Over the course of development, cells have to reliably commit to distinct cell-fates by inferring their position on a tissue. Waddington proposed that cellular dynamics can be viewed as ``natural trajectories'' in an evolving landscape. Using an energy function formalism, we explore the role of intra-cellular signalling in enhancing the robustness of tissue segmentation from the perspective of Waddington landscape. We also show how the model can be coarse-grained at the tissue scale, and discuss how biological systems can be fine-tuned near criticality.

Chaos is a ubiquitous feature of nature, and quantum chaos provides a fundamental framework for understanding complex behavior in quantum systems. In this talk, I will present two novel approaches to characterizing quantum chaos. The first method will be based on the Krylov space approach, offering a computationally efficient framework for studying non-equilibrium dynamics in many-body systems. The second approach examines the statistical independence of operator evolution through the lens of free probability theory, providing a complementary perspective on operator dynamics. I will discuss recent developments and future prospects in both directions and outline a program to bridge these frameworks, illustrating the ideas with examples from random matrix theory, strongly correlated systems, and quantum gravity.

Join Zoom Meeting https://zoom.us/j/91383430608 Meeting ID: 913 8343 0608 Passcode: moonshine Tensor categories offer a common language for symmetry. I will begin with a foundational example, the category of representations Rep(G) of a finite group G, and discuss the Tannakian viewpoint (Milne–Deligne). From there, I will explain why non-semisimple tensor categories naturally arise in diverse contexts, such as in positive characteristic, at roots of unity, and in logarithmic CFT. Along the way, I will highlight connections to subfactors, algebraic geometry, number theory, and low-dimensional topology. The final part will focus on understanding the representation categories of Vertex Operator Algebras (VOAs). A recursive approach is useful here: one can analyze a few key examples (due to seminal works of Feigin, Frenkel, Kazhdan, Lusztig, Arakawa etc.) and then relate many others via constructions like extensions, cosets, and orbifolds. I will concentrate on VOA extensions and the underlying categorical mechanism, which involves commutative algebra objects and their local modules. This provides a clean framework for transferring properties like rationality and rigidity from one VOA to another, which we will illustrate with concrete examples.

Join Zoom Meeting https://zoom.us/j/91383430608 Meeting ID: 913 8343 0608 Passcode: moonshine Tensor categories offer a common language for symmetry. I will begin with a foundational example, the category of representations Rep(G) of a finite group G, and discuss the Tannakian viewpoint (Milne–Deligne). From there, I will explain why non-semisimple tensor categories naturally arise in diverse contexts, such as in positive characteristic, at roots of unity, and in logarithmic CFT. Along the way, I will highlight connections to subfactors, algebraic geometry, number theory, and low-dimensional topology. The final part will focus on understanding the representation categories of Vertex Operator Algebras (VOAs). A recursive approach is useful here: one can analyze a few key examples (due to seminal works of Feigin, Frenkel, Kazhdan, Lusztig, Arakawa etc.) and then relate many others via constructions like extensions, cosets, and orbifolds. I will concentrate on VOA extensions and the underlying categorical mechanism, which involves commutative algebra objects and their local modules. This provides a clean framework for transferring properties like rationality and rigidity from one VOA to another, which we will illustrate with concrete examples.