List of Talks

Hassan Babaei - A Brief Introduction on Hitchin Equations and Higgs Bundles (cancelled)

Abstract: In this talk, I will give a brief summary of Hitchin's foundational paper on self-duality equations on a Riemann surface. In particular, we will see how, by reducing self-dual Yang-Mills equations from four dimensions to two, one can obtain Hitchin equations. These equations link a Higgs field Φ to a connection on a principle G-bundle over a Riemann surface. In this view, a Higgs bundle is just a holomorphic vector bundle paired together with a Higgs field. I will talk about some features of Higgs bundles, and if time permits, I will look at the moduli space of solutions of Hitchin equations and show that it is a manifold with some very interesting geometric structures.

Keywords: Higgs bundles, Hitchin equations, Vector bundles.

References:

[1] N. J. Hitchin, The self-duality equations on a Riemann surface, Proc Lond Math Soc, 55 (1987) 59-126.

Nazmi Burak Budanur - Disentangling Turbulence One Loop at a Time

Abstract: Turbulence is frequently referred to as the oldest unsolved problem in physics. Although there is an agreement among many researchers on the existence of a turbulence problem, a consensus has yet to be reached on what constitutes the problem, or even, what turbulence is. In this talk, I am going to present a modern perspective on this problem based on a view of fluid flow as an infinite-dimensional dynamical system. Through examples from our recent work [1, 2], I will explain how a deterministic approach to turbulence can improve our understanding of this immensely complicated phenomenon. Specifically, I will consider the sinusoidally forced Navier–Stokes equation in a triply-periodic domain, and explain how a finite-dimensional approximation to the state space of this system is constructed in a computational setting. I will give an overview of the tools from the theory of non-linear dynamics and topological data analysis, which we utilize in our explorations of this high-dimensional space.

References:

[1] G. Yalnız, N. B. Budanur, Inferring symbolic dynamics of chaotic flows from persistence, Chaos 30 (2020), arXiv: 1910.04584.

[2] G. Yalnız, B. Hof, N. B. Budanur, Coarse graining the state space of a turbulent flow using periodic orbits (2020), arXiv:2007.02584.

Ezgi Canay - Effective Screening Length from Discrete Cosmology and Linear Perturbation Theory Combined

Abstract: Formulation of cosmological perturbations within discrete cosmology reveals the Yukawa behaviour of gravitational interaction with the associated interaction range interpreted as an upper bound for the dimensions of cosmic structures in favour of the cosmological principle [1]. The key feature in this approach lies in the nonperturbative treatment of the mass density which additionally ensures the correct description of nonlinear dynamics at small scales where the scheme of linear perturbation theory breaks down. Yukawa screening of gravity hinted by discrete cosmology arises also within the linear perturbation theory when the gravitational potential is only weakly dependent on time [2]. Exploiting both approaches towards cosmic screening, we will elaborate on developing a unified scheme and obtain the effective screening length to be compared to the sizes of the largest known objects in the Universe [3]. We will then briefly discuss certain features of the analytical expression for the scalar perturbation derived in the combined approach.

Keywords: Inhomogeneous universe, Large-scale structure, Cosmological perturbations, Gravitational potential, Yukawa interaction, Screening length.

This is a joint work with Maxim Eingorn.

References:

[1] M. Eingorn, First-order cosmological perturbations engendered by point-like masses, ApJ, 825 84 (2016), arXiv:1509.03835.

[2] O. Hahn, A. Paranjape, General relativistic screening in cosmological simulations, Phys. Rev. D, 94 083511 (2016), arXiv:1602.07699.

[3] E. Canay, M. Eingorn, Duel of cosmological screening lengths, Phys. Dark Univ., 29 100565 (2020), arXiv:2002.00437.

Nils Carqueville - A First Taste of Topological Quantum Field Theory

Abstract: I'll review the functorial approach to topological quantum field theory with defects. After a short reminder on the category-theoretic setup (which will be presented in more detail in Ekin Kaan's talk), I will describe several examples of 2-dimensional TQFTs with and without defects. Time permitting, we will also discuss higher dimensional constructions.

