List of Talks

Prof. Murat Limoncu - The Ricci Flow in Riemannian Manifolds

The Ricci flow is an important tool in understanding the geometry of manifolds. I will outline the main points of the Ricci flow and Perelman's modified Ricci flow.

(This talk will be held in Turkish.)

Dr. Can Kozçaz - AGT Conjecture and Its Embedding in String Theory

Alday-Gaiotto and Tachickawa conjectured a remarkable relationship between 2d Liouville conformal field theory and 4d Seiberg-Witten theory following the work of Gaiotto to construct 4d N=2 theories from 6d (2,0) superconformal field theory. The original conjecture has been extended in many different directions using various string theory constructions. In this talk, I will review some of them and review some results.

Dr. Nihan Katırcı - (An)Isotropy and Cosmic Acceleration

We discuss anisotropy in expansion of Universe in this talk. After giving the standard evolution of expansion anisotropy, we then elaborate on expansion dynamics both in standard general relativity in the presence of anisotropic sources (e.g., restrained anisotropy [1] ) and in modified gravity theories (e.g., Brans-Dicke theory [2] ) which can be recast as effective dark energy source in general relativity. This raises the question: Which of the following can cause accelerated expansion of the Universe today, dark energy or modified gravity? We conclude the talk with a discussion about distinguishing them considering the anisotropy in expansion.

References:

[1] Extending ΛCDM model with restrained anisotropy, O. Akarsu, N. Katirci, A. A. Sen and J. A. Vazquez.

[2] Anisotropic massive Brans-Dicke gravity extension of the standard ΛCDM model, O. Akarsu, N. Katirci, N. Ozdemir and J. A. Vazquez, arXiv: 1903.06679.

Dr. Razieh Morad - Jets in Quark-Gluon Plasma

The spectacular measurements from the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) provide compelling evidence that the matter produced in heavy ion collision is a deconfined state of QCD, Quark- Gluon Plasma (QGP), at temperatures above ~160 MeV which appears to be nearly perfect, with an extremely low viscosity-to-entropy ratio η/s ~ 1/4π.

The “AdS/CFT correspondence” which imposes the duality between the gauge theory and gravity is a novel tool provides valuable insight into the strongly coupled plasma. The most important result of AdS/CFT is calculating the value of shear viscosity to entropy density ratio which is in remarkable agreement with the hydrodynamics predictions.

We study the energy loss rate of light quarks in the hot, strongly coupled plasma via AdS/CFT correspondence. Unlike heavy quarks, light quark energy loss in AdS/CFT is surprisingly dependent on both the string initial conditions, and the very definition of the jet itself in the gravity theory. Jets in general thermalize very quickly in a strongly-coupled plasma compare to the experimental data. We aim to more closely match the gravity dual to QGP and the string initial conditions to those expected from pQCD by computing the energy-momentum tensor associated with the propagation of the classical string solution.

Kadri İlker Berktav - Towards the Stacky Formulation of Einstein Gravity

This talk, which essentially consists of three parts, serves as a conceptional introduction to the formulation of Einstein gravity in the context of derived algebraic geometry. The upshot is as follows: we shall first outline main ingredients of category theory, and using the functorial approach, we define the notion of a stack in a relatively succinct and naive way. Having adopted the language of stacks, one is able to make sense of a notion so-called a moduli problem which, roughly speaking, is about constructing a classifying space (or a moduli space) for certain geometric objects (such as manifolds, algebraic varieties, vector bundles etc...) up to their intrinsic symmetries (e.g. gauge equivalences, diffeomorphism invariance etc...). As an analyzing a classical field theory with an action functional S boils down to the study of the moduli space of solutions to the corresponding Euler-Lagrange equations, the notion of a moduli problem in fact provides an alternative and a beautiful mathematical framework for recording and organizing the moduli data in a more elegant way. In the second part of the talk, we shall revisit main aspects of 2+1 dimensional vacuum Einstein gravity on a pseudo-Riemannian manifold M especially in the context of Cartan geometry, and introduce, in the case of M = Σ × (0, ∞) and Λ = 0 where Σ is a closed Riemann surface of genus g > 1, the equivalence of the quantum gravity with a gauge theory in the sense that the moduli space E(M) of such a 2+1 dimensional Einstein gravity is isomorphic to that of flat Cartan ISO(2, 1)-connections, denoted by M_flat. In the final part, we shall briefly discuss (i) how to construct the appropriate stacks associated to E(M) and M_flat respectively, and (ii) how to extend the isomorphism that essentially captures the equivalence of the quantum gravity with a gauge theory in the above setup to an isomorphism of associated stacks.

