Emel Altaş - Basics of Apparent Horizons in Black Hole Physics
Karamanoğlu Mehmetbey University, Department of Physics
Abstract: Event Horizon, a null hypersurface defining the boundary of the black hole region of a spacetime, is not particularly useful for evolving black holes since it is non-local in time. Instead, one uses the more tangible concept of Apparent Horizon for dynamical black holes out there in the sky that do all sorts of things: evolve, merge and feed on the environment. Event Horizon, being a gauge-independent, global property of the total spacetime is easy to define and locate in the stationary case; on the other hand, Apparent Horizon depends on the embedding of the surface in spacetime and hence it is somewhat tricky to define. But for numerical simulations in General Relativity, locating the Apparent Horizon helps one to excise the black hole region and the singularity to have a stable computation. Moreover, for stationary solutions the two horizons match. Here we give a detailed pedagogical exposition of the subject and work out the non-trivial case of a slowly moving and spinning black hole.
Ayşe Hümeyra Bilge - Topological Methods in Gauge Theories
Kadir Has University, Department of Industrial Engineering
Abstract: The set up for gauge theories is a vector bundle (E) over a differentiable manifold (M), with a structure group (G). The manifold is equipped with a connection (A) taking values in the Lie algebra of the structure group (g). Let F be the curvature of this connection. Locally, with respect to an orthonormal basis of the sections of E, F is represented by a g valued matrix whose entries are 2-forms. As 2-forms commute, it makes sense to compute P(k) = det(F - k I) where I is the identity matrix. The coefficients of k in P(k) are even forms of degree 2,4, 2j, ... denoted as σ2j .The integrals of the powers of these forms over the manifold M are related to the Chern and Pontryagin classes of the vector bundle hence they are topological invariants.
Consider gauge theories defined in terms of inner products involving the curvature F of the bundle. The inner products of forms involve Hodge duals hence the action integral depends on the metric. In most cases it is possible to use various inequalities to express the integrand as a wedge product of forms σ2j so that the action integral is bounded below by the characteristic classes of the bundle. A typical example for this set up is the Yang-Mills theory over a 4-manifold, for which the norm of the curvature 2-form F is bounded below by the Pontryagin classes of the bundle.
In the lecture we describe the expression of characteristic classes in terms of the curvature 2-form F and give examples for action integrals with topological lower bounds in 4 and 8 dimensions.
Samuel Blitz - Conformal Fundamental Forms
University of California, Davis, Department of Physics and Astronomy
Abstract: The geometry of conformally-embedded hypersurfaces in general compact manifolds is important for the study of boundary value PDEs. As part of a larger program studying the conformal geometry of such embeddings, I will construct a sequence of conformally invariant tensors that generalize the second fundamental form. Like the second fundamental form, these tensors encode the local extrinsic curvatures of such an embedding. In particular, our main result shows that these tensors characterize the failure of a conformally compact manifold to have an asymptotic Poincaré-Einstein structure. The frequency with which these tensors appear in the calculus of conformally-embedded hypersurfaces suggests a deeper picture which is yet to be fully understood.
Keywords: Conformal geometry, hypersurface embeddings, Poincaré-Einstein metrics, Yamabe problem
This is a joint work with Andrew Waldron and A. Rod Gover.
References:
[1] S. Blitz, A. R. Gover, A. Waldron, "Conformal fundamental forms and the asymptotically Poincaré-Einstein condition", preprint, arxiv: 2107.10381.
[2] S. Blitz, A. R. Gover, A. Waldron, "Generalized Willmore energies, Q-curvatures, extrinsic Paneitz operators, and extrinsic Laplacian powers", preprint, arxiv: 2111.00179.
Deniz Bozkurt - S-Matrices for 4D N = 2 SCFT Spin Chains
University of Hamburg, Department of Physics
Abstract: Most of the 4d N=2 Superconformal field theories (SCFTs) can be obtained by orbifolding and marginally deforming the N=4 Super Yang-Mills theory. The study of spin chains of 4d N=2 SCFTs in the planar limit shows that there is a quasi-Hopf symmetry algebra underlying the spectral problem which can be seen from the R-matrix formalism. For the time being these N=2 theories are not considered integrable because the S-matrices do not satisfy the Yang-Baxter equation. In order to revisit this argument, we study the dynamical chains of Z_2 quiver theory by trying to solve one-, two- and three-magnon problems with the coordinate Bethe ansatz approach in the light of quasi-Hopf Yang-Baxter relations.
