School of Basic Sciences

- Complex Analysis
- Geometric Function Theory
- Harmonic Mappings in the Plane

- School of Basic Sciences, Room No:125
- +91-674-7135120
- avrao@iitbbs.ac.in, alluvasudevarao(AT)gmail(DOT)com

Degree | Discipline | Year | School |
---|---|---|---|

Post Doctoral Fellow | Mathematics | 2011 | Technion-Israel Institute of Technology, Haifa, Israel |

Ph.D. | Mathematics | 2010 | Indian Institute of Technology Madras |

M.Sc. | Mathematics | 2002 | University Of Hyderabad |

Dr. Vasudeva Rao Allu** **has** **received M.Sc. (Mathematics) from University of Hyderabad, Ph.D. from Indian Institute of Technology Madras and Post-Doctoral studies from Technion-Israel Institute of Technology, Haifa as well as from IIT Madras (with NBHM Fellowship). Currently, Dr. Allu is a Professor of Mathematics at the School of Basic Sciences, IIT Bhubaneswar. He was a visiting Research Scholar at University of Turku, Finland (2007 and 2009) with the Distinguished CIMO (Center for International Mobility) Fellowship. Dr. Allu was a visiting faculty at Yamaguchi University, Japan in December 2011.

Dr. Allu received **Gold Medal** and **Aryabhatta Award** for securing **State First Rank** in **Andhra Pradesh Mathematical Olympiad** at M.Sc. level conducted by Andhra Pradesh Association of Mathematics Teachers (A.P.A.M.T.) (2002). He received the Best Paper Presentation Award at 22^{nd} Annual Conference of Ramanujan Mathematical Society (2007). He has been selected for International Congress of Mathematicians 2018-Open Arms Travel Grant. (2018) and Chebyshev Grant from International Congress of Mathematicians 2022.

Dr. Allu is a member of Editorial Board of the Journal of Mathematical Inequalities (since 2021). Dr. Allu has received **Teaching Excellence Award** (2020) from IIT Bhubaneswar. He is an elected Member of the London Mathematical Society (Since 2018) and Member of the National Academy of Sciences, India (2019).

**Spring (2021-2022)**: Mathematics -II (B.Tech. 2nd Semester) and Complex Analysis (M.Sc. 2nd Semester)

**Autumn (2021-2022)**: Mathematics -I (B.Tech. 1st Semester) and Functions of Several Variables (M.Sc. 3rd Semester)

**Autumn (2020-2021)**: Mathematics -I (B.Tech. 1st Semester)

**Spring (2019-2020)**: Mathematics -II (B.Tech. 2nd Semester) and Advanced Complex Analysis (M.Sc/Ph.D.)

**Autumn(2019-2020)**: Mathematics -I (B.Tech. 1st Semester) and Differential Geometry (M.Sc. 4th Semester)

**Summer Quarter (2018-2019)**: Transform Calculus (B.Tech. 3rd Semester)

**Spring (2018-2019) **Math-II and Measure Theory and Integration (M.Sc./Ph.D.)

** **

1) Title of the Project: **A study of harmonic analogue of certain univalent and analytic functions**

Funding Agency: **SERB,** MATRICS (**Mathematical Research Impact Centric Support**)

Duration: 2020-2022.

2) Title of the Project: **An enquiry into the problems in Geometric Function Theory**

Funding Agency: **SERB,** CRG (Core Research Grant)

Duration: 2021-2023.

1) Title of the project : **Certain conjectures on univalent and**

Principal Investigator : Dr. Vasudeva Rao Allu

Co-Principal-Investigators : None

Funding Agency : SERB, Govt. of India (under the scheme

“Start Up Research Grant (Young Scientist))”

Cost of the Project : Rs. 15,30,100/-

Status : Completed

2) Title of the project: **Problems and Conjectures in Geometric**

Principal Investigator : Dr. Vasudeva Rao Allu

Co-Principal-Investigators : None

Funding Agency : NBHM “(Department of Atomic Energy), Govt. of India

Cost of the Project : Rs. 1,50,0000/–

Status: Completed

3) Title of the project: **Coefficient bounds, distrotion condition or subclasses**

Principal Investigator : Dr. Vasudeva Rao Allu

Co-Principal-Investigators : None

Funding Agency : ISIRD, SRIC, IIT Kharagpur

Cost of the Project : Rs. 3,70,000/-

Status: Completed

1Vasudevarao Allu and Himadri Halder, Bohr radius for Banach spaces on simply connected domains, Proceedings of the Edinburgh Mathematical Society (Accepted for publication) (2023) DOI: https://doi.org/10.1017/S0013091523000688

