28/04/2021

Shangjie Yang defends thesis aiming for postdoctoral studies.

Observing the time required for phenomena to occur can be an activity with philosophical overtones. But in the case of Shangjie Yang, the task is mostly mathematical. A doctoral student at IMPA, the Chinese scientist will defend his thesis “Mixing Time for Interface Models and Particle Systems” on Thursday (29), supervised by Hubert Lacoin. From 9 am, there will be a live stream on IMPA’s YouTube channel .

In this work, the interface model analyzed is that of polymer fixation interacting with an impenetrable defective line. And in the repulsive phase, Yang shows that the total variation distance to equilibrium drops from one to zero. The second interface model is a variant of the polymer fixation model, also subject to another external force, pulling the interface away from the defective line.

The thesis also addresses how the asymmetric simple exclusion process occurs in a random environment, where the jump rates of the particles are obtained independently of a common law. "In short, my goal is to understand how long a random algorithm (Markov chain) needs to be close to equilibrium," he points out.

Born in rural Guangdong province, China, Yang came to Brazil in 2015 to pursue a master's degree at IMPA. Before leaving his home country, he completed undergraduate degrees in mathematics and applied mathematics at Sun Yat-Sen University. "Afterwards, I went to Nankai University in Tianjin as a master's student for a year and a half, but I didn't finish."

Already settled in Rio de Janeiro, the partnership with his current advisor, Hubert Lacoin, has yielded good results. Among the articles, the future PhD highlights the work "Metastability for expanding bubbles on a sticky substrate" . "When we finished solving this problem, I was so excited that I couldn't sleep that night," he confesses. Yang also highlights the publication "Mixing time for the asymmetric simple exclusion process in a random environment" .

“Lacoin has a good intuition for mathematics and mechanical physics. Today, I see myself well prepared to do research in these areas. IMPA has a very good academic environment,” observes the future PhD. In July, the mathematician's life will take on a new dimension. That's when he begins his postdoctoral studies at Bar-Ilan University in Tel Aviv, Israel. “For me, mathematics is a way to describe the world to understand what it is, how it works. But it can also be a very interesting game,” he considers.