Souvik Dhara

Souvik Dhara received the cum laude distinction for his PhD thesis entitled “Critical Percolation on Random Graphs with Prescribed Degree Sequences”. The thesis gives an impressively complete description of the possible behaviors of critical percolation on random graphs, in which the degree sequence is fixed. This behavior is characterized in terms of scaling limits, which describe the sizes of clusters, but also their structural properties, when the network is on the verge of breaking down. The precise behavior is governed by the amount of inhomogeneity of the model, as characterized by how large the largest degrees are as a function of the network size. Such settings are inspired by real-world networks, where this inhomogeneity has also been observed.  

 

Souvik proved that there are three regimes or universality classes in terms of the degree power-law exponent, in which rather different behavior is observed for cluster sizes as well as the metric structure of critical clusters. Souvik's work is remarkably deep, and many of the concepts and techniques far transcend the context of the specific models.  The results are also mathematically sophisticated, original and of consistently high quality, as evidenced by the fact that they have led to several publications in major journals, in particular the Electronic Journal of Probability and the Journal of Statistical Physics, as well as in the SIGMETRIC conference. Many papers have only recently been completed, and are thus not yet accepted in journals. The works that form Souvik's thesis give an almost complete characterization of the possible behaviors that can occur for critical configuration models, as well as the critical behavior of percolation on it. Frank den Hollander, who was on Souvik’s thesis committee, states `It is impressive to see that, for the configuration model, he was able to give an almost complete description of percolation in the critical window... The long introduction, which is clearly put together, makes the panaroma of the thesis completely clear. A wonderful and overarching research.’ Aside from the work in the thesis, Souvik also wrote several other papers on various topics in random graphs, such as jamming limits and combinatorial optimization problems on random graphs.

 

Debankur Mukherjee

Debankur Mukherjee received the cum laude distinction for his PhD thesis entitled "Scalable Load Balancing in Networked Systems".  The thesis contains a stunning collection of groundbreaking results at the frontier of a booming and highly competitive domain of research.  Debankur has in particular pioneered the notion of asymptotic optimality and universality of load balancing algorithms, as an overarching perspective on scalability issues in large-scale data centers.  He superbly combines this unifying conceptual angle with stochastic coupling as a common methodological framework in order to break major new ground.  The results involve advanced probabilistic techniques, but also provide valuable insights for algorithm design.  The exceptional quality of the thesis is reflected by a staggering record of publications in top-notch journals, such as Annals of Applied Probability, Journal of Applied Probability, Mathematics of Operations Research and Stochastic Systems, as well two papers at the highly prestigious and selective ACM SIGMETRICS Conference, one of which received the Best Student Paper Award in June.

 

New Positions

Souvik Dhara has been awarded the prestigious Oded Schramm Postdoctoral Fellowship. This is a three year postdoctoral position awarded jointly by Microsoft Research Lab New England and MIT Mathematics. In the first year, Souvik will work at Microsoft Research reporting to Christian Borgs and Jennifer Chayes and he will also hold a research affiliate position at MIT Mathematics. In the next two years, he will hold a postdoctoral position at MIT Mathematics and will carry out research in the theory of graph convergence and its relation to stochastic processes.

Debankur Mukherjee has recently joined Brown University as a postdoc with Prof. Kavita Ramanan for one year. After that, as from August 2019 he will be joining as a tenure-track Assistant Professor in ISyE at Georgia Institute of Technology.

 

We wish Souvik and Debankur all the best in their new careers!

 

Photo credit: Odette Beekmans