the-art on Meyniel’s conjecture, and explore other conjectures on cop number ranging from topics within computational, probabilistic, and topological graph theory.

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### Fyrirlesari: Sylvain Arguillère

Titill: Constrained Shape Analysis Through Flows of Diffeomorphisms

Staðsetning: TG-227 (Tæknigarður, 2. hæð)

Tími: Föstudagur 24. júní kl. 13:20.

### Ágrip:

The general purpose of shape analysis is to compare different shapes in a way that takes into account their geometric properties, such as smoothness, number of self-intersection points, convexity… One way to do this is to find a flow of diffeomorphisms that brings one (template) shape as close as possible to the other (target) shape while minimizing a certain energy. This is the so-called LDDMM method (Large Deformation Diffeomorphic Metric Matching).

Finding this minimizing flow requires solving an optimal control problem that can be seen as looking for (sub-)Riemannian geodesics on the infinite dimensional group of diffeomorphisms with respect to a right-invariant (sub-)Riemannian structure, creating a framework reminiscent of fluid mechanics, and opening the door to some new and exciting infinite dimensional geometries.

In this talk, I will introduce all these concepts, and give the geodesic equations for such structures. Then, I will extend this framework to the case where constraints are added to the shape, in order to better describe the objects they represent, and give some applications in computational anatomy.

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### Fyrirlesari: Adam Timar, Renyi Institute, Budapest

Titill: Allocation rules for the Poisson point process

Staðsetning: Árnagarður 101.

Tími: Föstudagur 3. júní, klukkan 13:20-14:20.

### Ágrip:

Consider the Poisson point process in Euclidean space. We are interested in functions on this random point set whose value in each configuration point is given by some „local“ rule (no „central planning“). One example is the so-called allocation problem, where we want to partition R^d to sets of measure 1 and match them with the point process, in a translation equivariant way. We want to make the allocated set optimal in some sense (e.g., the distribution of the diameter shows fast decay). We will present some allocation schemes, among them one with an optimal tail, which is joint work with R. Marko.

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### Fyrirlesari: Alessandra Cagnazzo

Titill: Anomalous dimension in 2d non-linear sigma models.

Staðsetning: TG-227, (tæknistofan, annarri hæð í Tæknigarði)

Tími: Föstudagur 20. maí kl. 13:20.

### Ágrip:

2d non-linear sigma models are widely used in high and low energy physics. In my talk I will present how to compute the one-loop anomalous dimension for fields in some cases in which the background is a coset space. I will review the formula for the case in which the background is a symmetric coset (that admits a \(Z_2\) automorphism) and present the new result for \(Z_4\)-cosets. The last result is applicable to the string described by the pure spinor formalism on \(\mathrm{AdS}_5\times S^5\) and it is relevant for AdS/CFT.

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### Fyrirlesari: Eggert Briem

Titill: Real Banach algebras and norms on real \(C(X)\) spaces.

Staðsetning: V-157, VRII.

Tími: Föstudagur 8. apríl kl. 13:20.

### Ágrip:

A commutative *complex* unital Banach algebra can be represented as a space of continuous functions on a compact Hausdorff space via the Gelfand transform. However, in general it is not possible to represent a commutative *real* unital Banach algebra as a space of continuous real-valued functions on some compact Hausdorff space, additional conditions are needed. We shall discuss conditions which imply isomorphic representations and also discuss various complete algebra norm on real \(C(X)\) spaces which arise from such representations.

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### Fyrirlesari: Jakob Björnberg

Titill: Random permutations and quantum Heisenberg models

Staðsetning: V-157, VRII.

Tími: Föstudagur 1. apríl kl. 13:20.

### Ágrip:

The interchange process (or random-transposition random walk) is a model for random permutations which is closely related to a model from quantum statistical physics (the ferromagnetic Heisenberg model). In fact, certain ‘cycle-weighted’ interchange processes are equivalent to the latter, and in this talk we present results on such processes. Magnetic ordering in the physical model translates to the occurrence of large cycles in the random permutation.

We focus on the case when the underlying graph is the complete graph (i.e. the ‘mean-field’ case in physical jargon). By a combination of probabilistic techniques and some group character theory we can obtain nice formulas for expectation values in the model, and then use these to identify the critical point.

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### Fyrirlesari: François David

Titill: Planar maps, circle patterns and 2D gravity

Staðsetning: V-157, VRII.

Tími: Föstudagur 11. mars kl. 13:20.

### Ágrip:

I present a model of random planar triangulations (planar maps) based on circle patterns and discuss its properties. It exemplifies the relations between discrete random geometries in the plane, conformally invariant point processes and two dimensional quantum gravity (Liouville theory and topological gravity).