[Zoom Seminar] The Discrete Dirac operator and the mass of simple and higher-order networks | Professor Ginestra Bianconi (Queen Mary University London)

Title:

The Discrete Dirac operator and the mass of simple and higher-order networks

Abstract:

We discuss the properties of the discrete Dirac operator on simple and higher-order and its relevance to capture the coupled dynamics topological signals defined on nodes, links of graphs and even higher dimensional simplices.

We will show how the Dirac operator can be coupled with the algebra of gamma matrices to define a Dirac field theory in discrete Lorentzian spacetime in  which the spinor is given a geometrical interpretation. The field theory also includes metric degree of freedom interpreted as the weights of the links for which we can define an action. 

We use the discrete topological Dirac operator to define an action for a massless self-interacting topological Dirac field inspired by the Nambu–Jona-Lasinio model. We propose a theoretical framework that explains how the mass of simple and higher-order networks emerges from their topology and geometry. The mass of the network is strictly speaking the mass of this topological Dirac field defined on the network; it results from the chiral symmetry breaking of the model and satisfies a self-consistent gap equation. Interestingly, it is shown that the mass of a network depends on its spectral properties, topology, and geometry.

Seminars by Prof. Mahir Bilen Can (Tulane University) and Prof. Andrew Lobb (Durham University), L4F01

Speaker 1: Mahir Bilen Can (Tulane University)

Title: Graded locally semialgebraic spaces and graded Nash manifolds. 

Speaker 2: Andrew Lobb (Durham University)

Title: Four-sided pegs fitting round holes fit all smooth holes.

[Seminar] Dimensional reduction in causal sets by Dr. David Meyer, UC San Diego, L4E01

 "Dimensional reduction in causal sets" by Dr. David Meyer, UC San Diego

OIST Workshop "Invitation to Recursion, Resurgence, and Combinatorics"

OIST Workshop | Website | Main organizers: Reiko Toriumi (Gravity, Quantum Geometry and Field Theory Unit) and Kento Osuga (University of Tokyo) | OIST members are welcome to attend all scientific sessions (registration required).

Women at the Intersection of Mathematics and Theoretical Physics Meet in Okinawa

OIST Workshop | Website | Main organizer: Reiko Toriumi (Gravity, Quantum Geometry and Field Theory Unit) | OIST members are welcome to attend all scientific sessions (registration required).  

Women in Mathematics Photography Exhibits

Photographs taken by Noel Tovia Matoff of women mathematicians from around the world.
 

Statistical Mechanics, Critical Phenomena and Renorm

Statistical Mechanics, Critical Phenomena and Renorm

[Seminar] Vacua of Large-N QCD3 (Prof. Adi Armoni, Swansea University) , University of Sheffield, UK)

Title: "Vacua of Large-N QCD3"

Abstract: 3d QCD in the 't Hooft large-N limit admits a rich structure. In this talk I will review the dynamics of this theory and its vacuum structure.  I will also mention the gravity dual of the theory.

SYK Seminar, Part VI: JT Gravity 2/2 (Rotation Project)

As part of my rotation project I will give a series of introductory lectures on the SYK model. In Part VI, I continue my talk about black holes, 2d dilaton theory, JT gravity and Schwarzian theory. We will finally close the ark started in Part I by making contact with the IR limit of the SYK model.

SYK Seminar, Part V: JT Gravity 1/2 (Rotation Project)

As part of my rotation project I will give a series of introductory lectures on the SYK model. In Part V, I begin an interlude about black holes, 2d dilaton theory and JT gravity.