My name is Aanjaneya Kumar and I am a PhD student at the Indian Institute of Science Education and Research Pune working under the supervision of Prof. M. S. Santhanam. My primary interest is in obtaining insight into practically relevant problems, which could arise in various fields including (but not restricted to) physics, biology, and the social sciences, by first formulating them as mathematical models and then analyzing them using tools from Statistical Physics, Graph Theory and Game Theory.

Here are some important links for my review:

1. Teaching Report: May 2022 - April 2023

2. Progress Report: May 2022 - April 2023

3. Academic CV

Summary

A very high-level goal of statistical physics is to provide a low-dimensional representation of high-dimensional complex systems. This is not always an easy task. Ideally, one wants to arrive at a description which captures essential features of the complex system at hand, but one which is also simple enough, so that it is tractable, and further insight into the system can be generated from it. This is where stochastic processes play an important role, which is a unifying theme of my research interests. The general philosophy behind stochastic modelling is that when you are faced with unmanageable complexity, a good first step is to model that with randomness. The pursuit of describing elements of a complex system in the simplest manner possible, and the remarkable success of stochastic modelling in doing so has shaped my research interests significantly.

The general philosophy described above, in fact, goes much beyond statistical physics and can be thought of as a guiding principle for fruitful research across disciplines. I try my best to keep this approach in mind while tackling research problems. Some of my research endeavours end up in the form of publications and a list of them can be found here. A lot of things that I gain from my research do not end up being part of the final research paper that I write but I would be very happy to talk to you about them. I strongly believe in science being a collective and collaborative effort and I look forward to discussing ideas with you.

Publications (from the last review period May 2022 - April 2023)

• Inference from Gated First-Passage Times, with Yuval Scher, Prof. Shlomi Reuveni, and Prof. M.S. Santhanam, ArXiv:2210.00678 (2022)
• Continuous Gated First-Passage Processes, with Yuval Scher, Prof. M.S. Santhanam, and Prof. Shlomi Reuveni, ArXiv:2211.09164 (2022)
• Depolarization of Opinions on Social Networks through Random Nudges, with Ritam Pal, and Prof. M.S. Santhanam, ArXiv:2212.06920 (2022)
• First-Passage Times of Multiple Diffusing Particles with Reversible Target-Binding Kinetics. with Prof. Denis Grebenkov, J. Phys. A: Math. Theor. 55 325002 (2022)
• Universal Framework for Record Ages under Restart, with Prof. Arnab Pal, Phys. Rev. Lett. 130, 157101 (2023)

Manuscripts in preparation

• Optimal detection of gated processes, with Yuval Scher, Prof. Shlomi Reuveni, and Prof. M.S. Santhanam (2023)
• Extreme value statistics of partially-observed time series, with Prof. M.S. Santhanam (2023)

Complete list of published work is available in my CV and Google Scholar page.

Research Interests

My current research interests include:

• Stochastic models of complex systems
• Inference from partial information
• Extreme events
• Complex networks
• Statistical physics
• Evolutionary game theory

Publications

1. Universal Framework for Record Ages under Restart
   • with Prof. Arnab Pal, in Physical Review Letters (2023)
2. Depolarization of Opinions on Social Networks through Random Nudges
   • With Ritam Pal, and Prof. M.S. Santhanam, ArXiv:2212.06920 (2022)
3. Continuous Gated First-Passage Processes
   • With Yuval Scher, Prof. M.S. Santhanam, and Prof. Shlomi Reuveni, ArXiv:2211.09164 (2022)
4. Inference from Gated First-Passage Times
   • With Yuval Scher, Prof. Shlomi Reuveni, and Prof. M.S. Santhanam, ArXiv:2210.00678 (2022)
5. First-Passage Times of Multiple Diffusing Particles with Reversible Target-Binding Kinetics
   • With Prof. Denis Grebenkov, in Journal of Physics A: Mathematical and Theoretical (2022)
6. Reversible Target-Binding Kinetics of Multiple Impatient Particles
   • With Prof. Denis Grebenkov, in The Journal of Chemical Physics (2022)
7. First Detection of Threshold Crossing Events under Intermittent Sensing
   • With Aniket Zodage, and Prof. M. S. Santhanam, in Physical Review E (Letter) (2021)
8. The Evolution of Honesty in Higher-Order Social Networks
   • With Sandeep Chowdhary, Prof. Valerio Capraro, and Prof. Matjaz Perc, in Physical Review E (2021)
9. Simplicial Contagion in Temporal Higher-Order Networks
   • With Sandeep Chowdhary, Dr. Iacopo Iacopini, Dr. Giulia Cencetti, and Dr. Federico Battiston, in Journal of Physics: Complexity (2021)
10. Chase-Escape Percolation on the 2D Square Lattice
    • With Prof. Peter Grassberger, and Prof. Deepak Dhar, in Physica A (2021)
11. The Evolution of Trust and Trustworthiness
    • With Prof. Valerio Capraro, and Prof. Matjaz Perc, in Journal of The Royal Society Interface (2020)
12. Extreme Events in Stochastic Transport on Networks
    • With Suman Kulkarni, and Prof. M. S. Santhanam, in Chaos (2020)
13. Improved Upper Bounds on the Asymptotic Growth Velocity of Eden Clusters
    • With Prof. Deepak Dhar, in Journal of Statistical Physics (2020)
14. TASEP Speed Process: An Effective Medium Approach
    • With Prof. Deepak Dhar, in Journal of Statistical Mechanics (2020)
15. Distinct Nodes Visited by Random Walkers on Scale-Free Networks
    • With Yagyik Goswami and Prof. M. S. Santhanam, in Physica A (2019)
16. Record Statistics of Equities and Market Indices
    • With Prof. M. S. Santhanam, in Econophysics and Sociophysics: Recent Progress and Future Directions (2017)

Teaching

• Grader for:
  • Advanced Quantum Mechanics (Spring 2019), Course coordinator: Prof. Deepak Dhar
• Teaching Assistant for:
  • Nonlinear Dynamics and Chaos (Spring 2020), Course coordinator: Prof. M. S. Santhanam
  • Statistical and Thermal Physics (Spring 2021), Course coordinator: Prof. Seema Sharma, Prof. Vijaykumar Chikkadi
• Lecturer:
  • Mathematical Methods in Physics (Spring 2021), at Fergusson College, Pune
  • Statistical Mechanics (Summer 2021), at Fergusson College, Pune
  • Mathematical Methods in Physics (Fall 2021), at Fergusson College, Pune
  • Statistical Mechanics (Spring 2022), at Fergusson College, Pune
  • Mathematical Methods in Physics (Fall 2022), at Fergusson College, Pune
  • Statistical Mechanics (Spring 2023), at Fergusson College, Pune

Teaching certificate for the last review period is available here.