Mrinal Kanti Roychowdhury
Associate Professor

School of Mathematical and Statistical Sciences
                             The University of Texas Rio Grande Valley                        



Office: MAGC Building 3.702
Phone: (956) 665-3555
Email: mrinal.roychowdhury@utrgv.edu

Fax:
(956) 665-5091

Contents:

Teaching and Evaluations:
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Education:
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Research Interest: Quantization: Theory and Applications, Fractal Geometry and Dynamical Systems.
 
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Research Grant: Home

Publications and some selected preprints:
(arXiv papers may be updated until they are accepted)
  1. G. Pena, H. Rodrigo, M. Roychowdhury, J. Sifuentes, and E. Suazo, Quantization for uniform distributions on hexagonal, semicircular, and elliptical curves, arXiv:1902.03887 [math.PR].
  2. M.K. Roychowdhury, and B. Selmi, Estimate of some measure-dimensions associated with hyperbolic recurrent IFS, arXiv:1902.00938 [math.DS].
  3. M.K. Roychowdhury, Optimal quantization for some triadic uniform Cantor distributions with exact bounds, arXiv:1811.06845 [math.DS].
  4. J. Atnip, M.K. Roychowdhury, and M. Urbanski, Quantization dimension for infinite conformal iterated function systems, arXiv:1811.00299 [math.DS].
  5. M.K. Roychowdhury, The quantization of the standard triadic Cantor distribution, arXiv:1809.07913 [math.DS].
  6. J. Rosenblatt and M.K. Roychowdhury, Uniform distributions on curves and quantization, arXiv:1809.08364 [math.PR].
  7. J. Rosenblatt and M.K. Roychowdhury, Shrinking targets in dynamical systems, arXiv:1809.09780 [math.DS].
  8. J. Rosenblatt and M.K. Roychowdhury, Optimal quantization via dynamics, arXiv:1804.01224 [math.DS]. 
  9. M.K. Roychowdhury, Center of mass and the optimal quantizers for some continuous and discrete uniform distributions, arXiv:1707.01630 [math.PR].
  10. S. Chakraborty, M.K. Roychowdhury, and J. Sifuentes, High precision numerical computation of principal points for univariate distributions, arXiv:1807.10970 [math.PR].
  11. M.K. Roychowdhury, An overview of the quantization for mixed distributions, arXiv:1703.06518 [math.PR].
  12. D. Comez and M.K. Roychowdhury, Canonical sequences of optimal quantization for condensation measures, arXiv:1705.08811 [math.DS]. 
  13. M.K. Roychowdhury, Optimal quantizers for probability distributions on nonhomogeneous R-triangles, arXiv:1606.00963 [cs.IT].
  14. D. Comez and M.K. Roychowdhury, Quantization of probability distributions on R-triangles, arXiv:1605.09701 [math.DS].
  15. M.K. Roychowdhury, Nonhomogeneous distributions and optimal quantizers for Sierpiński carpets, arXiv:1605.02281 [cs.IT].
  16. D. Comez and M.K. Roychowdhury, Probability distributions supported on sets generated by infinite affine transformations and optimal quantization, arXiv:1604.04261 [math.DS].
  17. L. Roychowdhury and M.K. Roychowdhury, Optimal quantization for infinite nonhomogeneous distributions on the real line, arXiv:1603.00731 [math.DS].
  18. C.P. Dettmann and M.K. Roychowdhury, An algorithm to compute CVTs for finitely generated Cantor distributions, arXiv:1512.01907 [cs.IT].
  19. D. Comez and M.K. Roychowdhury, Quantization for uniform distributions of Cantor dusts on $\mathbb{R}^2$, arXiv:1511.01990 [math.DS].
  20. M.K. Roychowdhury, Topological pressure and fractal dimensions of cookie-cutter-like sets, to appear, Southeast Asian Bulletin of Mathematics.
  21. M.K. Roychowdhury, Optimal quantization for the Cantor distribution generated by infinite similutudes, to appear, Israel Journal of Mathematics.
  22. M.K. Roychowdhury, Least upper bound of the exact formula for optimal quantization of some uniform Cantor distributions, Discrete and Continuous Dynamical Systems- Series A, Volume 38, Number 9, September 2018, pp. 4555-4570.
  23. J. Rosenblatt and M.K. Roychowdhury, Optimal quantization for piecewise uniform distributions, Uniform Distribution Theory 13 (2018), no. 2, 23-55. 
  24. M.K. Roychowdhury, Optimal quantizers for some absolutely continuous probability measures, Real Analysis Exchange, Vol. 43(1), 2017, pp. 105-136. 
