Math Colloquium

### Speaker: Þórður Jónsson, University of Iceland

Title: Exponential bounds on the number of triangulations

Location: Naustið, Endurmenntun (here)

Time: Thursday, March 26., at 15:00-16:00.

### Abstract:

We discuss the problem of bounding the number of 3-dimensional triangulations of the sphere as a function of the number of tetrahedra. We show how to establish an exponential bound in the case of locally constructible triangulations as well as causal triangulations. We also discuss the same problem in 4 dimensions.

Math Colloquium

### Speaker: Razieh Pourhasan, University of Iceland

Title: Out of the white hole: a holographic origin for the Big Bang

Location: Naustið, Endurmenntun (here)

Time: Thursday, February 26., at 15:00-16:00.

### Abstract:

While most of the singularities of General Relativity are expected to be safely hidden behind the event horizons by the cosmic censorship conjecture, we happen to live in the causal future of the classical big bang singularity, whose resolution constitutes the active field of early universe cosmology. Could the big bang be also hidden behind a causal horizon, making us immune to the decadent impacts of a naked singularity? We describe a braneworld description of cosmology with both 4d induced and 5d bulk gravity (otherwise known as Dvali- Gabadadze-Porati, or DGP model), which exhibits this feature: The universe emerges as a spherical 3-brane from the gravitational collapse of 5d matter, in the process of formation of a 5d Schwarzschild black hole. That is, in this holographic picture, it is possible to avoid the big bang singularity. We further propose a holographic origin for the big bang: a pressure singularity of the holographic fluid, which happens inside the white hole horizon, and thus need not be real or imply any pathology.

This is a talk based on my recent paper published in JCAP 04 (2014) 005 [arXiv:1309.1487], a collaboration with Niayesh Afshordi at the Perimeter Institute and Robert B. Mann at the University of Waterloo. Because of the novelty of the model, this work attracted a great deal of attention in the media particularly featured in Nature News in September 2013, and also in the August 2014 edition of Scientific American as the cover article.

Math Colloquium

### Speaker: Timo Alho, University of Iceland

Title: Clifford algebra as the fundamental structure of geometry, Part II

Location: Naustið, Endurmenntun (hér)

Time: Thursday, February 12., at** 16:00-17:00.**

### Abstract:

Today, elementary geometry is practiced in a variety of formalisms, such as Gibbs-Heaviside vector calculus, quaternions, exterior algebra and calculus, index gymnastics, and so on. Each of these formalisms has a number of advantages and a number of disadvantages. The aim of this talk is to acquaint the audience with a formalism called Geometric Algebra (GA), originated by Clifford and developed in its modern form by

Hestenes. All of the aforementioned formalisms are special cases of Geometric Algebra, which provides a unified and coordinate-free system for geometry in inner product spaces. We intend in this talk to make and justify the claim that GA is superior to all standard methods of doing geometry, and should be more widely known, studied, taught and used in research.

#### References:

Math Colloquium

### Speaker: Timo Alho, University of Iceland

Title: Clifford algebra as the fundamental structure of geometry

Location: Naustið, Endurmenntun (hér)

Time: Thursday, February 5., at 15:00-16:00.

### Abstract:

Today, elementary geometry is practiced in a variety of formalisms, such as Gibbs-Heaviside vector calculus, quaternions, exterior algebra and calculus, index gymnastics, and so on. Each of these formalisms has a number of advantages and a number of disadvantages. The aim of this talk is to acquaint the audience with a formalism called Geometric Algebra (GA), originated by Clifford and developed in its modern form by

Hestenes. All of the aforementioned formalisms are special cases of Geometric Algebra, which provides a unified and coordinate-free system for geometry in inner product spaces. We intend in this talk to make and justify the claim that GA is superior to all standard methods of doing geometry, and should be more widely known, studied, taught and used in research.

Mini course

### Speaker: Andrzej Borowiec

Title: Twisted techniques in deformation quantization.

Part 2: Thursday, September 11th, 16:00-17:30 in room V-156, VR-II.

Part 3: Friday, September 12th, 15:00-16:30 in room V-155, VR-II.

### Abstract:

Deformation quantization is a generalization of Weyl quantization extended to Poisson manifolds (Fedosov, Kontsevich). It is based on deformation theory of algebraic structures introduced by Gerstenhaber.

Twisted tensor techniques proposed by Drinfeld in the context of quantum groups become an important tool of noncommutative geometry for constructing new quantum spaces and their symmetries. I will show how these notions are related and briefly discuss some recent results.

Part 2 will start with a brief summary of Part 1.

Math Colloquium

### Speaker: Andrzej Frydryszak, Institute for Theoretical Physics, University of Wroclaw

Title: Heisenberg supergroup in phase superspace

Location: V-157, VRII

Time: Monday September 8th, at 15:00-16:00.

### Abstract:

I will discuss a generalization of the Heisenberg group and the harmonic analysis on it to superspace, and show that the super-Heisenberg group plays similar role to its original when super-Schroedinger quantization is considered. I will comment on recent developments in the representations of nilpotent supergroups.

Math Colloquium

### Speaker: Jerzy Lukierski, Institute for Theoretical Physics, University of Wroclaw

Title: Quantum Gravity – a brief conceptual summary

Location: V-156, VRII

Time: Thursday Sept. 4th, at 15:00-16:00.

### Abstract:

After short historical overview we describe the difficulties with

application of standard QFT methods in quantum gravity (QG). The

incompatibility of QG with the use of classical continuous space-time required conceptually new approach. We present briefly three proposals: loop quantum gravity (LQG), the field-theoretic framework on noncommutative space-time and QG models formulated on discretized (triangularized) space-time. We evaluate these models as realizing expected important properties of QG: background independence, consistent quantum diffeomorphisms, noncommutative or discrete structure of space-time at very short distances, finite/renormalizable QG corrections. We only briefly outline an important issue of embedding QG into larger geometric and dynamical frameworks (e.g. supergravity, (super)strings, p-branes, M-theory), with the aim to achieve full unification of all fundamental interactions. [Based on arXiv:1404:6797[hep-th]].

Math Colloquium

### Speaker: Andrzej Borowiec, University of Wroclaw, Institute for Theoretical Physics

Title: Twisted techniques in deformation quantization

Location: V-155, VRII

Time: Thursday August 28., at 16:00 – 17:30.

### Abstract:

Deformation quantization is a generalization of Weyl quantization extended to Poisson manifolds (Fedosov, Kontsevich). It is based on deformation theory of algebraic structures introduced by Gerstenhaber. Twisted tensor techniques proposed by Drinfeld in the context of quantum groups become an important tool of noncommutative geometry for constructing new quantum spaces and their symmetries. I will show how these notions are related and briefly discuss some recent results.

Math Colloquium

Location: V-158, VR-II.

Time: Tuesday April 29, 2014, at 12:00 to 13:00.

### Abstract:

In the last 10 years two-dimensional integrable models have been largely employed in string theory, and in particular in the context of the so-called gauge/gravity duality. Indeed, the discovery of these infinitely many “hidden’’ conserved charges, i.e. the integrability, has lead to immense progresses in understanding and confirming the duality. I will mostly review fundamental concepts and properties of those integrable models which are relevant to string theory (symmetric and semi-symmetric sigma-models), and I will briefly illustrate the main motivations behind this success.