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YOUNGST@RS - Combinatorics in Fundamental Physics

Nov 26 – 29, 2024
Mainz Institute for Theoretical Physics, Johannes Gutenberg University
Europe/Berlin timezone

Contact @ MITP : Guest Relations Team

Contribution List

11 / 11
8. Timothy Budd: Random geometry and the enumerative combinatorics of maps
11/26/24, 9:30 AM

In this talk I will give an introduction to the study of the random metrics on surfaces via the combinatorics of planar maps, a topic with a long history in math and physics. I will highlight the use of bijective methods, that have played an important role in establishing scaling limits of random maps towards two-dimensional quantum gravity.
11. Reiko Toriumi: Random tensor models for quantum gravity (a look at tensor models with a mixed U(N) and O(D) symmetry)
11/26/24, 10:30 AM

I will discuss random tensor models for quantum gravity, of a particular case with mixed U(N) and O(D) symmetry.

A certain U(N)^2 \otimes O(D) order-3 tensor model can be viewed as a complex multi-matrix model with D copies of complex matrices. This model admits an expansion in two parameters owing to the presence of N and D, and yields a more refined classification of Feynman graphs...
12. Luca Lionni: Current challenges in the random geometry approach to quantum gravity
11/26/24, 11:30 AM
4. Nosiphiwo Zwane: Closeness of Lorentzian manifolds
11/27/24, 4:00 PM

In some theories of quantum gravity spacetime is assumed to have an underlying structure from which spacetimes arise as an approximation. In these theories it is important to show that the spacetime arising from the underlying structure is approximately isometric to General relativity spacetime in the classical limit. We will discuss how one can measure how close two spacetimes are from being...
5. Yasaman Yazdi: Can One Hear the Shape of a Causal Set?
11/27/24, 5:00 PM

Spectral geometry offers a powerful means to describe the geometric information of manifolds using the spectra of operators defined on them. While much work has been done on the spectral geometry of Riemannian manifolds, comparatively little work has been done on Lorentzian manifolds. Causal sets, being a discrete realization of Lorentzian manifolds, provide an ideal setting for such a...
6. Jane Gao: Evolution of random graph orders and their dimensions
11/27/24, 6:00 PM

A poset P is a set X equipped with a partial order. A causal set is a locally finite poset, which was introduced to model the space-time universe in physics. In this talk I will briefly review the literature of different models on random orders and their relations to causal set theory. Then we focus on an open problem proposed by Erdos on the evolution of the dimensions of random graph orders....
1. Alessandra Frabetti: Algebraic view on renormalization
11/28/24, 4:00 PM

Renormalization Hopf algebras represent a pro-algebraic group linking the BPHZ and Dyson renormalization formulas, where Feynman graphs are "virtual" coordinates for correlation functions and renormalization factors. In this talk I clarify the mathematical background of this statement and show how it can help improve the BPHZ formula. Time permitting, I also show how this naturally leads to a...
2. Michael Borinsky: Bivariate exponential integrals and edge-bicolored graphs
11/28/24, 4:45 PM

We show that specific exponential bivariate integrals serve as
generating functions of labeled edge-bicolored graphs. Based on this, we
prove an asymptotic formula for the number of regular edge-bicolored
graphs with arbitrary weights assigned to different vertex structures.
The asymptotic behavior is governed by the critical points of a
polynomial. As an application, we discuss the...
9. Simone Hu: Orientation forms on the odd graph complex
11/28/24, 5:20 PM

In this talk we will introduce Kontsevich's odd commutative graph complex and describe a program to detect its non-trivial (co)homology classes via associating convergent integrals to combinatorial graphs, in the spirit of Feynman integrals. In particular, we study closed differential forms constructed using the Pfaffian of skew-symmetric matrices and whose integrals give rise to cocycles in...
10. Johannes Thürigen: Tensor combinatorics in the renormalization group
11/28/24, 5:55 PM

Generalizations of vector field theories to tensors allow to similarly apply large-N techniques but find a richer though often still tractable structure. Generating discrete geometries via their perturbative series, they are furthermore candidates for Quantum Gravity. However, the potential of such tensor theories has not been fully exploited since only a symmetry-reduced ``isotropic'' part...
3. Nathan Pagliaroli: Map enumeration from path integrals over noncommutative geometries
11/28/24, 6:30 PM

In this talk we will explore path integrals over finite spectral triples as models of Euclidean Quantum Gravity, first proposed by J. W. Barrett. Such integrals can be expressed as bi-tracial multi-matrix integrals. The Feynman diagrams of these integrals are decorated maps, and they satisfy their own Schwinger-Dyson equations which are generalizations of Tutte's recursion. I will outline how...
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