Wednesday, February 1, 2023
Time | Items |
---|---|
All day |
|
1pm |
02/01/2023 - 1:00pm Abstract: In this talk I will introduce an efficient method for solving 2nd order, linear, homogeneous ODEs whose solutions may vary between highly oscillatory and slowly changing over the solution interval. The solver employs two methods: in regions where the solution varies slowly, it uses Chebyshev-grid based collocation with an adaptive stepsize, but in the highly oscillatory phase it automatically switches to constructing a local phase function. I propose a defect-correction iteration that gives an asymptotic series for such a phase function; this is numerically approximated on a Chebyshev grid. In the talk I will present how the method fits in the landscape of oscillatory solvers, details of the algorithm, results from numerical experiments, and a brief error analysis. Location:
AKW 200
|
4pm |
02/01/2023 - 4:15pm Liouville quantum gravity (LQG) is a theory of random surfaces that originated from string theory. Schramm Loewner evolution (SLE) is a family of random planar curves describing scaling limits of many 2D lattice models at their criticality. Before the rigorous study via LQG and SLE in probability, random surfaces and scaling limits of lattice models have been studied via another approach in theoretical physics called conformal field theory (CFT) since the 1980s. In this talk, I will demonstrate how a combination of ideas from LQG/SLE and CFT can be used to rigorously prove several long standing predictions in physics on random surfaces and planar lattice models, including the law of the random modulus of the scaling limit of uniform triangulation of the annular topology, and the crossing formula for critical planar percolation on an annulus. I will then present some conjectures which further illustrate the deep and rich interaction between LQG/SLE and CFT. Based on joint works with Ang, Holden, Remy, Xu, and Zhuang.
Location:
LOM 214
|