Keywords: Topological quantum field theory.

This is a joint work with Ingo Runkel and Gregor Schaumann.

Keremcan Doğan - Anti-Commutable Pre-Leibniz Algebroids and Admissible Connections

Abstract: Algebroids are mathematical structures that have been widely used in field theories. For example, metric-affine geometries, which are mathematical frameworks that are suitable for generalizations of general relativity, can be constructed on Lie algebroids. Similarly, generalized geometries, which are closely related to local double field theory and T-duality, can be constructed on Courant algebroids. Both of these algebroids are special cases for local pre-Leibniz algebroids in which analogous geometrical structures such as metric, connection, non-metricity, torsion, and curvature tensors can be defined [1]. In particular, the naïve torsion and curvature maps should be deformed by a locality structure to achieve tensoriality [2]. In order to have a better understanding of this deformation, 'anti-commutable' pre-Leibniz algebroids, which satisfy an anti-commutativity-like property, are introduced [3]. This property depends on the choice of a certain equivalence class of connections, whose elements are called 'admissible'. One can show that both Lie and Courant algebroids, along with higher Courant algebroids, are anti-commutable. Moreover, one can prove that while all connections on a Lie algebroid are admissible, only metric-compatible connections on a Courant algebroid are admissible. Additionally, for an admissible connection, one can prove most of the familiar properties of usual metric-affine geometry, including the Koszul formula and Schouten's trick for the decomposition of connection coefficients.

Keywords: Pre-Leibniz algebroids, Generalized geometry, Metric-affine geometry.

This is a joint work with Tekin Dereli.

References:

[1] T. Dereli, K. Doğan, Metric-connection geometries on pre-Leibniz algebroids: a search for geometric structure in string models (accepted to Journal of Mathematical Physics), arXiv: 2006.05957.

[2] B. Jurco, J. Vysoky, Leibniz algebroids, generalized Bismut connections and Einstein-Hilbert actions. Journal of Geometry and Physics 97, 25-33 (2015), arXiv: 1503.03069.

[3] K. Doğan, Geometry on 'anti-commutable' pre-Leibniz algebroids: generalized geometry with two connections, (in preparation).

Maxim Eingorn - Cosmological Perturbations in Lattice Universe

Abstract: The question of spatial topology of the universe belongs to a class of fundamental open questions of cosmology and theoretical physics. Since topology is not dictated by general relativity, there is no theoretical hint of whether space is simply connected (as assumed within the concordance cosmological model) or multiply connected. We briefly review the observational data relevant to the presumed nontrivial shape of the world and enjoy describing the weak gravitational field generated by a lattice of discrete masses.

Keywords: Cosmological perturbations, Lattice universe, Spatial topology.

This is a joint work with Alexander Zhuk, Maxim Brilenkov, Ezgi Canay, Jacob Monroe Metcalf, Andrew McLaughlin II, Katie Arzu, Niah O'Briant.

Harold Erbin - Machine Learning for Complete Intersection Calabi-Yau Manifolds

Abstract: In this talk, I will explain how to compute both Hodge numbers for complete intersection Calabi-Yau (CICY) 3-folds using machine learning. I will first make a tour of various machine learning algorithms and explain how exploratory data analysis can help in improving results for most of them. Then, I will describe a neural network inspired from the Google's Inception model which reaches nearly perfect accuracy for h1,1 using much less data than other approaches. The same architecture also performs much better than any other algorithm for h2,1.

Keywords: Machine learning, Calabi-Yau manifold, String theory.

This is a joint work with Riccardo Finotello (Università di Torino, Italy).

References:

[1] H. Erbin, R. Finotello, Machine learning for complete intersection Calabi-Yau manifolds: a methodological study, arXiv:2007.15706.

[2] H. Erbin, R. Finotello, Inception neural network for complete intersection Calabi-Yau 3-folds, arXiv:2007.13379.

