Conference

Symmetries are fundamental to our understanding of nature. In Quantum Field Theory, they have become the guidelines for the formulation of fundamental theories. In this talk, I will go into the importance of symmetries and the concept of spontaneous symmetry breaking to understand the early Universe. Then, I will discuss gauge symmetries and their fundamental differences with physical symmetries, and the subsequent contradiction in our understanding of the Higgs mechanism as a spontaneously broken gauge symmetry. I will discuss alternative understandings of the Higgs mechanism and the importance of gauge symmetries despite their seemingly redundant nature.

Quantization of general relativity in four dimensions is not straightforward because Newton's constant carries units of (length)^2 which means the theory is non-renormalizable. Up to now, the only quantum-mechanical approach which has allowed the perturbative computation of graviton scattering at all energy scales is superstring theory. Although it might be a long time before experimental tests of quantum gravity will be able to tell us if superstring theory correctly describes our universe, the theory has other interesting properties such as supersymmetry and duality symmetry whose study has been useful for several branches of physics and mathematics.

here are two notions of a symmetry of a group G on a 3d topological order (TO): an "algebraic" symmetry, where G acts by automorphisms on the tensor category defining the (TO), and a "field-theoretic" symmetry, where the TFT corresponding to the TO is extended to manifolds with a principal G-bundle. The "field-theoretic" notion is stronger than the "algebraic" one, and the obstruction is sometimes referred to as the anomaly of the TO. The goal of this talk is to discuss a project joint with Weicheng Ye and Matthew Yu on computing these anomalies for fermionic TOs/spin TFTs: we develop a general framework employing Gaiotto-Kapustin's bosonic shadow construction. I will discuss both the mathematical conjectures our framework rests on as well as its use in examples. The Smith long exact sequence appears in our computations.

Motivated by the dagger category of Hilbert spaces, we explore the mathematical axiomatization of unitary topological field theory (TFT) using dagger categories. Recent advancements have elucidated the structure of higher dagger categories, paving the way for a precise definition of extended unitary TFTs. I will present an explicit formulation of once extended TFTs utilizing various versions of dagger bicategories. This framework enables a complete classification of unitary extended two-dimensional TFTs with arbitrary symmetry groups in terms of their unitary 2-representations. This is joint work in progress with Lukas Muller.

Foraging is a ubiquitous behavior performed by all animals and human beings as they search for food needed to survive. Foraging theory has been key to understanding a variety of model systems but it still lacks mechanistic insights that relate it to neurobiological and other physiological mechanisms. In this talk, I will present work that aims to develop a quantitative mechanistic framework of foraging with a specific focus on patch foraging either of an individual agent or in a social context. I will also present a learning model that accounts for how agents learn the structure of the environment