Dual Perspectives Meetings

The goal of these 1-day events is to foster communication and collaboration between mathematicians and theoretical physicists. Meetings will take place on Friday's at Feza Gürsey Center for Physics and Mathematics which is located in the Kandilli campus of Boğaziçi University. For transportation and other practical information please check here. There will be two sessions in each event. The morning session 10:30-12:00 will be elementary and will give a basic introduction to the subject. It will be followed by an afternoon session 13:30-15:00, which will be a continuation towards more advanced aspects.

Below is the schedule for Spring 2023. Click for the abstracts!

10.03.2023 - Tekin Dereli (Maltepe University and Koç University) - Where Does Simple Supergravity Theory Stand Today?

Abstract: N=1 supergravity theory in d=4 dimensions is the simplest locally supersymmetric extension of Einstein's general theory of relativity. A short overview of its many remarkable properties will be given. In particular I will introduce the notion of complex quaternionic exterior differential forms and discuss their relevance for simple supergravity.

17.03.2023 - Francesco Lin (Columbia University) - Geometry and spectra of hyperbolic three-manifolds

Abstract: The spectral properties of natural self-adjoint operators such as the Hodge Laplacian and the Dirac operator play a fundamental role in understanding many geometric and physical problems. I will discuss some aspects of the theory in the very rich context of closed hyperbolic three-manifolds, and highlight connections with geometry, low-dimensional topology, and number theory.

07.04.2023 - Jan Rosseel (Boskovic Institute, Zagreb) - Non-Lorentzian Geometry

Abstract: Non-Lorentzian geometry refers to a differential geometric framework for space-times with a degenerate metric structure and a local causal structure that differs from the one of Lorentzian geometry. It has recently found new applications, e.g., in the study of field and gravitational theories in non- and ultra-relativistic regimes. In the first of these two lectures, I will provide an introduction to non-Lorentzian geometry, focusing on the examples of Galilean and Newton-Cartan geometry that describe non-relativistic space-times. I will discuss their metric structure and metric-compatible affine connections with and without torsion in a frame formulation. I will furthermore comment on the physical interpretation of these structures and outline differences with Lorentzian geometry. The second lecture will focus on the appearance of non-Lorentzian geometry in non-relativistic string theory, a consistent and UV-complete string theory whose excitations exhibit non-relativistic dispersion relations and Newtonian gravitational interactions. After an introduction to non-relativistic string theory, I will argue that its target space-time geometry is given by an extension of Newton-Cartan geometry, called string Newton-Cartan geometry. I will discuss the structure of string Newton-Cartan geometry and show how it can be viewed as a particular limit of Lorentzian geometry equipped with an extra two-form Kalb-Ramond gauge field. If time permits, I will outline how this limit can be used to obtain effective gravitational field equations for non-relativistic string theory and comment on T-duality in non-relativistic string theory.

14.04.2023 - Ivan Cheltsov (University of Edinburgh) - K-moduli of Fano threefolds in the family 3-10

Abstract: Smooth Fano 3-folds are classified in 105 families (Iskovskikh, Mori, Mukai). For the description of these families, see https://www.fanography.info . We know which deformation families have K-polystable (Kahler-Einstein) members and which do not (Araujo, Castravet, Cheltsov, Fujita, Kaloghiros, Martinez-Garcia, Shramov, Suess, Viswanathan). Since K-polystable Fano threefolds form good moduli spaces, it would be interesting to describe K-moduli of smoothable Fano 3-folds (moduli that parametrize K-polystable smooth members of a given deformation family and their K-polystable limits). This is a very active area of research, but the problem has only been solved for the following 52 deformation families: zero-dimensional families (47 families), two one-dimensional families (families 2-24 and 2-25), cubic 3-folds (Liu, Xu), complete intersection of two quadrics (Spotti, Sun), quartic double solids (Ascher, DeVleming, Liu). In this talk, I will speak about K-moduli of Fano 3-folds in the family 3-10, see https://www.fanography.info/3-10 . This is a two-dimensional family whose smooth members can be obtained by blowing up a smooth quadric 3-fold along two disjoint conics. We know that a general member of this family is K-stable (Kahler-Einstein and finite automorphism groups), but some smooth members are not K-polystable (not Kahler-Einstein), and some members have infinite automorphism group (Cheltsov, Przyjalkowski, Shramov). In the talk, I will give explicit classification of all smooth members of the family 3-10 (normal forms), explain which smooth Fano 3-folds in this family are K-polystable and which are not (Araujo, Castravet, Cheltsov, Fujita, Kaloghiros, Martinez-Garcia, Shramov, Suess, Viswanathan), and describe all singular K-polystable members of this family (work in progress with Alan Thompson from Loughborough). If time permits, I will explain how to prove K-polystability of one singular and very symmetric member of this deformation family.

28.04.2023 - Gleb Arutyunov (II. Institute for Theoretical Physics, Hamburg University) - Geometric construction of integrable models

Abstract:In the first lecture I will present the geometric construction of a wide class of integrable many-body systems by using the Hamiltonian and Poisson reduction techniques. I will demonstrate that in some cases the corresponding reduction scheme pertains to quantisation where it shows up as a special factorisation problem in quantum algebras. In the second lecture I will discuss an advanced application of the reduction technique to the construction of the hyperbolic Ruijsenaars-Schneider model with spin. I will show that the model enjoys the Poisson-Lie symmetry which explains its superintegrability. For the quantum model without spin I will present the L-operator algebra and integrals of motion in the formalism of the quantum inverse scattering method.

12.05.2023 - Hermann Nicolai (Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut) - Title


26.05.2023 - Shinichi Tajima (Niigata University) - Title


09.06.2023 - Felix Schlenk (University of Neuchatel) - Title


Organizers : Nihat Sadık Değer, Umut Varolgüneş

These events are partially supported by TÜBİTAK grant number 121C034.