Ömer Güleryüz - A Brief Introduction to String Inflation via Supergravity

Abstract: The main challenge in string inflation is to specify a low-energy effective Lagrangian, which is capable of deriving inflation that is consistent with current observational data. In this presentation, I will start with a case where supergravity (N=1, D=4) coupled to a real (chiral) multiplet. Here, it is convenient to consider the Kähler potential and superpotential as a part of the potential that causes inflation. I will also show the suggested de Sitter swampland conjectures [1, 2], which can be used to distinguish the effective field theories whether a theory is in the landscape, a quantum theory of gravity. The aim of this talk is to build some insight and understanding of the topic for graduate students.

Keywords: String inflation, Supergravity, Landscape.

References:

[1] Georges Obied, Hirosi Ooguri, Lev Spodyneiko, and Cumrun Vafa, De Sitter space and the swampland (2018).

[2] Hirosi Ooguri, Eran Palti, Gary Shiu, and Cumrun Vafa, Distance and de Sitter conjectures on the swampland. Phys. Lett. B, 788:180-184 (2019).

Umut Gürsoy - Hydrodynamics and Holography of Spin Flow

Abstract: Recent observations of vorticity induced spin flow both in liquid metals and the quark-gluon plasma suggests a new research direction for theory. I will argue that both hydrodynamics and holography are essential tools to study spin transport coupled to energy-momentum, electric and axial charge in strongly correlated quantum fluids. Torsion plays a central role as it directly sources the spin current. I will describe the hydrodynamic theory of spin current coupled to energy-momentum tensor, including decomposition of all sources in 3+1 dimensions and the constitutive relations. Finally, I will present a toy holographic model based on Lovelock-Einstein-Cartan theory in five dimensions. Application of the fluid-gravity correspondence on black hole solutions in this theory determines the spin transport coefficients analytically at the lowest and first order in the hydrodynamic expansion.

Marcel Hughes - Insights into Black Hole Microstates from AdS3 Holography

Abstract: The fuzzball proposal [1] aims at a unitary resolution within string theory to the information paradox. As part of this drive to understand black holes at microscopic scales, families of regular and horizon-less microstate geometries have been explicitly constructed [2] for the Strominger-Vafa black hole [3]. Via the AdS3/CFT2 correspondence, it is also possible to study this black hole using powerful techniques of 2d conformal field theories. Specifically, reviewing the connection between classes of pure heavy states in the D1-D5 CFT and the above-mentioned microstate geometries, I will look at how CFT data can be extracted from the bulk by considering heavy-heavy-light-light correlators in the Regge limit [4].

Keywords: Black holes, CFT, 1/N expansion, AdS/CFT.

This is a joint work with Nejc Čeplak, Stefano Giusto and Rodolfo Russo.

References:

[1] S. Mathur, Fuzzballs and the information paradox: a summary and conjectures, arXiv:0810.4525 [hep-th].

[2] N. P. Warner, Lectures on microstate geometries, arXiv:1912.13108 [hep-th].

[3] A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys.Lett. B379 (1996) 99–104, hep-th/9601029.

[4] S. Giusto, M. R. R. Hughes and R. Russo, The Regge limit of AdS3 holographic correlators, JHEP, arXiv:2007.12118.

Ekin Kaan - A Brief Introduction to Categories and Topological Quantum Field Theories

Abstract: I will introduce basic category theory concepts to define topological quantum field theories. After motivating topological quantum field theories, categories, functors and symmetric monoidal structure will be discussed with examples. Finally, we will be able to define topological quantum field theories axiomatically for the generic case.

Keywords: TQFT, Category theory.

References:

[1] Joachim Kock, Frobenius algebras and 2D topological quantum field theories, Cambridge University Press (2003).

[2] Michael Atiyah, Topological quantum field theories, Institut des Hautes Études Scientifiques (1988).

Abhiram Kidambi - Introduction to Moonshines in String Theory

Abstract: I will give an introduction to aspects of moonshine phenomena which connects q-expansion series of certain modular forms, representations of finite simple sporadic groups, lattices via vertex operator algebras (CFT's). I will discuss what it means to have a moonshine phenomenon and discuss the cases of Monster and Mathieu moonshines.

