Abstract: Interacting particle models are often employed to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. These individual-based models capture fine details, including randomness and discreteness of individuals, that are not considered in continuum models such as partial differential equations (PDE) and integral-differential equations. The challenge is how to simultaneously […]
Abstract: The Dirac equation is a relativistic equation that describes the spin-1/2 particles. We talk about Dirac equations in Minkowski spacetime. In a geometric viewpoint, we can see that the spinor fields satisfying the Dirac equations enjoy the so-called peeling properties. It means the null components of the solution will decay at different rates along the […]
Member Seminar Speaker: Juven Wang Title: C-P-T Fractionalization, and Quantum Criticality Beyond the Standard Model Abstract: Discrete spacetime symmetries of parity P or reflection R, and time-reversal T, act naively as a Z2-involution on the spacetime coordinates; but together with a charge conjugation C and the fermion parity (−1)^F, these symmetries can be further fractionalized […]
During the 2021–22 academic year, the CMSA will be hosting a seminar on General Relativity, organized by Aghil Alaee, Jue Liu, Daniel Kapec, and Puskar Mondal. This seminar will take place on Thursdays at 9:30am – 10:30am (Eastern time). The meetings will take place virtually on Zoom. To learn how to attend, please fill out this form. The schedule […]
Abstract: I will explain what the Festina Lente bound means and where it comes from. Then I discuss its possible implications for phenomenology, both top-down and bottom-up.
Title: Ising model, total positivity, and criticality Abstract: The Ising model, introduced in 1920, is one of the most well-studied models in statistical mechanics. It is known to undergo a phase transition at critical temperature, and has attracted considerable interest over the last two decades due to special properties of its scaling limit at criticality. The totally nonnegative Grassmannian […]
Abstract: D-critical schemes and Artin stacks were introduced by Joyce in 2015, and play a central role in Donaldson-Thomas theory. They typically occur as truncations of (-1)-shifted symplectic derived schemes, but the problem of constructing the d-critical structure on a “DT moduli space” without passing through derived geometry is wide open. We discuss this problem, and […]
Abstract: (joint with S. Venugopalan) I will describe version of the Fukaya algebra that appears in a tropical degeneration with the Lagrangian being one of the “tropical fibers”. An example is the count of “twenty-one disks in the cubic surface” (suggested by Sheridan) which is an open analog of the twenty-seven lines. As an application, I will explain why the Floer […]
Speaker: Peng Shan (Tsinghua University) Title: Categorification and applications Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.
Title: Electric-magnetic duality and the Geometric Langlands duality Abstract: I will give a pedagogical review of the connection between electric-magnetic duality and the Geometric Langlands duality.
Title: Mathematical resolution of the Liouville conformal field theory. Abstract: The Liouville conformal field theory is a well-known beautiful quantum field theory in physics describing random surfaces. Only recently a mathematical approach based on a well-defined path integral to this theory has been proposed using probability by David, Kupiainen, Rhodes, Vargas. Many works since the […]
Abstract: Taking the large dimension limit of Einstein’s equations is a useful strategy for solving and understanding the dynamics that these equations encode. I will introduce the underlying ideas and the progress that has resulted in recent years from this line of research. Most of the discussion will be classical in nature and will concern situations […]