Keremcan Doğan - Spectral Singularities in Mathematical Optics (Cancelled)

Spectral singularities are certain points of the continuous spectrum of a complex scattering potential. They bring obstructions for a non-Hermitian operator to be Hermitizable. For certain complex potentials, these spectral singularities describe some key optical properties. Together with non-linear generalizations, their existence yields simple mathematical derivations of some basic results of laser physics. By using two basic postulates in the examination of spectral singularities for TE modes of a slab Fabry-Perot resonator, one can reveal the details of the threshold gain and the output intensity.

Reference:

K. Doğan, A. Mostafazadeh, and M. Sarisaman, “Spectral Singularities, Threshold Gain, and Output Intensity for a Slab Laser with Mirrors,” Ann. Phys. (Amsterdam) 392, 165-178 (2018); arXiv:1710.02825.

Behzat Ergun - Chiral Algebras for 4d N ≥ 2 SCFTs

In any 4d N=2 superconformal field theory one can find a set of operators which will yield a 2d chiral algebra when restricted to a plane that allows one to port over machinery from 2d CFTs to make prediction about 4d physics [1]. Chiral algebras can be used to explore questions of existence or isomorphisms among various 4d theories especially when theories in question have no known Lagrangian description. I will outline the construction of these chiral algebras for various examples in N=2 and N=3 theories [2] and present some preliminary results.

[1] C. Beem, M. Lemos, P. Liendo, W. Peelaers, L. Rastelli, B. van Rees. arXiv:1312.5344

[2] F. Bonetti, C. Meneghelli, L. Rastelli. arXiv:1810.03612

Narçiçeği Kıran - Analog Gravity in BEC

Analogue gravity is based on the idea that physical systems can be used to mimic some kinematic aspects of general relativity. The propagation of sound waves in a Bose-Einstein Condensate (BEC) is the typical candidate for such systems by the reason of the BEC's characteristic properties. With these properties, Klein-Gordon (KG) equation describes the propagation of sound waves in an effective space-time.

This talk has two major purposes: (1) to investigate analogue gravity for draining bathtub vortex model and superradiance which is one of the analogue effects. (2) to calculate scattering coefficients of acoustic wave from a vortex due to superradiance and search the possibility of construction an exact solution to the radial part of KG equation which is a Heun class differential equation.

After brief introduction to analogue gravity, I will revisit calculations of scattering coefficients with asymptotic expansions for hypergeometric equations to demonstrate superradiance (e.g. Reflection coefficient for superresonant scattering [1]). Secondly, I explore an example to calculate the scattering coefficients with Heun equation (e.g. An exactly soluable Schrödinger equation with smooth position dependent mass [2]). Thirdly, I discuss the possibility of constructing an exact solution to radial KG equation for the draining bathtub model with the use of cHeun equation properties. cHeun equation is a linear second order homogenous differential equation which has one irregular singular point at infinity and two regular singular points. And finally, I conclude with arguing the connection problem with vicinity of irregular singularity at infinity for cHeun equation via Stokes phenomenon.

[1]Basak, Soumen, and Parthasarathi Majumdar. "Reflection coefficient for superresonant scattering." Classical and Quantum Gravity 20.13 (2003): 2929.

[2] Dekar, Liès, Lyazid Chetouani, and Théophile F. Hammann. "An exactly soluble Schrödinger equation with smooth position-dependent mass." Journal of Mathematical Physics 39.5 (1998): 2551-2563.