İlim İrfan Çimdiker - Inflation and Black Hole Solutions in Induced Gravity Theories
Karadeniz Technical University, Department of Physics
Abstract: Inducing the gravity from quantum field theory is the first fundamental technique that we encounter in the search for a theory of quantum gravity. In this talk, we will introduce two different ideas about inducing gravity. First is Sakharov's idea where the Planck scale emerges from the Ultra-Violet cutoff and the second is a novel idea called symmergent gravity where the curvature sector emerges from the cutoff in the standard model action via restoring broken gauge symmetries. We will also talk about possible implications of such models such as inflationary and black hole solutions.
Keywords: Induced gravity, black hole solutions, inflation
This is a joint work with D. Demir and A. Övgün.
References:
[1] İ. İ. Çimdiker, "Starobinsky inflation in emergent gravity", Phys. Dark Univ. 30 (2020), 100736 doi:10.1016/j.dark.2020.100736.
[2] İ. İ. Çimdiker, D. Demir, A. Övgün, "Black hole shadow in symmergent gravity", Phys. Dark Univ. 34 (2021), 100900 doi:10.1016/j.dark.2021.100900, arXiv:2110.11904 [gr-qc].
Birses Debir - Initial Steps of Vessel Formation: A Quantitative Model
Boğaziçi University, Department of Physics
Abstract: Cell differentiation is an important process in the formation and maintenance of tissues which is driven by a complex system of intracellular and intercellular signaling mechanisms. Recent experiments have demonstrated that rapid calcium oscillations within active cells characterize this phenotype selection process and that these oscillations play a necessary role in governing phenotype selection [1, 2]. In this work, we develop a mathematical model capable of describing these oscillations and their role in phenotype selection then use it to improve our understanding of the biological mechanisms at play. We developed a model based on two previously published and experimentally validated mathematical models [3, 4] and use our resulting model to simulate various multi-cell scenarios. We are able to capture essential calcium oscillation dynamics and intercellular communication between neighboring cells. We also extended the model for calcium related mechano-chemical alterations in the cell. The results of our model show that although the late DLL4 (a transmembrane protein that activates Notch pathway) levels of a cell are connected with its initial IP3 (Inositol 1,4,5-trisphosphate) level, cell-to-cell communication determines its eventual phenotype.
Keywords: Angiogenesis, lateral inhibition, calcium
References:
[1] Aaron M Savage, Sathishkumar Kurusamy, Yan Chen, Zhen Jiang, Karishma Chhabria, Ryan B MacDonald, Hyejeong R Kim, Heather L Wilson, Fredericus JM van Eeden, Angel L Armesilla, et al. "tmem33 is essential for vegf-mediated endothelial calcium oscillations and angiogenesis", Nature communications, 10(1): 1–15, 2019.
[2] Yasuhiro Yokota, Hiroyuki Nakajima, Yuki Wakayama, Akira Muto, Koichi Kawakami, Shigetomo Fukuhara, and Naoki Mochizuki, "Endothelial ca2+ oscillations reflect vegfr signaling-regulated angiogenic capacity in vivo", elife, 4:e08817, 2015.
[3] Alireza Atri, Jeff Amundson, David Clapham, and James Sneyd, "A single-pool model for intracellular calcium oscillations and waves in the xenopus laevis oocyte", Biophysical Journal, 65(4): 1727–1739, 1993.
[4] Lakshmi Venkatraman, Erzs´ebet Ravasz Regan, and Katie Bentley, "Time to decide? Dynamical analysis predicts partial tip/stalk patterning states arise during angiogenesis", PLoS One, 11(11): e0166489, 2016.
Emine Diriöz - Pin(d, d) Covariance of Pure Spinor Equations for Supersymmetric Vacua and Non-Abelian T-Duality
Istanbul Technical University, Department of Mathematics Engineering
Abstract: In a supersymmetric compactification of Type II supergravity, preservation of N = 1 supersymmetry in four dimensions requires that the structure group of the generalized tangent bundle TM + T^*M of the six dimensional internal manifold M is reduced from SO(6, 6) to SU(3) x SU(3). From a topological point of view, it means that on the internal manifold there exists a pair of globally defined pure spinors Phi_1 and Phi_2 of non-vanishing norm. Furthermore, these pure spinors should satisfy certain first order differential equations which are best described in the framework of Generalized Geometry.
In my talk I will start with a brief introduction on basic concepts of Generalized Complex Geometry (GCG) programme of N. Hitchin. In this framework, a generalized complex structure can be given by the existence of a pure spinor satisfying a certain differential equation. I will discuss the description of Spin(d, d) pure spinors as nonhomogeneous differential forms and present the explicit form of the pure spinors associated with an SU(2) and with an U(3) stucture. Then, I will demonstrate that the pure spinor equations for supersymmetry are covariant under Pin(d, d) transformations. Finally, I will discuss Non-Abelian T-duality (NATD) transformation, which is a specific non-constant Pin(d, d) transformation and show how a background with SU(3) structure is transformed to a background with SU(2) structure.
