[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.

[Seminar] Resurgent Properties of Minimal Strings and Painlevé Equations (Mr. Roberto Vega, Instituto Superior Tecnico, University of Lisboa)

Title: "Resurgent Properties of Minimal Strings and Painlevé Equations"

Abstract: In this this talk we will introduce the concept of resurgence and how can it be applied to construct global, nonperturbative solutions. As complete examples, we will mention the cases of the Painlevé I and II, while we will end up by focusing on the current state of the Inhomogeneous PII and a q-deformed PII. All these equations (with the exception of the Inhomogeneous PII) appear in the context of Minimal Strings and represent interesting low-dimensional toy models of Quantum Gravity.

Seminar: Topological recursion for tensor models (Prof. Valentin Bonzom (LIPN - Combinatorics, Algorithms and Interactions - Paris University 13)

Title: Topological recursion for tensor models

Seminar: Unitary matrix models (Mr. Neetu, IISER, Bhopal, India)

Title: Unitary matrix models

Seminar: Triple scaling of a multimatrix model U(N)^2 x O(D), continued (Prof. Reiko Toriumi, OIST)

Seminar: Triple scaling of a multimatrix model U(N)^2 x O(D), continued.

Seminar: Kinematic algebra (Dr. Tianheng Wang, Humboldt University Berlin, Germany)

Title: Kinematic algebra

[Seminar] Matrix Models and Topological Recursion II (Dr. Kento Osuga, University of Sheffield, UK)

Title: Matrix Models and Topological Recursion II

Abstract: Continued from the previous lecture, we will study how the topological recursion was discovered in the study of Hermitian matrix models. More concretely, starting with the spectral curve of a 1-cut Hermitian matrix model, I will present a computational technique that recursively solves loop equations. If time permits, I will make the recursive technique more abstract, and "define" the topological recursion.

Seminar: Triple scaling of a multimatrix model U(N)^2 x O(D) (Prof. Reiko Toriumi, OIST)

Title: Triple scaling of a multimatrix model U(N)^2 x O(D)

[Seminar] Matrix Models and Topological Recursion (Dr. Kento Osuga, University of Sheffield, UK)

Title: Matrix Models and Topological Recursion

Abstract: Hermitian matrix models are simplest quantum gauge field theory, namely quantum gauge theory in zero dimensions, and their correlation functions can be computed by a mathematical framework, the so-called topological recursion. In this review talk, I first present properties of Hermitian matrix models such as the 1/N-expansion, Virasoro constraints, loop equations, and the associated spectral curve. I will then give a technical overview of how we can recursively solve the loop equations of Hermitian matrix models by utilising the geometry of the spectral curve. Collecting the key geometric features, I will define the topological recursion with great generalities which makes it possible to apply the topological recursion beyond Hermitian matrix models.

Tensor Overview I

I will give a pedagogical introduction to field theories at large-N, with emphasis on vectors and matrices. I will also rapidly present the intermediate field formalism.