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Arnab Roy

Ikerbasque Research Fellow and Ramón y Cajal Fellow

Applied Analysis

T +34 946 567 842
F +34 946 567 842
E aroy@bcamath.org

Information of interest

I am an Ikerbasque Researcher and Ramón y Cajal Fellow at the Basque Center for Applied Mathematics (BCAM) in Bilbao, Spain, affiliated with the Applied Analysisgroup. 

My research lies at the interface of fluid mechanics, partial differential equations, and control theory, with a primary focus on fluid–structure interaction (FSI). I am particularly interested in the mathematical analysis of complex coupled systems, addressing fundamental questions of existence, uniqueness, regularity, stability, singular limits, and long-time behavior of solutions. My work combines techniques from nonlinear PDE theory, functional analysis, and mathematical modeling, and is motivated by applications arising in biological flows, geophysical fluid dynamics. My long-term goal is to develop rigorous mathematical frameworks for multiscale and multiphysics models arising in fluid dynamics and continuum mechanics, bridging theoretical analysis with realistic applications. Current directions of interest include FSI with porous and elastic media, collective effects of particle flows, stochastic fluid–structure systems, and time-periodic dynamics.

I am currently the Principal Investigator of the Spanish National Project PID2023-146764NB-I00 (2024–2028) and a recipient of the Ikerbasque Research Fellowship and the Ramón y Cajal Fellowship, funded by the Spanish Ministry of Science.

Before joining BCAM, I held a Humboldt Research Fellowship at TU Darmstadt, Germany, and completed earlier postdoctoral work at the Czech Academy of Sciences and INRIA Nancy. I earned my Ph.D. from the Tata Institute of Fundamental Research-CAM (TIFR-CAM) in Bangalore.

I am always interested in collaborations, interdisciplinary projects, and the supervision of motivated Ph.D. students and postdoctoral researchers in the areas of PDEs, fluid mechanics, and control theory.

 

Invited Talks

  • Oberseminar Analysis, TU Darmstadt, December, 2025. 

  • Control, Problemas Inversos y Aprendizaje Automático (COPI2A), Third Meeting, Castro Urdiales, December, 2025.

  • Séminaire de EDP Physique Mathématique, Institut de Mathématiques de Bordeaux, November, 2025.

  • Bilbao-Barcelona Analysis and PDEs meeting, Bilbao, 3rd-5th September, 2025.

  • Mathematics with Applications 2025 on the occasion 60th birthday of Professor Sarka Necasova, Funchal, Portugal, 2-6th June, 2025.

  • Spring workshop on fluid solid interactions and related problems, CIRM-Marseille Luminy, France, 21-25 April, 2025.

  • Faculty of Mathematics, University of Seville, Spain. March 2025.

  • Young Researchers Congress of the RSME, Bilbao, 13-17th January, 2025.

  • Mathematics of fluids in motion: Recent results and trends, CIRM-Marseille Luminy, France, 11-15 November, 2024.

  • Analysis and PDE Seminar, University of the Basque Country, 19th September, 2024.

  • Minisymposium in Equadiff Conference 2024, Karlstad University, Sweden, 10th-14th June, 2024.

  • Oberseminar AG Mathematische Modellierung, TU Clausthal, 27th May, 2024.

  • Oberseminar Analysis, TU Darmstadt, April, 2024.

  • Seminar in IISER Mohali, India, February, 2024.

  • IntComSin Colloquium, FAU Erlangen-Nürnberg, 24th November, 2023.

  • Oberwolfach Seminar: Recent Topics on the Navier-Stokes Equations, 22nd-27th October 2023.

  • Minisymposium in ENUMATH Conference 2023, Instituto Superior Técnico, Lisbon, 4th-8th September, 2023.

  • Oberwolfach Workshop: Mathematical Advances in Geophysical Fluid Dynamics, 14th-18th November, 2022.

  • Oberseminar Analysis, TU Darmstadt, 3rd November, 2022.

  • BCAM-UPV Analysis and PDE Seminar, University of the Basque Country, 8th September, 2022.

  • Oberseminar Mathematik, University of Würzburg, 2nd August, 2022.

  • Weekly Seminar in IISER Mohali, India, 7th June, 2022.

  • National Institute of Science Education and Research (NISER), Odisha, India, 23th May, 2022.

  • Applied Mathematics and Numerical Analysis Seminar, Instituto Superior Técnico (CEMAT, IST), Lisbon, Portugal, 5th May, 2022.

  • Minisymposium in French German Portuguese Conference on Optimization 2022, University of Porto, Portugal, 3rd-4th May, 2022.

  • Analysis of Nematic Liquid Crystals Flows, CIRM-Marseille Luminy, France, 25th-29th April, 2022.