Efekan Kökçü - Gravitational Waves from Inspralling Binary Blackholes

Binary black hole systems have three phases: inspiralling, merger and ringdown phases. This thesis is a review of methods developed to study the inspiralling phase analytically. Those methods include post Minkowskian (PM) and post Newtonian (PN) expansions of the metric, which are perturbative expansions in G and 1/c respectively. By applying these expansions the general solution with reasonable boundary conditions is derived, and its near and far zone limits are studied. This solution is observed to be a multipolar expansion, consisting of multipole moments that cannot be calculated directly. By using PN and PM expansions together, those multipole moments are calculated. At last, the metric is expanded to a 1 PN order and equations of motion for a binary black hole system in inspiralling phase is calculated to 1 PN order.

Emine Şeyma Kutluk - Strolling Along Gravitational Vacua

We consider General Relativity (GR) on a space-time whose spatial slices are compact manifolds M with non-empty boundary ∂M. We argue that this theory has a non-trivial space of `vacua', consisting of spatial metrics obtained by an action on a reference flat metric by diffeomorphisms that are non-trivial at the boundary. In an adiabatic limit the Einstein equations reduce to geodesic motion on this space of vacua with respect to a particular pseudo-Riemannian metric that we identify. We show how the momentum constraint implies that this metric is fully determined by data on the boundary ∂M only, while the Hamiltonian constraint forces the geodesics to be null. We comment on how the conserved momenta of the geodesic motion correspond to an infinite set of conserved boundary charges of GR in this setup.

Sinan Sevim - Asymptotic Symmetries in 3D Gravity

In 3 dimensions gravity theories without a cosmological motivation still may shed light on some problems of 4-dimensional theory and may guide us the way to solve these problems. Fortunately, the simplicity of gravity theories in 3D makes calculations easier and provides a testing ground for quantum gravity. In this talk, we take a look at Chern-Simons theory, write Einstein’s equation as a Chern-Simons gauge theory and make its constraint analysis. After this procedure, we will check the theory for asymptotically AdS boundary conditions and observe how it gives rise to two copies of Virasoro algebra with a classical central charge on the boundary. To conclude, some features of asymptotic symmetry algebra and boundary charges will be discussed with an example.

Canberk Şanlı - N=2 Dyons at Low Energy

After a review of the manifestation of classical electric-magnetic duality for spontaneously broken gauge theories, we will see its key role in the exact solution found by Seiberg and Witten for the low energy description of N=2 supersymmetric gauge theories which were proven to be explaining quark confinement through dual Meissner effect. We will focus on the rich underlying structure of the theory, namely the interplay between symplectic, complex, and Riemannian structures. Then, duality covariant formalism enables us to see the nice implications of this interplay in the actual in 3+1 spacetime. The ultimate aim is the inclusion of 'sources' through the 'attractor flow' of the central charge governed by the BPS equations in order to understand the wall-crossing of mutually non-local BPS dyons.

Kıvanç Ünlütürk - Contact Geometry and Thermodynamics

Symplectic geometry is a structure on even-dimensional manifolds. On odd-dimensional manifolds one can construct an analogous framework called contact geometry. Similar to symplectic geometry, one can then study contact Hamiltonians and the dynamics generated by them. Just as classical mechanics has a natural symplectic structure, thermodynamics has a natural contact structure. In this talk I shall first review the basics of symplectic geometry, then introduce contact geometry and discuss its similarities and differences with symplectic geometry. I shall talk about the contact structure of thermodynamics.

Cem Yetişmişoğlu - Cartan Connections and Three Dimensional General Relativity

I will start with discussing Cartan geometries. Cartan geometry offers us a way to obtain a gauge theoretic approach to gravitation. Gauge theories of gravity are different than gauge theories of internal symmetries. This is because, in gauge theories of gravitation, gauge symmetries are related to the symmetries of space-time. Afterwards, I will define Cartan type gauge theories. Finally I will present how three dimensional general relativity can be seen as a Chern-Simons theory for a Cartan connection.

References:

[1] D. K. Wise, MacDowell-Mansouri Gravity and Cartan Geometry, CQG 27, 155010, 2010.

[2] D. K. Wise, Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions, SIGMA 5, 080, 2009.