  25. M.K. Roychowdhury, Quantization and centroidal Voronoi tessellations for probability measures on dyadic Cantor sets, Journal of Fractal Geometry, 4 (2017), 127146.
  26. C.P. Dettmann and M.K. Roychowdhury, Quantization for uniform distributions on equilateral triangles, Real Analysis Exchange, Vol. 42(1), 2017, pp. 149-166.
  27. E. Mihailescu and M.K. Roychowdhury, Quantization coefficients in infinite systems, Kyoto Journal of Mathematics, Vol. 55, No. 4 (2015), 857-873.
  28. M.K. Roychowdhury and N. Snigireva, Asymptotic of the geometric mean error in the quantization of recurrent self-similar measures, Journal of Mathematical Analysis and Applications, Vol. 431 (2015), 737-751.  
  29. M.K. Roychowdhury, Hausdorff and upper box dimension estimate of hyperbolic recurrent sets, Israel Journal of Mathematics, 201 (2014), 507523.
  30. M.K. Roychowdhury, Quantization dimension estimate of probability measures on hyperbolic recurrent sets, Dynamical Systems, Vol. 29, No. 2, 225-238, 2014.
  31. M.K. Roychowdhury, Quantization coefficients for ergodic measures on infinite symbolic space, Discrete and Continuous Dynamical Systems - Series A, Pages: 2829-2846, Vol. 34, Issue 7, July 2014.
  32. M.K. Roychowdhury, Quantization dimension for Gibbs-like measures on cookie-cutter sets, Kyoto Journal of Mathematics, Vol. 54, No. 2 (2014), 239-257.
  33. M.K. Roychowdhury, Quantization dimension estimate for condensation systems of conformal mappings, Real Analysis Exchange, 2013, Vol. 38, Issue 2, p 317-335.
  34. M.K. Roychowdhury, Quantization dimension estimate of inhomogeneous self-similar measures, Bulletin of the Polish Academy of Sciences Mathematics, Vol. 61, No. 1  (2013), 35-45.
  35. M.K. Roychowdhury, Quantization dimension and temperature function for bi-Lipschitz mappings, Israel Journal of Mathematics, 192 (2012), 473-488.
  36. M.K. Roychowdhury, Quantization dimension for infinite self-similar probabilitiesJournal of Mathematical Analysis and Applications, 383 (2011), 499505.
  37. M.K. Roychowdhury, Quantization dimension and temperature function for recurrent self-similar measures, Chaos, Solitons & Fractals, 44 (2011), 947-953.
  38. M.K. Roychowdhury, Lower quantization coefficient and the F-conformal measure, Colloquium Mathematicum, 122 (2011), 255-263.                       
  39. M.K. Roychowdhury, Quantization dimension function and Gibbs measure associated with Moran set, Journal of Mathematical Analysis and Applications, 373 (2011), 73-82.
  40. R.K. Bose and M.K. Roychowdhury, Fixed point theorems for some generalized contractive multi-valued mappings and fuzzy mappings, Matematicki Vesnik, 63 (2011), no. 1, 7-26.
  41. M.K. Roychowdhury, Quantization dimension for some Moran measures, Proceedings of the American Mathematical Society, 138 (2010), 4045-4057.
  42. R.K. Bose and M.K. Roychowdhury, Fixed point theorems for multi-valued mappings and fuzzy mappings, International Journal of Pure and Applied Mathematics, Vol 61, No. 1 (2010), 53-72.
  43. M.K. Roychowdhury, Quantization dimension function and ergodic measure with bounded distortion, Bulletin of the Polish Academy of Sciences Mathematics, 57 (2009), 251-262.
  44. R.K. Bose and M.K. Roychowdhury, Fixed point theorems for generalized weakly contractive mappings, Surveys in Mathematics and its Applications, Vol. 4 (2009), 215-238.
  45. M.K. Roychowdhury and D.J. Rudolph, Any two irreducible Markov chains are finitarily orbit equivalent, Israel Journal of Mathematics, 174 (2009), 349368.           
  46. M.K. Roychowdhury and D.J. Rudolph, Nearly continuous Kakutani equivalence of adding machines, Journal of Modern Dynamics, Volume 3, No. 1, 2009, 103-119.
  47. M.K. Roychowdhury and D.J. Rudolph, Any two irreducible Markov chains of equal entropy are finitarity Kakutani equivalent, Israel Journal of Mathematics, 165 (2008), no. 1, 29-41.
