Thursday, May 30, 2024

 

 

Session Chair: Fanghua Lin, NYU / NYU Shanghai

9:00-10:00 AM

 

 

 

 

 

Decay of excess for the abelian Higgs model

By Guido De Philippis, New York University

Entire critical points of the Yang-Mills-Higgs functional are known to blow down to (generalized) minimal surfaces. Goal of the talk is to prove an Allard’s type large scale regularity result for the zero set of the solution. In particular, in the “multiplicity one” energy regime, we show uniqueness blow-downs and we classify entire solutions in small dimensions and of entire minimizers in any dimension.  

This is based on a joint work with Aria Halavati and Alessandro Pigati.

10:00-10:30 AM

Morning Tea Break

10:30-11:30 AM

 

 

 

 

 

Heat kernel fluctuations and quantitative homogenizations for the one-dimensional Bouchaud trap model

By Takashi Kumagai, Waseda University

The Bouchaud trap model (BTM) is a random walk in a random medium given by a landscape of traps which retain the walk for some amount of time. In this talk, we consider one-dimensional versions of the model, and discuss scaling limits, heat kernel fluctuations and quantitative homogenization. We study how these properties change when the parameter of the distributions of the traps change.

This is a joint work with S. Andres (Braunschweig) and D. Croydon (Kyoto).

11:30 AM-12:10 PM

 

 

 

On the dynamics of nonlinear random and quasi-periodic systems

By Wei-Min Wang, NYU Shanghai

We discuss time evolution of nonlinear random and quasi-periodic systems. Examples of such systems include the nonlinear random and the nonlinear quasi-periodic Schr\"odinger equations on the lattice.  We shall elaborate on their similarities.

12:10 PM-3:00 PM

Lunch Break

 

Session Chair: Wei Wu, NYU Shanghai

3:00-4:00 PM

 

 

 

 

 

 

 

 

Tilted Solid-On-Solid is liquid (at least when thawed a little)

By Eyal Lubetzky, New York University

Eyal Lubetzky

4:00-4:30 PM

Afternoon Tea Break

4:30-5:10 PM

 

 

 

 

 

 

Rare transitions in noisy heteroclinic networks

By Hong-Bin Chen, Institut des Hautes Études Scientifiques (IHES)

We study white noise perturbations of planar dynamical systems with heteroclinic networks in the limit of vanishing noise. We show that the probabilities of transitions between various cells that the network tessellates the plane into decay as powers of the noise magnitude, and we describe the underlying mechanism. A metastability picture emerges, with a hierarchy of time scales and clusters of accessibility, similar to the classical Freidlin-Wentzell picture but with shorter transition times. We discuss applications of our results to homogenization problems and to the invariant distribution asymptotics. At the core of our results are local limit theorems for exit distributions obtained via methods of Malliavin calculus. Joint work with Yuri Bakhtin and Zsolt Pajor-Gyulai.

5:10-5:50 PM

 

 

 

 

 

Conformal Invariance of Random Currents: A Stability Result

By Jiaming Xia, Institut des Hautes Études Scientifiques (IHES)

The talk is based on our recent work on proving the convergence of the single sourceless critical random current to a limit identifiable with the nested CLE(3). In the talk, I will mainly focus on our approach, which views the random current as a perturbation of the Ising interface, known to converge to CLE(3). Instead of focusing solely on the random current, we provide a general framework for the stability of scaling limits under the perturbation by superimposing an independent Bernoulli percolation.