Alex Kontorovich - Interactions Between Mathematical Physics and Number Theory

Abstract: We discuss a number of areas where ideas from physics have influenced number theory, and vice-versa.

Keywords: Number theory

Todor Popov - Hydrogen Atom and Minkowski Space-Time Symmetries from One Jordan Algebra

Abstract: It has been realized long ago that the 15 dimensional conformal group, extending the Poincaré group with dilations and conformal inversions is a symmetry of the Maxwell equations. Conformal action yields a special mass-zero representation preserving the causal structure of Minkowski spacetime. On the other hand in the seventies in the works of Barut and collaborators [1] the conformal group emerged as a dynamical symmetry of the hydrogen atom.

We show that the conformal symmetry of Minkowski spacetime and the hydrogen atom dynamical symmetry are two sides of a same coin. These are the coordinate and the momentum massless conformal group representations of the Jordan algebra of Pauli matrices. The role of the structural Jordan algebra symmetries has been elucidated.

The talk is based on the work [2].

Applications of the "H-atom"-like conformal symmetry in hadronic physics which are under investigation in collaboration with Mariana Kirchbach will be discussed.

References:

[1] Barut, A. O., Bornzin, G. L. (1974). Unification of the external conformal symmetry group and the internal conformal dynamical group. Journal of Mathematical Physics, 15(7), 1000-1006.

[2] Popov, T. (2017). Jordan algebra and hydrogen atom. In Quantum Theory And Symmetries (pp. 231-244). Springer, Singapore.

Pavel Putrov - 3-manifolds and q-series

Abstract: In my talk I will review certain invariants of 3-manifolds with a physical origin. The invariants are valued in q-series with integer coefficients and play an important role in the problem of categorification of other known invariants, such as Witten-Reshetikhin-Turaev invariant (which is physically realized by Chern-Simons quantum field theory).

Keywords: Topological quantum field theory, 3-manifolds.

This is a joint work with Sergei Gukov, Francesca Ferrari, Marcos Mariño, Sunghyuk Park, Du Pei, Cumrun Vafa.

References:

[1] F. Ferrari and P. Putrov, [arXiv:2009.14196 [hep-th]].

[2] S. Gukov, S. Park and P. Putrov, [arXiv:2009.11874 [hep-th]].

[3] S. Gukov and C. Manolescu, [arXiv:1904.06057 [math.GT]].

[4] S. Gukov, D. Pei, P. Putrov and C. Vafa, J. Knot Theor. Ramifications 29 (2020) no.02, 2040003 doi:10.1142/S0218216520400039 [arXiv:1701.06567 [hep-th]].

[5] S. Gukov, M. Marino and P. Putrov, [arXiv:1605.07615 [hep-th]].

[6] S.Gukov, P. Putrov and C. Vafa, JHEP07 (2017), 071 doi:10.1007/JHEP07(2017)071 [arXiv:1602.05302 [hep-th]].

Réka Szabó - From Survival to Extinction of the Contact Process by the Removal of a Single Edge

Abstract: We present an example of interest to the discussion of how the behavior of the contact process (a particular type of interacting particle system) can be affected by local changes in the graph on which they are defined. The contact process is usually taken as a model of epidemics on a graph: vertices are individuals, which can be healthy or infected. Infected individuals recover with rate 1 and transmit the infection to each neighbor with rate λ . We give a construction of a tree in which the contact process with any positive infection rate survives but, if a certain privileged edge e* is removed, one obtains two subtrees in which the contact process with infection rate smaller than 1/4 dies out. We give a construction of a tree in which the contact process with any positive infection rate survives but, if a certain privileged edge e* is removed, one obtains two subtrees in which the contact process with infection rate smaller than 1/4 dies out.

Keywords: Interacting particle systems, Contact process, Phase transition.

This is a joint work with Daniel Valesin.

Reference:

[1] Réka Szabó, Daniel Valesin, From survival to extinction of the contact process by the removal of a single edge, Electronic Communications of Probability 21 (2016), arXiv:1601.06564.