  48. T. Hamachi, M.S. Keane and M.K. Roychowdhury, Finitary orbit equivalence and measured Bratteli diagrams, Colloquium Mathematicum, 110 (2008), no. 2, 363-382.
  49. M.K. Roychowdhury and D.J. Rudolph, The Morse minimal system is finitarily Kakutani equivalent to the binary odometer, Fundamenta Mathematicae, 198 (2008), no. 2, 149-163.
  50. M.K. Roychowdhury, Irrational rotation of the circle and the binary odometer are finitarily orbit equivalent, Publications of the Research Institute for Mathematical Sciences (Kyoto University), 43 (2007), no 2, 385-402.
  51. M.K. Roychowdhury, $\{m_n\}$-odometer and the binary odometer are finitarily orbit equivalent, Contemporary Mathematics, AMS, 430 (2007), 123-134. 
Preprint:
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Research Visit:
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Academic Award: Gold Medal (for the highest examination score in B.Sc.(Mathematics Honors) in the Tripura University system, Tripura, INDIA.

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Professional Qualifications:
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Student Supervision:
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Conference/symposium/special-session organized: 
  1. AMS Sectional Meeting#1138: Special session on Quantization for Probability Distributions and Dynamical Systems, April 14-15, 2018 (Saturday-Sunday), Vanderbilt University, Nashville, TN, USA.
  2. AMS Sectional Meeting#1133: Special session on Fractal Geometry, Dynamical Systems, and Their Applications, September 23-24, 2017 (Saturday-Sunday), University of Central Florida, Orlando, FL, USA.
  3. AMS Sectional Meeting#1131: Special session on Fractal Geometry and Ergodic Theory, September 09-10, 2017 (Saturday-Sunday), University of North Texas, Denton, TX, USA.
  4. AMS Joint Mathematics Meetings#1125: Special session on Ergodic Theory and Dynamical Systems, (organizers: Tamara Kucherenko and M.K. Roychowdhury), January 04-07 (Wednesday-Saturday), 2017, Atlanta, USA.
  5. AIMS Special session on Fractal Geometry, Dynamical Systems, and Their Applications (organizers: M. Barnsley, J. Keesling and M.K. Roychowdhury) at the 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Orlando, Florida, USA, July 1-5, 2016.
  6. Special session on Centroidal Voronoi Tessellations and Their Applications (organizers: M.K. Roychowdhury and Huayi Wei) at the SIAM Conference, Georgia State University, Georgia, USA, June 6-10, 2016.
  7. AMS Sectional Meeting#1120: Special session on Ergodic Theory and Dynamical Systems (organizers: Doğan mez and M.K. Roychowdhury), April 16-17, 2016 (Saturday-Sunday), North Dakota State University, Fargo, ND, USA.
  8. AMS Sectional Meeting#1113: Special session on Fractal Geometry and Dynamical Systems, October 17-18, 2015 (Saturday-Sunday), University of Memphis, Memphis, TN, USA.  
  9. Special session on Dynamics of Time Series, Dynamical Systems and Quantization (organizers: M.K. Roychowdhury and Milan Stehlik) at 9th International Conference on Differential Equations and Dynamical Systems, May 14-16, 2015, Dallas, Texas, USA. 
  10. AMS Sectional Meeting#1109: Special session on Fractal Geometry and Ergodic Theory, March 27-29 (Friday-Sunday), 2015, University of Alabama, Huntsville, USA, (to see the pictures click here).
  11. AMS Joint Mathematics Meetings#1106: Special session on Ergodic Theory and Dynamical Systems, January 10-13 (Saturday-Tuesday), 2015, San Antonio, USA, (to see the pictures click here). 
  12. AMS Sectional Meeting#2000: Special session on Fractal Geometry and Dynamical Systems, April 11-13 (Friday-Sunday), 2014, Texas Tech University, Lubbock, Texas, USA, (to see the pictures click here).
  13. AMS Sectional Meeting#1097: Special session on Fractal Geometry and Ergodic Theory, March 21-23 (Friday-Sunday), 2014, University of Tennessee, Knoxville, Tennessee, USA, (to see the pictures click here).
  14. AMS Sectional Meeting#1087: Special session on Fractal Geometry and Ergodic Theory, March 1-3 (Friday-Sunday), 2013, University of Mississippi, Oxford, MS, USA, (to see the pictures click here).
  15. Symposium on Fractal Geometry, Quantization Dimension and Related Topics, within ICNAAM 2012, Kypriotis Hotels and Conference Center, Kos, Greece, 19-25 September, 2012.
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Talks:
  1. (Colloquium Talk) April 12, 2019, Department of Mathematics, The University of Texas at San Antonio, San Antonio, Texas, USA. 
