Published on Department of Mathematics Calendar (https://calendar.math.yale.edu)

Week of April 14, 2024

April 15, 2024
Group Actions, Geometry and Dynamics [3]	Closed geodesics and stability of negatively curved metrics	Karen Butt - University of Chicago	4:00pm - KT205
Geometry, Symmetry and Physics [4]	Advances in flat space holography	Atul Sharma - Harvard	4:30pm - KT 217

April 17, 2024
Applied Mathematics [5]	Efficient Convergent Boundary Integral Methods for Slender Bodies	Dhairya Malhotra - Flatiron Institute	3:00pm - LOM 214

April 18, 2024
Geometry, Symmetry and Physics [4]	Classical Deformations of Celestial Symmetries	Simon Heuveline - Cambridge University	2:30pm - KT801
Analysis [6]	Rigidity of the quintic, nonlinear Schrodinger equation	Benjamin Dodson - John Hopkins	4:00pm - KT 201

April 19, 2024
Friday Morning Seminar [7]	Solid-On-Solid is liquid (at least when thawed a little)	Eyal Lubetzky - Courant Institute of Mathematical Sciences - NYU	10:00am - KT801

Abstracts

Week of April 14, 2024

April 15, 2024
Group Actions, Geometry and Dynamics [3]	Closed geodesics and stability of negatively curved metrics	4:00pm - KT205	The marked length spectrum of a closed Riemannian manifold of negative curvature is a function on the free homotopy classes of closed curves which assigns to each class the length of its unique geodesic representative. It is known in certain cases that the marked length spectrum determines the metric up to isometry, and this is conjectured to be true in general. In this talk, we explore to what extent the marked length spectrum on a sufficiently large finite set approximately determines the metric.
Geometry, Symmetry and Physics [4]	Advances in flat space holography	4:30pm - KT 217	I will review the highlights of Strominger’s program of celestial holography, focusing on emerging connections to twisted holography, topological strings and twistor theory. A running example of the talk will be holography for certain self-dual theories placed on an asymptotically flat, scalar-flat Kahler geometry known as Burns space. This is based on work done in collaboration with Kevin Costello and Natalie M. Paquette.

April 17, 2024
Applied Mathematics [5]	Efficient Convergent Boundary Integral Methods for Slender Bodies	3:00pm - LOM 214	The dynamics of active and passive filaments in viscous fluids is frequently used as a model for many complex fluids in biological systems such as: microtubules which are involved in intracellular transport and cell division; flagella and cilia which aid in locomotion. The numerical simulation of such systems is generally based on slender-body theory which give asymptotic approximations of the solution. However, these methods are low-order and cannot enforce no-slip boundary conditions to high-accuracy, uniformly over the boundary. Boundary-integral equation methods which completely resolve the fiber surface have so far been impractical due to the prohibitive cost of current layer-potential quadratures for such high aspect-ratio geometries. In this talk, I will present new quadrature schemes which make such computations possible and new integral equation formulations which lead to well-conditioned linear systems upon discretization. I will present numerical results to show the efficiency of our methods.

April 18, 2024
Geometry, Symmetry and Physics [4]	Classical Deformations of Celestial Symmetries	2:30pm - KT801	This talk is based on arXiv:2305.09451, arXiv:2403.18011 and work in progress. I will discuss several deformations of algebras which are closely related to $w_{1+\infty}$ and give bulk interpretations of the respective deformations. Some of these deformations arise naturally from a backreaction in self-dual Einstein gravity analogous to part of the recent top-down construction of Costello, Paquette and Sharma and I will highlight similarities and differences.
Analysis [6]	Rigidity of the quintic, nonlinear Schrodinger equation	4:00pm - KT 201

April 19, 2024
Friday Morning Seminar [7]	Solid-On-Solid is liquid (at least when thawed a little)	10:00am - KT801	The (2+1)D Solid-On-Solid (SOS) model famously exhibits a roughening transition: on an N×N torus with the height at the origin rooted at 0, the variance of h(x), the height at a point x is O(1) when the inverse-temperature β is large, vs O(log \|x\|) when β is small. The rigidity at large β is believed to fail once the surface is on a slope (tilted boundary conditions), which ought to destabilize it and induce the log-correlated behavior of the small β regine. The only rigorous result on this is by Sheffield (2005): if the slope θ is irrational, then Var(h(x)) diverges with \|x\| (with no known quantitative bound). We study this model at a large enough fixed β, on an N×N torus with a nonzero boundary condition slope θ, perturbed by a potential V of strength ε(β) per site (arbitrarily small). Our main result is (a) the measure on the height gradients ∇h has a weak limit μ as N→∞; and (b) the scaling limit of a sample from μ converges to a full plane GFF. In particular, we recover the asymptotics of Var(h(x)). To our knowledge, this is the first example of a random surface of the ∇ɸ family of models, or any perturbation of one, where the scaling limit is recovered at large finite β under tilted boundary conditions. The proof looks at random monotone surfaces that approximate the SOS surface, and shows that (i) these form a weakly interacting dimer model, and (ii) the renormalization framework of Giuliani, Mastropietro and Toninelli (2017) can be applied to it, leading to the scaling limit. Joint work with Benoît Laslier.

Links
[1] https://calendar.math.yale.edu/list/calendar/grid/week/2024-W15 [2] https://calendar.math.yale.edu/list/calendar/grid/week/2024-W17 [3] https://calendar.math.yale.edu/seminars/group-actions-geometry-and-dynamics [4] https://calendar.math.yale.edu/seminars/geometry-symmetry-and-physics [5] https://calendar.math.yale.edu/seminars/applied-mathematics [6] https://calendar.math.yale.edu/seminars/analysis [7] https://calendar.math.yale.edu/seminars/friday-morning-seminar [8] https://calendar.math.yale.edu/list/calendar/grid/week/abstract/2024-W15 [9] https://calendar.math.yale.edu/list/calendar/grid/week/abstract/2024-W17