Muzaffer Adak - The Non-minimally Coupled Symmetric Teleparallel Gravity with Electromagnetic Field
Pamukkale University, Department of Physics
Abstract: We construct a symmetric teleparallel gravity model which is non-minimally coupled with electromagnetic field in four dimensions inspired by its Riemannian equivalent. We derive the field equations by taking the variation of this model, which is written here for the first time. Then, we find some classes of spherically symmetric static solutions by the coincident gauge of symmetric teleparallel spacetime.
Murat Can Aşkaroğulları - The Leibniz PROP is a Crossed Presimplicial Algebra
Gebze Technical University, Department of Mathematics
Abstract: We prove that the Leibniz PROP is isomorphic as k-linear categories (not as monoidal categories) to the symmetric crossed presimplicial algebra k[(Δ^+)^op S] where Δ^+ is the skeletal category of finite well-ordered sets with surjections, but the distributive law between (Δ^+)^op and the symmetric groups S = \cup_{n≥1} S_n is not the standard one.
This is a joint work with Atabey Kaygun.
Begüm Ateşli - On the Structural Foundations and Dynamical Analysis of n-Lie Algebra(oid)s
Gebze Technical University, Department of Mathematics
Abstract: This talk consists of three main parts. We begin with the fundamentals of Lie algebroids, focusing on their interplay with Poisson geometry. As a specific example, we investigate how two vector bundles can be coupled through mutual actions and cocycle terms to form a Lie algebroid. This construction, known as the bicocycle double cross product, provides a unifying framework for extending various geometric structures. In the second part, we introduce the basics of 3-Lie algebroids, as well as bicocycle double cross product 3-Lie algebroids. Finally, in the third part, we present an algebraic approach to constructing a 3-Lie algebroid from a given Lie algebroid. This construction is developed in terms of differential operators, (n-)Lie connections, and (n-)Lie curvatures. Additionally, the notion of a Jacobi Lie algebroid is examined within this framework, leading to the construction of a Jacobi 3-Lie algebroid structure.
Kadri İlker Berktav - Stacks in Mathematical Physics
Bilkent University, Department of Mathematics
Abstract: This talk outlines stacky constructions in geometry and physics. We begin by providing background on stacks and then discuss various stacky constructions in physics, including some of our results on certain gravity theories.
Keywords: Stacks, higher structures, 3d gravity and gauge theory, derived geometry, moduli problems, sheaf-theoretic constructions
References:
1) M. Benini, A. Schenkel, U. Schreiber, "The stack of Yang–Mills fields on Lorentzian manifolds", Communications in Mathematical Physics (2018).
2) M. Benini, A. Schenkel, "Higher structures in algebraic quantum field theory", in: Higher Structures in M‐Theory, LMS/EPSRC Durham Symposium Proceedings (2018).
3) K. İ. Berktav, "Stacks in Einstein gravity", Turkish Journal of Physics (2024).
Ayşe Hümeyra Bilge - On the Construction of Type D Non-vacuum Metrics via Integrability Conditions
Kadir Has University, Department of Industrial Engineering
Abstract: In Newman-Penrose formalism, Type D metrics can be characterized by the conditions Φ0 = Φ1 = Φ3 = Φ4 = 0. The general solution of Type D vacuum metrics has been given by Kinnersley [2]. The spin coefficients of Type D vacuum metrics satisfy certain conditions. In particular the principal null directions of the Weyl spinor are geodesic and shearfree, i.e, κ = ν = σ = λ = 0. Among these metrics a class further investigated Newman, Unti and Tam3burino [3], known as the NUT metric, is characterized by the additional condition τ + π = 0 (*), which corresponds to the property that the principal null directions of the Weyl tensor form an integrable distribution. Using integrability conditions, it has been shown that the NUT metric is the unique Type D vacuum metric with the property (*). For the non-vacuum case, we investigate a special case where Φ01 = Φ12 = 0, for which the condition (*) implies that τ = π = 0, as for the vacuum case. Integrability conditions applied to the system of Newman-Penrose equations result in a system where Φ00 and Φ22 are algebraically determined and the differential equations for the remaining NP quantities form an integrable system, in the same sprit as the notion of “complete tables” as introduced by Edgar et.al. [1]. (This is a joint work with Tekin Dereli, Tolga Birkandan and Gülay Karakaya).
