## Daniel Friedan (26/08/16)

Sigurður Örn Stefánsson, ágúst 22, 2016

Málstofa í stærðfræði

### 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:

I will describe an attempt to define a mathematical structure – „quasi
Riemann surface“ – in which the points of a Riemann surface are replaced
by the integral 0-currents. The same structure is found in the spaces
of integral relative (n-1)-cycles in a conformal manifold M of dimension
d=2n >= 4. The quasi Riemann surfaces associated to M form a natural
fiber bundle Q(M) -> B(M) over the space of integral lines in the space
of integral (n-2)-currents in M.

A goal is to re-express analysis in Riemann surfaces as analysis in the
corresponding quasi Riemann surfaces, so that it will apply also to the
spaces of integral relative (n-1)-cycles in conformal manifolds M. I
hope to use this structure to construct a new class of quantum field
theories in space-time manifolds of dimension d=2n >= 4 from the known
quantum field theories in two-dimensional manifolds.

I offer some speculations on the classification of quasi Riemann
surfaces, leading to pictures of universal homogeneous bundles in which
all the Q(M) -> B(M) are naturally embedded. The strongest form of this
speculation would equate every quasi Riemann surface to a quasi Riemann
surface associated to some two-dimensional manifold. Such isomorphisms
could be used to transport two-dimensional quantum field theories
directly to higher dimensional manifolds M.

I am seeking mathematical advice — is this structure known? is it
feasible? — and trying to raise interest in making the structure
mathematically solid. Aside from possible applications to quantum field
theory, the structure might be useful in the study of manifolds.

## Brittany A. Erickson (08/08/16)

Sigurður Örn Stefánsson, ágúst 4, 2016

Málstofa í stærðfræði

### 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.

## Anthony Bonato (30/06/16)

Sigurður Örn Stefánsson, júní 27, 2016

Málstofa í stærðfræði

### 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.

## Sylvain Arguillère (24/06/16)

Sigurður Örn Stefánsson, júní 21, 2016

Málstofa í stærðfræði

### 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.

Benedikt Magnússon, maí 31, 2016

Málstofa í stærðfræði

### 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.

## Alessandra Cagnazzo (20/05/16)

Málstofa í stærðfræði

### 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.

Benedikt Magnússon, apríl 9, 2016

Applications are invited for a PhD position in theoretical high-energy physics at the University of Iceland with a starting date in Fall 2016. The position is funded by a grant from the Icelandic Research Fund.

The successful candidate will work in the area of quantum field theory and string theory with emphasis on gauge theory/gravity duality and holographic models for strongly coupled field theories. A master degree, or equivalent, in theoretical physics is required.

The application deadline is May 6, however applications will continue to be accepted until the position is filled.

Applications should be submitted electronically to

and should include a CV, transcripts from undergraduate and master studies, a short description of research interests, and names and e-mail addresses of two referees, who have agreed to provide recommendation letters.

Ass. Prof. Valentina Giangreco Puletti (e-mail: vgmp[at]hi.is) or
Prof. Lárus Thorlacius (e-mail: lth[at]hi.is)

Faculty of Physical Sciences
University of Iceland

## Eggert Briem (08/04/16)

Sigurður Örn Stefánsson, apríl 4, 2016

Málstofa í stærðfræði

### 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.

## Jakob Björnberg (01/04/16)

Málstofa í stærðfræði

### 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.

## François David (11/03/16)

Málstofa í stærðfræði

### 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).