**Colleen Delaney**, Indiana University

*Understanding Modular Isotopes*

Modular fusion categories form algebraic theories of anyons in (2+1)D bosonic topological phases of matter, making their structure theory of interest to mathematicians and physicists alike. In practice, modular fusion categories are often studied through their modular data: two matrices of topological invariants with nice representation theoretic properties. However, different modular fusion categories can have the same modular data, in which case we call them modular isotopes. This talk will explain how to understand and distinguish the currently known modular isotopes through a new construction called ribbon zesting.

**Astrid Eichhorn**, CP3-Origins, University of Southern Denmark

*Networks at the intersection of quantum gravity and ``real-world" applications*

**Mahumm Ghaffar**, Memorial University of Newfoundland

*Moller Parity Violating Asymmetry*

We calculated tree level Moller Parity violating Asymmetry which measures the Weak charge of electron which at one loop level is modified and depends on the energy scale at which the measurement is carried out.

**Lisa Glaser**, University of Vienna

*Spectral triples in quantum gravity*

**Sharmila Gunasekaran**, Memorial University of Newfoundland/University of Alberta

*Slow decay of waves in gravitational solitons*

Gravitational solitons are globally stationary horizonless asymptotically flat spacetimes. In this talk, I will describe the methodology used to prove that massless scalar waves in a particular family of soliton spacetimes decay very slowly. The proof involves the construction of quasimodes which are approximate solutions to the wave equation. This slow decay can be attributed to the stable trapping of null geodesics and is suggestive of instability at the nonlinear level. This is joint work with Hari Kunduri. (Ann. Henri Poincaré (2021). https://doi.org/10.1007/s00023-020-01010-3)

**Sabine Harribey**, CPHT Ecole Polytechnique - Heidelberg University

*Renormalization in tensor field theories and the melonic fixed point*

Tensor models exhibit a melonic large N limit: this is a non trivial family of Feynman graphs that can be explicitly summed in many situations. In d dimensions, they give rise to a new family of conformal field theories and provide interesting examples of the renormalization group flow from a free theory in the UV to a melonic large N CFT in the IR. We consider here a bosonic tensor model in rank three and d<4 dimensions. After giving a short introduction to tensor models, I will present the renormalization group flow of the model. At leading order in 1/N but non perturbatively in the coupling constants, we found a real and infrared fixed point.

**Roberta Iseppi**, Southern Denmark University

*Noncommutative geometry and the BV formalism: the case of finite dimensional noncommutative manifolds*

In this brief exposition we plan to give a glimpse on a novel approach to the study of the BV construction, based on the mathematical setting provided by noncommutative geometry.

**Eilind Karlsson**, TU München

*Dualizability in higher Morita categories - steps towards proving a conjecture about (n+1)-dualizability in the higher Morita category Alg_n*

**Maryam Khaqan**, Emory University

*Elliptic Curves and the Thompson group*

Can moonshine help answer questions in number theory? We give one example where the answer is, in fact, yes.

**Evelyn Yoczira Lira Torres**, Queen Mary University of London

*Quantum Gravity and Riemannian Geometry on the Fuzzy Sphere*

We study the quantum geometry of the fuzzy sphere defined as the angular momentum algebra [x_i,x_j]=2ıλ_p ε_{ijk}x_k modulo setting ∑x^{2}_i to a constant, using a recently introduced 3D rotationally invariant differential structure. Metrics are given by symmetric 3×3 matrices g and we show that for each metric there is a unique quantum Levi-Civita connection with constant coefficients, with scalar curvature 1/2[Tr(g^2)−Tr(g)^2]/det(g). As an application, we construct Euclidean quantum gravity on the fuzzy unit sphere.

**Adrian Tanasa**, University of Bordeaux

*Tensor models in a nutshell*

Tensor models are a natural quantum field theoretical (QFT) generalization, in dimension higher than 2, of the celebrated matrix models (known, for example, to give a succesfull discrete geometrical, QFT approach to 2D Quantum Gravity). Moreover, Witten showed recently that tensor models are related in a non-trivial way to holography, via the Sachdev-Ye-Kitaev (SYK) model. In this talk I will give a snapshot view of tensor models and of their relations to the SYK model.

**Maria Elena Tejeda-Yeomans**, Facultad de Ciencias, Universidad de Colima

*QFTs in extreme conditions (finite Temperature, magnetic fields,etc). *

My talk will highlight the singular/analytical structure of QFT amplitudes under these conditions, focusing on the mathematical challenges posed in these calculations and possible open problems.

**Philine van Vliet**, DESY Hamburg

*Conformal defects and emergent supersymmetry. *

The conformal bootstrap is a powerful, nonperturbative method to study (supersymmetric) conformal field theories ((S)CFTs). Advancements in especially the numerical bootstrap have led to extremely precise results for the computation of critical exponents in various (S)CFTs, and the conformal bootstrap has gained a lot of attention in recent years. (S)CFTs can be generalized by adding extended objects. These extended objects break the (super-)conformal symmetry group into a smaller (super-)conformal subgroup, and the resulting defect theory can be studied with the defect bootstrap. Defect theories appear in many places in theoretical physics: from Wilson lines in high-energy string theory, to boundary CFTs found in low-energy condensed matter physics. In recent work we studied three-dimensional boundary CFTs with N=2 supersymmetry, which have possible phenomenological applications in condensed matter physics as an example of emergent supersymmetry. Such theories allow two types of boundaries, on which we have studied various important observables. One of the boundaries can be analytically continued to d=4, and we bootstrapped the observables in the 4 - \epsilon expansion. The programme can be expanded to include line defects, which is work in progress.

**Karen Yeats**, University of Waterloo

*TBA*