References:
[1] S. B. Edgar, A. G. Gomez-Lobo, J. M. Martin-Garcia, ”Petrov D vacuum spaces revisited: identities and invariant classification,” Classical and Quantum Gravity (2009).
[2] W. Kinnersley, “Type D vacuum metrics,” Journal of Mathematical Physics (1969).
[3] E. Newman, L. Tamburino, T. Unti, “Empty space generalization of the Schwarzschild metric,” Journal of Mathematical Physics (1963).
Sermet Çağan - Stability Analysis of O(D, D) Complete Stringy Gravity (Canceled, replaced by Murat Can Aşkaroğulları)
İstanbul Technical University, Department of Physics
Abstract: In this talk, I will present a dynamical systems approach to cosmology within the framework of Double Field Theory (DFT), a T-duality covariant formulation of supergravity that introduces string-inspired modifications to General Relativity. Focusing on the massless fields of the universal NS-NS sector, which transform as O(D, D) multiplets, I will show the autonomous form of the O(D, D)-complete Friedmann equations. This formulation allows for a systematic stability analysis of critical points, providing qualitative insights into cosmic evolution without relying on explicit solutions. To illustrate the phase space dynamics, I will present phase portraits and explore cosmologically relevant scenarios, including models with scalar fields, radiation, and matter, drawing comparisons with Chameleon cosmology. I will also discuss conditions for cosmic acceleration, identifying potential mechanisms that drive it within this dynamical framework. Finally, I will examine open universe configurations, highlighting their distinct dynamical properties and implications in O(D, D)-symmetric cosmological models.
References:
[1] A. S. Arapoglu, S. Cagan, A. Çatal-Özer, "Stability analysis of O(D, D) complete stringy gravity", arXiv: 2405.07825 [gr-qc].
Ceren Ayşe Deral & Aritra Saha (Joint Talk) - New Supersymmetric Solutions in D=3, N=4 Supergravity with Timelike and Null Killing Vectors and Their Uplifts to 6D
Boğaziçi University, Department of Mathematics & Feza Gürsey Institute for Physics and Mathematics
Abstract: In this talk, we shall make a general Killing spinor analysis of a particular gauged supergravity in 3D that comes from a consistent S^3 reduction of N=(1,0) supergravity coupled to a chiral tensor multiplet in 6D. We shall first focus on the supersymmetric solutions with a null Killing vector in 3D, and find three new ones. We shall then study their uplifts to 6D. As we shall see, two of these newly found solutions in 3D, namely a null warped AdS_3 solution and a charged domain wall solution, admit non-trivial gauge fields. The uplift of the first one will produce an interesting AdS_3 × S^3 solution with a non-trivial rotation. The uplift of the second one will lead to the well-known rotating dyonic string solution. Finally the uplift of the third solution, which is an uncharged domain wall in 3D, will result in a distribution of dyonic strings. In the second part, we shall study the supersymmetric solutions with a timelike Killing vector in this gauged 3D supergravity and in its ungauged limit. In the ungauged limit, the supergravity couples to a non-linear sigma model with a homogeneous target space H^2 (hyperbolic 2-manifold), and admits interesting solutions where all of them can be expressed using two arbitrary holomorphic functions. Under certain constraints, the sigma model target space metric becomes a part of the spacetime metric, with a warp factor containing the Kahler potential of the target space, as well as a harmonic function determined by both holomorphic functions. This talk will be based on the following works: arXiv:2408.03197, arXiv:2411.04437.
Mahmut Elbistan - Memory Effects in Plane Waves
Bilgi University, Department of Energy System Engineering
Abstract: We review recent results regarding the displacement memory effect (DME) of plane gravitational waves using supersymmetric quantum mechanics. This novel approach provides a unified framework for Pöschl-Teller and Scarf profiles and restores the critical values of wave amplitudes for DME in an elegant way. We also comment on the DME of a wave profile with 1/U^2 singularity inspired by supersymmetric quantum mechanics.