This is based on a joint work with Assoc. Prof. Aybike Çatal-Özer [1].
Reference:
[1] A. Çatal-Özer, E. Diriöz, "Pin(d, d) covariance of pure spinor equations for supersymmetric vacua and non-Abelian T-duality", accepted for publication at JHEP, arXiv:2109.14580 [hep-th].
Eda Kılınçarslan - Semiclassical Chiral Kinetic Theories for Massless and Massive Spin-1/2 Particles
Boğaziçi University, Department of Physics
Abstract: In this talk, I will review the development of the chiral kinetic theory (CKT), and give the interesting transport phenomena found by the CKT. In this concept, we will begin by investigating the quantum anomalies such as the chiral magnetic effect and the chiral vortical effect, which have been recently observed in the quark-gluon plasma as well as the condensed matter systems. Then, I will show how such transport anomalies can be obtained from the three-dimensional kinetic theories [1, 2]. Finally, by using the Wigner-function formalism, I will establish the relativistic kinetic theory for massive spin-1/2 particles in rotating coordinate frames. We will argue the mass corrections to the chiral vector and axial-vector currents produced in this theory [3, 4].
Keywords: Chiral kinetic theory, vorticity, Berry monopole, chiral anomalies, quark-gluon plasma, heavy-ion collisions, Wigner-function formalism
This is a joint work with Ömer Faruk Dayı and Elif Yunt.
References:
[1] Ö. F. Dayı, E. Kılınçarslan, E. Yunt, "Semiclassical dynamics of Dirac and Weyl particles in rotating coordinates", Phys. Rev. D 95, 085005 (2017), arXiv:1605.05451v3 [hep-th].
[2] Ö. F. Dayı, E. Kılınçarslan, "Quantum kinetic equation in the rotating frame and chiral kinetic theory", Phys. Rev. D 98, 081701 (2018), arXiv:1807.05912v3 [hep-th].
[3] Ö. F. Dayı, E. Kılınçarslan, "Semiclassical transport equations of Dirac particles in rotating frames", Phys. Rev. D 102, 045015 (2020), arXiv:2004.07510v2 [hep-th].
[4] Ö. F. Dayı, E. Kılınçarslan, "Quantum kinetic equation for fluids of spin-1/2 fermions", (2021), arXiv:2106.12780v2 [hep-th].
Narçiçeği Kıran - The Response of Network Dynamics to Link Modification
Kadir Has University, Department of Bioinformatics and Genetics
Abstract: A major issue in the study of complex network systems, such as neuroscience, ecological networks, and power grids, is to understand the response of network synchronization to link modifications. The local stability of the globally synchronized state depends on the spectral properties of the Laplacian matrix representing the network. Due to the asymmetry of the Laplacian matrix of a directed graph, adding directed links might cause a decrease in the real part of the second minimum eigenvalue of the Laplacian, and hence synchronization loss in the network. We consider a weakly connected directed graph consisting of two strongly connected components connected by a directed link (called cutset). We study the transitions to synchronization in such networks when a new directed link between the components, in the opposite direction of the cutset, is added to the network and makes the whole network strongly connected. We explore which properties of underlying graphs and their connected components may hinder the synchronization (i.e., decreasing in the real part of the second minimum eigenvalue of the Laplacian). We are aiming to find optimal strategies to modify networks to stabilize the synchronized solutions.
This is a joint work with Sajjad Bakrani, Deniz Eroğlu and Tiago Pereira.
Sneh Pandya - Weighing Black Holes with Deep Learning
Northeastern University, Department of Physics
Abstract: Supermassive black holes (SMBHs) are ubiquitously found at the centers of most massive galaxies. Measuring SMBH mass is important for understanding the origin and evolution of SMBHs. However, traditional methods require spectroscopic data which is expensive to gather. We present an algorithm that weighs SMBHs using quasar light time series, circumventing the need for expensive spectra. We train, validate, and test neural networks that directly learn from the Sloan Digital Sky Survey (SDSS) Stripe 82 light curves for a sample of 38939 spectroscopically confirmed quasars to map out the nonlinear encoding between SMBH mass and multi-color optical light curves. We find a 1σ scatter of 0.37 dex between the predicted SMBH mass and the fiducial virial mass estimate based on SDSS single-epoch spectra, which is comparable to the systematic uncertainty in the virial mass estimate. Our results have direct implications for more efficient applications with future observations from the Vera C. Rubin Observatory.
This is a joint work with Joshua Yao-Yu Lin, Devanshi Pratap, Xin Liu, Matias Carrasco Kind, Volodymyr Kindratenko.