Burak Şahinoğlu - A Tensor Network Framework for Topological Phases of Quantum Matter

Abstract: We describe a general tensor network framework that describes topologically ordered models in any d+1 spacetime dimension. We furthermore show that state-sum TQFTs are a subclass of examples in this framework. In the talk, we first go through a short background on tensor networks and state-sum TQFTs, and then go over the results with a final discussion on open problems.

Ceyda Şimşek - A Brief Introduction to Non-relativistic Gravity

Abstract: Non-relativistic symmetries appear in many physical systems such as condensed matter, fluid dynamics, Lifshitz holography, non-relativistic string theory etc. In this talk, I will focus on the latter which caught some attention recently since it promises new insights in non-relativistic quantum gravity and holography. We will discuss briefly how to get the Newton-Cartan geometry which is the correct geometrical framework for the Newtonian gravity and generalise this geometry to the case relevant for string theory. Lastly, I will make some remarks on its underlying “super” gravity theory and compare it with recent beta-function calculations.

This is a joint work with E. A. Bergshoeff, J. Lahnsteiner, L. Romano, J. Rosseel.

Teoman Turgut - Existence of Hamiltonians for Singular Systems

Abstract: Typical realistic quantum field theories are singular and require renormalization. One possible approach is to render possibly singular correlation functions to finite expressions via renormalization and then show that this indeed defines a sensible measure. Another one is a Hamiltonian approach, where one shows that there is a well-defined Hamiltonian after renormalization. Here we take a modest approach and look at simpler systems (toy models) which exhibit some form of singularity that require renormalization and show that there are sensible Hamiltonians after renromalization. These toy models hopefully give us some insight for more realistic problems. One such problem is the delta function potential, the other one is a bosonic field interacting with a fixed two level source. We show that these singular systems define sensible Hamiltonians after renormalization and we discuss some subtle aspects of the resulting resolvents.

Keywords: Renormalization, Nonperturbative methods, Singular interactions.

This is an ongoing project over the years in collaboration with Erman, Unel, Jagvaral, Kaynak and Dogan.

Meltem Ünel - Not Just a Tree: Introduction to Quantum Geometries

Abstract: In this talk, some results from an ongoing work on a random tree model will be presented with the focus being on the ideas motivating the study of ‘quantum’ geometries. Dynamical Triangulations (DT) and Causal Dynamical Triangulations (CDT) provide non-perturbative formulations of (Euclidean(DT) and Lorentzian(CDT)) quantum gravity. I will introduce the ideas and motivations behind these methods of summing over spacetimes. Thanks to the bijective correspondence between CDT’s and random trees, it is possible to define the problem of height-coupling on the latter. I will explore some of the properties of this particular model, such as its critical behavior and the question of existence of a limiting measure on the ensemble of infinite trees.

Keywords: Dynamical triangulations, Causal dynamical triangulations, Random planar trees.

This is a joint work with Bergfinnur Durhuus.

References:

[1] Jan Ambjørn, Bergfinnur Durhuus, Thordur Jonsson, Quantum geometry: a statistical field theory approach, Cambridge University Press (1997).

[2] Bergfinnur Durhuus, Probabilistic aspects of infinite trees and surfaces, Acta Physica Polonica Series B 34.10 (2003).

[3] Renate Loll, Quantum gravity from causal dynamical triangulations: a review, Classical and Quantum Gravity 37.1 (2019), arXiv:1905.08669.

Andrew Waldron - Quantization and Geometry

Abstract: Geometric quantization addresses the problem of quantizing the algebra of functions on a symplectic or Poisson manifold. However, once dynamics are included, a more fundamental structure is an odd-dimensional symplectic manifold or phase-spacetime which can be used to describe classical dynamical systems quite generally. Key examples of these structures are contact geometries. We show that the problem of quantizing classical dynamics is the geometric one of finding flat connections on a bundle of Hilbert spaces over phase-spacetime. Solving the resulting quantum dynamics amounts to finding parallel sections for such a connection. We also sketch various applications of this approach to quantum systems.

Keywords: Quantum mechanics, Contact geometry, Quantization.

This is joint work with Roger Casals, Olindo Corradini, Gabiel Herczeg and Emanuele Latini.