## Title and Abstract

### Dario Martelli

**Extremization principles and the entropy of supersymmetric black holes**

I will discuss statistical properties of supersymmetric black holes in AdS and related extremization principles. In particular, I will show how the entropy of supersymmetric black holes in AdS_5 is obtained as a Legendre transformation of a suitably defined on-shell gravitational action. Moreover, I will discuss a microscopic interpretation of this on-shell action in terms of a generalization of the supersymmetric Casimir energy of the holographically dual N=1 SCFTs. More generally, I will argue that in the context of the AdS/CFT correspondence, it is natural to regard the “entropy functions” that govern the statistical properties of supersymmetric AdS black holes as instances of extremization principles, characterizing both SCFTs and a class of extremal problems in odd-dimensional Riemannian geometry underlying supersymmetric AdS solutions.

### Mauricio Romo

**B-brane Transport in Anomalous Gauged Linear Sigma Models**

Mapping of B-branes in SCFTs determined by the different phases of a non-anomalous gauged linear sigma model (GLSM) is a well established subject in physics and mathematics. From the point of view of the GLSM, a fundamental tool to determine such functors is the so-called grade restriction rule (GRR). When the axial R-symmetry is anomalous, this picture changes and determining the functors is not so simple. Some such cases are understood in physics and mathematics as well. In this talk I will present a GLSM approach to understand how the GRR must be modified for the anomalous cases, by using results in supersymmetric localization as a guide. I will illustrate this in simple cases, mainly Hirzebruch-Jung resolutions of A_n singularities.

### Minxin Huang

**Refined topological strings on compact Calabi-Yau spaces**

Refined topological string theory is motivated by Omega background in supersymmetric gauge theory. Previous works consider only non-compact Calabi-Yau spaces. In this talk we discuss a class compact elliptic Calabi-Yau spaces and compare the results with geometric calculations. The talk is based on parts of a work in progress with S. Katz and A. Klemm.

### Tarek Anous

**ETH at large c and a scrambling phase transition in eigenstates**

Two dimensional conformal field theories at large central charge are chaotic. Despite this seeming obstruction, recent developments have allowed us to identify how bulk physics in AdS_3, with all its inconsistencies, emerges from a precise piece of CFT correlation functions in the OPE expansion. I will overview some of these recent developments and describe how to characterize the thermal properties of pure black-hole microstates. Additionally, I discuss how well these pure states scramble information.