Ref: arXiv:2504.05043 (With E. Catak and M. Mullahasanoglu)
Behzat Ergun - N = 1 Conformal Manifolds of Class S
Technion - Israel Institute of Technology
Abstract: In this talk, I will discuss N = 1 exactly marginal deformations of class-S theories. Even when one does not have any N = 2 preserving exactly marginal deformations, one can obtain a rich set of deformations that break half of the supersymmetry in the presence of specific punctures. I will outline the general story and give specific examples where one obtains an N=1 dual Lagrangian on the conformal manifold.
Ali Mostafazadeh - Dynamical Formulation of Stationary Scattering, Propagating-wave Approximation, and Exactness of the Born Approximation
Koç University, Department of Mathematics & Physics
Abstract: Potential scattering admits a formulation in terms of a fundamental notion of transfer matrix which is a linear operator given in terms of a Dyson series for an effective non-Hermitian Hamiltonian operator. This approach to potential scattering has so far led to several interesting developments. The most notable are the construction of the first examples of short-range potentials for which the N-th order Born approximation is exact, potentials that display broadband omnidirectional or directional invisibility, and a singularity free treatment of delta-function potentials lying on a line in two dimensions and on a plane in three dimensions. This approach to scattering theory has also been generalized to electromagnetic scattering and used to deal with certain electromagnetic radiation problems. This talk presents a first step towards a rigorous proof of the existence of the fundamental transfer matrix in two dimensions. It offers a solution of this problem within the context of propagating-wave approximation. This is an approximation scheme that ignores the contribution of the evanescent waves to the scattering amplitude and is valid for high energies and weak potentials. It becomes exact for a class of complex potentials. The latter includes an infinite subclass of potentials for which the N-th order Born approximation is exact, where N depends on the frequency of the incident wave.
References:
[1] F. Loran and A. Mostafazadeh, Phys. Rev. A 104, 032222 (2021); arXiv: 2109.06528.
[2] F. Loran and A. Mostafazadeh, Phys. Rev. A 106, 032207 (2022); arXiv: 2204.05153.
[3] F. Loran and A. Mostafazadeh, Appl. Phys. Lett 123, 191104 (2023); arXiv: 2308.03689.
[4] F. Loran and A. Mostafazadeh, J. Phys. A 55, 435202 (2022); arXiv: 2207.10054.
[5]F. Loran and A. Mostafazadeh, J. Phys. A 57, 335205 (2024); arXiv:2407.19983.
Burak Oğuz - Some Lower Dimensional Quantum Field Theories Reduced from Chern-Simons Gauge Theories
Middle East Technical University, Department of Physics
Abstract: I will talk about a recent work where we study symmetry reductions in the context of Chern-Simons gauge theories to obtain lower dimensional field theories. Symmetry reduction in gauge theories is a common tool for constructing explicit soliton solutions. Although pure Chern-Simons theories do not have such solutions, symmetry reduction still leads to interesting results. In particular, we establish relations at the semiclassical regime between pure Chern-Simons theories on S3 and the reduced Quantum Field Theories, based on actions obtained by the symmetry reduction of the Chern-Simons action, spherical symmetry being the prominent one. We also discuss symmetry reductions of Chern-Simons theories on the disk, yielding BF-theory in two dimensions, which signals a curious relationship between symmetry reductions and the boundary conformal field theories. Finally, we study the Chern-Simons-Higgs instanton-monopoles and show that under certain circumstances, the reduced action for the monopoles can formally be viewed as the action of a supersymmetric quantum mechanical model. We discuss the extent to which the reduced actions, obtained from the Chern-Simons theory, have a fermionic nature at the level of the partition function.
References:
[1] B. Oguz, B. Tekin, "Some lower dimensional quantum field theories reduced from Chern-Simons gauge theories", Physical Review D (2024).
