Math
Phys seminar

**Fyrirlesari: ****Jakob Björnberg****,
****Chalmers University of Technology**

**Titill: **Random permutations and Heisenberg models.

#### Ágrip:

We discuss probabilistic representations of
certain quantum spin systems, including the ferromagnetic Heisenberg model, in
terms of random permutations. Properties of the cycle structure of the random
permutations are connected with phase transitions in the spin-system. In particular, it is expected that the cycle
structure converges to a distribution known as Poisson–Dirichlet, in the limit
of large systems. This problem is open
but we present some partial progress.

Math
colloquium

**Fyrirlesari: Lukas
Schneiderbauer, Háskóli Íslands**

**Titill: **Non-Commutative Geometry: An introduction.

#### Ágrip:

This is my attempt to introduce non-commutative
geometry to mathematicians. After putting forward the main ideas and main theorem(s),
I will concentrate on the construction of simple examples in the context of
fuzzy spaces (special cases of non-commutative geometries). In case time still
allows it, I shall tell you about my past research in this area.

Math
colloquium

**Fyrirlesari: Anna Helga Jónsdóttir og Benedikt Steinar Magnússon, Háskóli Íslands**

**Titill 1: ** Student evaluations of teaching at the University of Iceland – analysis of data from 2013 – 2017

#### Ágrip 1:

Student evaluations of teaching (ísl. kennslukönnun) is administrated at the end of each and every course at the University of Iceland with the purpose of improving teaching and learning. In the talk, analysis of data from student evaluations from 2013 to 2017 at the UI will be presented. Mixed effect models were used to investigate possible relationships between the grades students give courses and several variables, such as the age and gender of the student and the teacher, number of students taking the course and the average final grade in the course.

**Titill 2: **Online course notes in Edbook and the role of the textbook

#### Ágrip 2:

In the last years I, with the help of many good people, have been developing a platform for online course notes called Edbook (http://edbook.hi.is). It consists of using Sphinx, which was developed for and in Python, along with specialized extension suited for teaching material in Mathematics. We have been using these notes in a few courses, mostly big calculus courses. The students have overall been very happy with them but in the spring of 2019 I had students in Mathematical Analysis II (STÆ205G) answer a more detailed survey about their usage of the teaching material they used. I will introduce the Edbook platform and the results of the survey which raises some questions about the role of the textbook today.

Staðsetning: HB5 (Háskólabíó)

Tími: Föstudag 15.nóvember kl. 11:40

Room: HB5 (Háskólabíó)

Time: Friday 22^{th} November, 11:40hrs

Math
colloquium

**Fyrirlesari: ****Sigurður Freyr Hafstein****, **Háskóli
Íslands

**Titill: **Lyapunov functions for stochastic differential equations and their
computation

Staðsetning:
HB5 (Háskólabíó)

Tími: Föstudag 15.nóvember kl. 11:40

#### Ágrip:

Attractors and their basins of attraction in deterministic dynamical systems are most commonly studied using the Lyapunov stability theory. Its centerpiece is the Lyapunov function, which is an energy-like function from the state-space that is decreasing along all solution trajectories.

The Lyapunov stability theory for stochastic differential equations is much less developed and, in particular, numerical methods for the construction of Lyapunov functions for such systems are few and far between. We discuss the general problem and present some novel numerical methods.

Math colloquium

**Fyrirlesari: Iman Mehrabinezhad, **Háskóli Íslands

**Titill: **A new method for computation and verification of contraction
metrics

Staðsetning: HB5 (Háskólabíó)

Tími: Föstudag 8.nóvember kl. 11:40

#### Ágrip:

The determination of exponentially stable equilibria and their basin of attraction for a dynamical system given by a general autonomous ordinary differential equation can be achieved by means of a contraction metric. A contraction metric is a Riemannian metric with respect to which the distance between adjacent solutions decreases as time increases.

The Riemannian metric can be expressed by a matrix-valued function on the phase space.The determination of a contraction metric can be achieved by approximately solving a matrix-valued partial differential equation by mesh-free collocation using Radial Basis Functions (RBF).

Then, we combine the RBF method (to compute a contraction metric) with the CPA method to rigorously verify it. In particular, the computed contraction metric is interpolated by a continuous piecewise affine (CPA) metric at the vertices of a fixed triangulation, and by checking finitely many inequalities, we can verify that the interpolation is a contraction metric. Moreover, we show that, using sufficiently dense collocation points and a sufficiently fine triangulation, we always succeed with the construction and verification.

This presentation is based on a joint work with Prof. Sigurdur Hafstein (University of Iceland), and Prof. Peter Giesl (University of Sussex, UK).