  • NS-FSI Research Group Seminar, Politecnico di Milano, Italy, 24th September, 2021.

  • 12th Forum of Partial Differential Equations, Bedlewo, Poland 19th–25th September, 2021.

  • SysConTalks, Department of Systems and Control, IIT-Bombay, Mumbai, India, 9th August, 2021.

  • Brijuni Applied Mathematics Workshop, Croatia, 4th–10th July, 2021.

  • Minisymposium in 8th European Congress of Mathematics, 20th–26th June 2021.

  • Nečas Seminar on Continuum Mechanics, Charles University, Dec 07, 2020.

  • Seminar on PDEs, Czech Academy of Sciences, June 23, 2020.

  • IIT-Bombay, Mumbai, India, Nov 13, 2019.

  • IFSMACS Réunion, Institut Élie Cartan de Lorraine, Nancy, France, Jan 21–22, 2019.

  • Institute of Mathematics, Czech Academy of Sciences, Dec 18, 2018.

  • Institute for Mathematics, University of Würzburg, June 08, 2018.

 

Organization

  • Special session “Fluid-structure interaction and free boundary problems", 15th AIMS Conference in Athens, Greece, 6–10th July, 2026.

  • 2nd Bilbao Workshop on Fluid Dynamics, Basque Center for Applied Mathematics (BCAM), 3rd-5th November, 2025.

  • Analysis and PDE seminar, Bilbao for 2024/25 (Weekly Seminar in BCAM and University of Basque Country).

  • Minisymposium in the “Young Researchers Congress of the RSME", Bilbao, 13-17th January, 2025.

  • Minisymposium in the “XXVIII Congress of differential equations and applications” CEDYA, Bilbao, 2024.

  • Long night of Mathematics (Die Lange Nacht der Mathematik), TU Darmstadt 2024.

  • Long night of Mathematics (Die Lange Nacht der Mathematik), TU Darmstadt 2023.

  • Local Coordinator in “Fluids under control” workshop, Prague, 2021.

 

Teaching Experience

  1. Spring 2025: Introduction to Compressible fluids Part I and II (Lecturer), BCAM, Spain. 

  2. Spring 2024: Fourier Analysis and application to PDEs (Lecturer), TU Darmstadt.

  3.  Fall 2023: Advance topics in Fluid Mechanics (Lecturer), TU Darmstadt.

  4.  Spring 2022: Short course on Control of Fluid Flows.

  5.  Fall 2017 : Linear Partial Differential Equations, Master level (Teaching Assistant), TIFR- CAM. 

  6.  Spring 2017 : PDE III, Master level (Teaching Assistant), TIFR- CAM.

  7.  Spring 2016 : PDE III, Master level (Teaching Assistant), TIFR- CAM.

  8.  Fall 2015 : Real Analysis, Master level (Teaching Assistant), TIFR- CAM.

  9.  Fall 2014 : Complex Analysis, Master level (Teaching Assistant), TIFR- CAM.

 

 

Supervision

  1. Claudiu Mîndrilă, Basque Center for Applied Mathematics. PostDoctoral Fellow, 2024-2026.

  2. Meriem Essadik, L’Aquilla University, Italy. Master thesis, 2025.

  3. Eder Garcia Martinez, University of Basque Country. Internship, 2025.

  4. Hosted Master student under Erasmus Traineeship, 2025.

 

 

 

  • Awarded Spanish National Project PID2023-146764NB-I00 (2024-2028) funded by the Spanish Ministry of Science.

  • Awarded Ikerbasque Research Fellowship (2024-2029) funded by the Ikerbasque Foundation, Spain.

  • Awarded Ramón y Cajal Fellowship (2024-2029) funded by the Spanish Ministry of Science.

  • Awarded INSPIRE Faculty Fellowship for 5 years by Dept. of Science and Technology (DST), Govt. of India.

  • Awarded HUMBOLDT Research Fellowship (2022-2024) funded by the Alexander Von Hum- boldt Foundation.

  • Postdoctoral fellowship supported by Grant Agency of the Czech Republic (GAČR).

  • Postdoctoral fellowship supported by ANR research project IFSMACS.

  • Senior Research Scholar fellowship from TIFR CAM (2015–2018).

  • Junior Research Scholar fellowship from TIFR CAM (2012–2015).

  • Secured 15th rank (JRF,CSIR) in NET (National Eligibility Test), JUNE, 2013.

  • M C Nag award for First class first in Mathematics in B.Sc.

  • Recipient of the SWAMI LOKESWARANANDA AWARD, 2012 for all-round performance at the Graduate level.

  • Awarded INSPIRE Scholarship (2009-2012) by Govt. of India.

  • Awarded WBCHSE Scholarship by State Govt. (2007-2009).