Bayram Tekin - Consistency Problems in Modified Theories of Gravity: Two Recent Examples, Cotton Gravity and Conformal Killing Gravity
Middle East Technical University, Department of Physics
Abstract: Many models of gravity, put forward to explain the IR and UV problems of General Relativity, suffer from inconsistencies. In this talk, I will give two recent examples that caught some attention in the recent literature: Cotton gravity and Conformal Killing Gravity. Integration constants of the solutions, such as the black hole solutions in these
theories, cannot be identified with conserved quantities such as mass and angular momentum. As such the models are not physically viable. I will talk about the existence of absolute structures in these theories that do not exist in General Relativity.
References:
[1] E. Altas, B. Tekin, "Vanishing of conserved charges in Cotton gravity", Phys. Rev. D 111, no.2, 021503 (2025).
[2] E. Altas, B. Tekin, "Consistency problems of conformal Killing gravity", Phys. Rev. D 111, no.6, 064083 (2025).
Teoman Turgut - Some Observations on Singular interactions
Boğaziçi University, Department of Physics
Abstract: Recently, we have shown that the new energy eigenstates of a particle moving on a compact manifold under the influence of a singular delta potential can be understood thinking about an extension of the Sturm comparison theorem to this case. It is well-known that in two dimensions this problem requires a renormalization and can best be formulated via a Green's function approach. It is often informative to show directly that the resulting wave functions form a complete orthonormal family, which is one of the fundamental postulates of quantum mechanics. We show that this is the case, moreover, this approach gives an alternative proof of self-adjointness which is quite elegant.
Filiz Çağatay Uçgun - Dynamics over Cocycle Double Cross Products
Maltepe University, Department of Mathematics
Abstract: We present the Euler-Lagrange and Hamilton’s equations for a system whose configuration space is a unified product Lie group G = M ×_γ H, for some γ : M × M → H. By reduction, then, we obtain the Euler-Lagrange type and Hamilton’s type equations of the same form for the quotient space M = G/H, although it is not necessarily a Lie group. We observe, through further reduction, that it is possible to formulate the Euler-Poincaré type and Lie-Poisson type equations on the corresponding quotient m = g/h of Lie algebras, which is not a priori a Lie algebra. We illustrate our results in the realm of the Kepler problem, and the non-linear tokamak plasma dynamics.
Kıvanç Ünlütürk - Nature of Phase Transitions and Metastability in Scalar-Tensor Theories
Turkish-German University, Department of Electrical Electronics Engineering
Abstract: In some scalar-tensor theories, compact stars above a critical stellar mass develop scalar clouds in a process called spontaneous scalarization. The underlying mechanism for the onset of scalarization is often depicted as a second-order phase transition. In this talk, we will show that a first-order phase transition is in fact the most common mechanism. This means that metastability and transitions between locally stable compact object configurations are much more likely than previously believed, opening vast new avenues for observational prospects.
Ekin Sıla Yörük - Jordan Algebraic Formulation of Landau Problem with a Non-commutative Parameter
Koç University, Department of Physics
Abstract: In this talk, we will provide a Jordan algebraic, non-associative formulation of the Landau problem with a non-commutative parameter coupled to a harmonic potential as an inclusive example. To achieve this, we further extend the work of Schupp and Szabo [1] to infinite dimensional Jordan algebras and the Landau problem. In particular, we present an alternative formulation of the Hilbert space version of quantum mechanics in order to obtain the Hilbert space corresponding to this problem. Choosing the coordinates as the center of the cyclotron motion, one obtains a non-commutative parameter. That parameter is then described in terms of an associator in the Jordan algebraic setting by obtaining results which are potentially applicable to other non-associative formulations as well. Moreover, pure states and density matrices arising from our construction are characterized. This in turn leads us to the explicit description of split operators for the corresponding Hamiltonian and the Jordan-Schrödinger time-evolution equation for the state vectors in this specific problem [2].
References:
[1] P. Schupp, R. J. Szabo, "An algebraic formulation of nonassociative quantum mechanics", Journal of Physics A (2024).
[2] T. Dereli, E. S. Yoruk, "Jordan algebraic formulation of quantum mechanics and the non-commutative Landau problem", arXiv: 2312.12047 [quant-ph].