  2. March 23, 2019, 4th Coastal Bend Mathematics and Statistics Conference, University of Texas Rio Grande Valley, Edinburg, Texas, USA. 
  3. March 15-17, 2019, Spring Southeastern Sectional Meeting: Special Session on Probability and Stochastic Processes, Auburn University, Auburn, AL, USA.
  4. March 15-17, 2019, Spring Southeastern Sectional Meeting: Special Session on Clustering Methods and Applications, Auburn University, Auburn, AL, USA.
  5. (Colloquium Talk) February 21, 2019, Department of Mathematics, The University of Iowa, Iowa City, Iowa, USA. 
  6. January 24-27, 2019, Ergodic Theory Workshops, Department of Mathematics, University of North Carolina-Chapel Hill, NC, USA.
  7. January 16, 2019, AMS-ASL Special Session on Algorithmic Dimensions and Fractal Geometry, Joint Mathematics Meetings, January 16-19, 2019, Baltimore, Maryland, USA.
  8. April 21-22, 2018, AMS Spring Eastern Sectional Meeting: Special session on Ergodic Theory and Dynamics on Combinatorial Number Theory, Northeastern University, Boston, MA, USA. 
  9. April 19-22, 2018, Ergodic Theory Workshops, Department of Mathematics, University of North Carolina-Chapel Hill, NC, USA.
  10. April 14-15, 2018, AMS Spring Southeastern Sectional Meeting: Special session on Quantization for Probability Distributions and Dynamical Systems, Vanderbilt University, Nashville, TN, USA. 
  11. (Colloquium Talk) March 16, 2018, Department of Mathematical Sciences, The University of Memphis, Memphis, Tennessee, USA.
  12. (Colloquium Talk) February 09, 2018, Department of Mathematics, The University of Alabama at Birmingham, Birmingham, Alabama, USA. 
  13. (Colloquium Talk) February 08, 2018, Department of Mathematics and Statistics,  University of South Alabama, Mobile, Alabama, USA. 
  14. (Colloquium Talk) November 09, 2017, Department of Mathematics, The City College of New York, New York, USA. 
  15. November 04-05, 2017, AMS Fall Western Sectional Meeting: Special Session on Analysis and Geometry of Fractals, University of California, Riverside, CA, USA.
  16. October 23, 2017, Dynamical Systems Seminar, University of Houston, Houston, TX, USA.
  17. September 23-24, 2017, AMS Southeastern Sectional Meeting: Special session on Fractal Geometry, Dynamical Systems, and Their Applications, University of Central Florida, Orlando, FL, USA.
  18. September 09-10, 2017, AMS Fall Central Sectional Meeting: Special session on Fractal Geometry and Ergodic Theory, University of North Texas, Denton, TX, USA.
  19. July 10, 2017, Workshop in Analysis and Probability Seminar, Texas A&M University, College Station, TX, USA.
  20. April 20-23, 2017, Ergodic Theory Workshops, Department of Mathematics, University of North Carolina-Chapel Hill, NC, USA.
  21. April 01-02, 2017, AMS Spring Central Sectional Meeting: Special Session on Dependence in Probability and Statistics, Indiana University, Bloomington, IN, USA.
  22. January 04-07, 2017, Special Session on Measure and Measurable Dynamics (In Memory of Dorothy Maharam, 1917-2014), AMS Joint Mathematics Meetings 2017, Atlanta, GA, USA.
  23. July 1-5, 2016, Special Session on Inverse Limits in Dynamical Systems, at the 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Orlando, Florida, USA.
  24. July 1-5, 2016, Special Session on Fractal Geometry, Dynamical Systems, and Their Applications, at the 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Orlando, Florida, USA.
  25. June 6-10, 2016, Special Session on Centroidal Voronoi Tessellations and Their Applications, SIAM Conference on Discrete Mathematics, Georgia State University, Georgia, USA.
  26. April 16-17, 2016, AMS Spring Central Sectional Meeting: Special session on Ergodic Theory and Dynamical Systems, North Dakota State University, Fargo, ND, USA.  
  27. March 10-13, 2016, 50th Spring Topology and Dynamical Systems Conference, Baylor University, Waco, TX, USA.
  28. October 17-18, 2015, AMS Fall Southeastern Sectional Meeting: Special session on Fractal Geometry and Dynamical Systems, University of Memphis, Memphis, TN, USA.
  29. May 18-20, 2015, The Dynamical Systems, Ergodic Theory, and Probability Conference dedicated to the memory of Nikolai Chernov, University of Alabama at Birmingham, USA.
