We show explicitly how the exact renormalization group equation of interacting vector models in the large N limit can be mapped into certain higher-spin equations of motion. The equations of
motion are generalized to incorporate a multiparticle extension of the higher-spin algebra, which reflects the "multitrace" nature of the interactions in the dual field theory from the holographic point of view.
One of the main challenges that we face both as individual persons and as a species concerns the distribution and use of resources, such as water, time, capital, computing power or negatively valued resources like nuclear waste. Also within theoretical physics, one
frequently deals with resources like free energy or quantum entanglement. I will describe a mathematical theory of resources which makes quantitative predictions about how many resources are required for
producing a certain commodity and outline some applications to information theory.
From prehistoric times onward, people have always found ways to incorporate mathematical thinking into art. Today, we have sophisticated mathematical machinery that we can use both to understand the rules that underlie historical patterns and to describe new designs of great beauty and originality. Better yet, computers can serve as a powerful artistic tool, helping make these mathematical visions a reality. This talk will explore some of the exciting contemporary work that lies in the intersection of mathematics and art.
We discuss how bipartite graphs on Riemann surfaces encapture a wealth of information about the physics of large classes of supersymmetric gauge theories, especially those with quiver structure and arising from the AdS/CFT context. The correspondence between the gauge theory, the underlying algebraic geometry of it space of vacua, the combinatorics of dimers and toric varieties, as well as the number theory of dessin d'enfants becomes particular intricate under this light.
In two spatial dimensions, there is a good correspondence between TQFTs and topological phases of matter for spin systems. I will discuss this correspondence in one and three spatial dimensions for spin systems. If time permits, I will also discuss the situation for fermion systems.
Based on her book, The Calculus Diaries, join, Jennifer Ouellette as she shows how calculus can be applied to everything from gas mileage, diet, the rides at Disneyland, surfing in Hawaii, shooting craps in Vegas and warding off zombies. Even the mathematically challenged, can-and-should learn the fundamentals of the universal language.
It has been known for twenty years that a class of
two-dimensional gauge theories are intimately connected to toric geometry, as
well as to hypersurfaces or complete intersections in a toric varieties, and to
generalizations thereof. Under renormalization
group flow, the two-dimensional gauge theory flows to a conformal field theory
that describes string propagation on the associated geometry. This provides a connection between certain
quantities in the gauge theory and topological invariants of the associated
String- and M-theory inspired scenarios for the cosmology of the early universe. Replacing the unphysical Big Bang-like beginning of our universe with bouncing scenarios of accelerated expansion followed by familiar evolution.