Math Phys seminar

### Fyrirlesari: Daniel Fernández Moreno, Háskóli Íslands

### Titill: The philosophy of emergent spacetime

Staðsetning: HB5 (Háskólabíó)

Tími: Föstudag 18.oktúber kl. 11:40

Ágrip:

One of the most startling observations in recent theoretical physics is that certain phenomena are better described as resulting from a higher dimensional spacetime. The gauge-gravity correspondence projects them into a surface infinitely far away. The existence of such a duality between two fully consistent physical theories reduces the number of spacetime dimensions to a mere choice, one that can be more or less useful depending on the physics we want to describe.

This observation brought forth the idea that Spacetime should be understood as an emergent property from quantum field theory. This is usually presented in abstract grounds, disconnected from its consequences on our theoretical perspective of fundamental physics. Consequences which challenge the basic intuitions from classical physics that are otherwise vastly useful in most situations. For this reason, as opposed to most seminars in the topic, this talk will ignore the structure of the reasoning and the mathematical rigor. Instead, I will present to you the topic of emergent Spacetime focused on gaining an intuitive feeling about the connection of such a seemingly abstract concept with the real world.

Math colloquium

#### Fyrirlesari: Danny Brattan, University of Genoa

#### Titill: Hydrodynamical charge density wave description for transport in the strange metal phase of cuprates

Staðsetning: Naustið-Endurmenntun

Tími: Miðvikudag 9.oktúber kl. 11:00

**Ágrip:**

The mechanism controlling the exotic behavior of the transport properties in the strange metallic phase of high temperature superconductors is one of the main unresolved problems in condensed matter physics. I will discuss our recent paper (1909.07991) where we develop a framework for describing the hydrodynamics of charge density wave (CDW) order in a magnetic field (extending earlier theoretical developments) and where we determine the DC transport coefficients within this formalism. In this work we performed a complete characterization of the DC transport coefficients (including less common ones like transverse thermal conductivity and Nernst effect) of a single crystal of Bi-2201 close to optimal doping and we found complete self-consistent agreement of this data with the CDW model. This suggests CDW order may be sufficient to explain the unusual properties of the strange metal phase of the cuprates.

Math phys colloquium

**Fyrirlesari: **Emil Have, University of Edinburgh

**Titill: **Newton-Cartan Submanifolds and Biophysical (Fluid) Membranes

Staðsetning: L-201 Lögberg

Tími: Þriðjudag 8.oktúber kl. 11:00

#### Ágrip:

Originally developed to provide a geometric foundation for
Newtonian gravity, Newton-Cartan geometry and its torsionful generalization
have recently experienced a revival of interest, particularly in the contexts
of non-AdS holography and various condensed matter problems — notably the quantum
Hall effect. In this talk, I will describe a general theory of Newton-Cartan
submanifolds. A covariant description of non-relativistic fluids on surfaces is
an important open problem with a wide range of applications in for example
biophysics. Recasting ‘elastic’ models, such as the Canham-Helfrich bending
energy, in a Newton-Cartan setting allows for a covariant notion of
non-relativistic time and provides the ideal starting point for a treatment of
Galilean fluids on extremal submanifolds using the technology of hydrostatic
partition functions.

Math colloquium

**Fyrirlesari: Henning Arnór Úlfarsson,
Háskólinn í Reykjavík**

**Titill: **Pattern avoidance in various domains

Staðsetning: HB5 (Háskólabíó)

Tími: Föstudag 25.oktúber kl. 11:40

#### Ágrip:

When one searches the web for „pattern avoidance“ most of the results are about pattern avoiding permutations and their variants, such as colored, partial, multi-, affine, signed, and poset permutations. However there are definitions and results about similar concepts in other objects, such as graphs and topological spaces. We will survey these examples of pattern avoidance as well as highlighting more recent variants, such as polyominoes, integer partitions and alternating sign matrices.

This talk will be accessible to any student who has walked past a room where discrete mathematics was being taught.

Math Phys seminar

**Fyrirlesari: Jesús Zavala Franco, Háskóli
Íslands og Javier Israel Reynoso Córdoba, Universidad de Guanajuato**

**Titill: **The Boltzmann equation for a rarefied fluid in linear perturbation
theory

Staðsetning: HB5 (Háskólabíó)

Tími: Föstudag 4.oktúber kl. 11:40

#### Ágrip:

Linear perturbation theory is the basis upon which we understand
the initial growth of density perturbations in the early Universe. This theory
has been developed and studied extensively in two extreme regimes: i) the fluid
regime and ii) the collisionless regime. The former is applicable to the
photon-baryon plasma, while the latter is commonly used to describe dark
matter. There is however, a relevant class of dark matter models, known
generically as self-interacting dark matter, where the Knudsen number is around
1, which lies in between these regimes. Linear perturbation theory in this
regime remains essentially unexplored, requiring a full treatment of the
Collisional Boltzmann equation. In this talk, we will present an overview of
the problem and present our preliminary progress towards describing this regime.