  30. May 14-16, 2015, Special session on Dynamics of Time Series, Dynamical Systems and Quantization at 9th International Conference on Differential Equations and Dynamical Systems, Dallas, Texas, USA.
  31. March 27-29, 2015, AMS Spring Southeastern Sectional Meeting: Special session on Fractal Geometry and Dynamical Systems, University of Alabama in Huntsville, Huntsville, Al, USA. 
  32. January 10-13, 2015, Special Session on Topological Measures of Complexity: Inverse Limits, Entropy, and Structures of Attractors, AMS Joint Mathematics Meetings 2015, San Antonio, TX, USA. 
  33. June 2-6, 2014, RTG Research Conference: Logic, Dynamics, and their Interactions II, University of North Texas, TX, USA. 
  34. April 11-13 (Friday-Sunday), 2014, AMS Spring Central Sectional Meeting: Special session on Fractal Geometry and Dynamical Systems, Texas Tech University, Lubbock, Texas, USA. 
  35. March 21-23 (Friday-Sunday), 2014, AMS Southeastern Spring Sectional Meeting: Special session on Fractal Geometry and Ergodic Theory, University of Tennessee, Knoxville, Tennessee, USA.
  36. April 24, 2013, Workshop on Applied Analysis and Differential Equations, Department of Mathematics, University of Texas-Pan American, TX, USA.
  37. April 13, 2013, South Texas Mathematics Consortium, University of Texas at San Antonio, San Antonio, TX, USA.
  38. March 21-24, 2013, Ergodic Theory Workshop, Department of Mathematics, UNC Chapel Hill, NC, USA.
  39. March 1-3, 2013, AMS Spring Southeastern Sectional Meeting: Special session on Fractal Geometry and Ergodic Theory, University of Mississippi, Oxford, MS, USA.
  40. December 17-21, 2012, International Conference on the Theory, Methods and Applications of Nonlinear Equations, Texas A&M University-Kingsville, Texas, USA.
  41. June 4-8, 2012, RTG Research Conference: Logic, Dynamics and their Interactions with a Celebration of the Work of Dan Mauldin, University of North Texas, TX, USA.
  42. March 22-25, 2012, Workshop on Groups, Geometry and Random Structures, Department of Mathematics, Texas A&M University, College Station, Texas, USA.
  43. January 5, 2012, Geometric Functional Analysis & Probability Seminar, Department of Mathematics, Weizmann Institute, ISRAEL.
  44. December 20, 2011, Ergodic Theory and Probability Theory Seminar, Department of Mathematics, Ben-Gurion University of the Negev, ISRAEL.
  45. October 7, 2011, RTG Logic and Dynamics Seminar, University of North Texas, TX, USA.
  46. (Colloquium Talk) July 21, 2011, School of Mathematics, Tata Institute of Fundamental Research (TIFR), Mumbai, INDIA. 
  47. July 08, 2011, Statistics & Probability Seminar, Dept of Mathematics, Indian Institute of Technology (IIT), Mumbai, INDIA. 
  48. March 24-27, 2011, Group action on measure spaces, Texas A&M University, Texas, USA.
  49. February 19, 2011, 19th Annual South Texas Mathematics Consortium, Texas, USA.
  50. January 06-09, 2011, AMS Joint Mathematics Meetings, New Orleans, Louisiana, USA.
  51. January 04-05, 2011, Workshop in Analysis and Geometry, Louisiana State University, Baton Rouge, LA, USA.
  52. May 17-21, 2010, NSF/CBMS Regional Research Conference, The University of Texas-Pan American, USA.
  53. January 13-16, 2010, AMS Joint Mathematics Meetings, San Francisco, California, USA.
  54. November 7-8, 2009, AMS Fall Western Sectional Meetings, University of California, Riverside, CA, USA.
  55. February 19-22, 2009, Probability and Ergodic Theory Workshop, Department of Mathematics, UNC Chapel Hill, NC, USA.
  56. June 18-20, 2008, Pingree Park Dynamics Workshop, Colorado State University, Fort Collins, CO, USA.  .
  57. October 5-6, 2007, AMS Fall Sectional Meetings, Depaul University,Chicago, IL, USA.  
  58. February 16-19, 2006, Probability and Ergodic Theory Workshop at UNC Chapel Hill, NC, USA.
  59. March 19-22, 2005, Maryland-Penn State Dynamics Workshop, University of Maryland, College Park, MD, USA.
  60. February 18-20, 2005, Probability and Ergodic Theory Workshop, Department of Mathematics, UNC Chapel Hill, NC, USA.
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