2Molla Basir Ahamed and Vasudevarao Allu, Improved Bohr inequalities for certain classes of harmonic mappings, Journal of Ramanujan Mathematical Society (Accepted for publication) (2023)

3Molla Basir Ahamed and Vasudeva Rao Allu, Transcendental solutions of Fermat-type functional equations in $ \mathbb{C}^n $, Analysis and Mathematical Physics 13(2023), no.5, Paper No. 69, 17 pp.

4Vasudevarao Allu and Himadri Halder, Bohr operator on operator valued polyanalytic functions on simply connected domains, Canadian Mathematical Bulletin (2023) (Accepted for publication)

5Molla Basir Ahamed and Vasudevarao Allu, Harmonic analogue of Bohr phenomenon of certain classes of univalent and analytic functions, Mathematica Scandinavica (Accepted for publication) (2023)

6Vasudevarao Allu and Nirupam Ghosh, Bohr type inequality for Cesaro and Bernardi integral operator on simply connected domain, Proc. Indian Acad. Sci. 133(2023), no.2, Paper No. 22, 10 pp.

7Vasudevarao Allu and Vibhuti Arora, Second Hankel determinant of logarithmic coefficients of certain analytic functions, Rocky Mountain Journal of Mathematics (Accepted for publication) (2023)

8Molla Basir Ahamed, Vasudevarao Allu and Himadri Halder, Asymptotic behaviour of Bohr's Radii for Polynomials on simply connected domains, C. R. Math. Acad. Sci. Paris (2023)(To appear)

9 Vasudeavarao Allu, Vibhuti Arora and Amal Shaji, On the Second Hankel determinant of Logarithmic Coefficients for certain univalent functions, Mediterranean Journal of Mathematics 20 (2023), no. 2, Paper No. 81, 10 pp

10Molla Basir Ahamed, Vasudevarao Allu and Himadri Halder, Improved Bohr inequalities for certain class of harmonic univalent functions, Complex Variables and Elliptic Equations 68(2023), 267--290.

11Molla Basir Ahamed and Vasudevarao Allu, Bohr-Rogosinski radius for a certain class of close-to-convex harmonic mappings, Canadian Mathematical Bulletin (2023) (To appear),doi: https://doi.org/10.4153/S0008439523000115

12Vasudevarao Allu, Himadri Halder and Subhadip Pal, Bohr and Rogosinski inequalities for operator valued holomorphic functions, Bulletin des Sciences Math 182 (2023) 103214.

13Vasudevarao Allu and Vibhuti Arora, Bohr-Rogosinski type inequalities for concave univalent functions, Journal of Mathematical Analysis and Applications 520 (2023) no.1, Paper No. 126845, 14 pp.

14Daoud Bshouty, Abdallah Lyzzaik, Antti Rasila and Allu Vasudevarao, Moduli of doubly connected domains under univalent harmonic maps, The Journal of Geometric Analysis, (2022) 32:152 , DOI: 10.1007/s12220-022-00895-2

15Vasudevarao Allu and Himadri Halder, Operator valued analogues of multidimensional Bohr's inequality, Canadian Mathematical Bulletin 65 (2022), DOI: https://doi.org/10.4153/S0008439521001077

16Vasudevarao Allu and Himadri Halder, The Bohr inequality for certain harmonic mappings, Indagationes Mathematicae 33 (2022), 581--597.

17Vasudevarao Allu and Himadri Halder, Bohr phenomenon for certain close-to-convex analytic functions, Computational Methods and Function Theory 22 (2022), 491--517.

18Molla Basir Ahamed and Vasudevarao Allu, Bohr phenomenon for certain classes of harmonic mappings, Rocky Mountain Journal of Mathematics 52(2022), 1205-1225.

19Md Firoz Ali, Vasudevarao Allu, Hiroshi Yanagihara, An application of Schur algorithm to variability regions of certain analytic functions-II, Bulletin of the Australian Mathematical Society 105 (2022), 468 -- 481.

20Vasudevarao Allu, Adam Lecko and Derek Keith Thomas, Hankel, Toeplitz and Hermitian-Toeplitz determinants for certain Close-to-convex Functions, Mediterranean Journal of Mathematics 19 (2022), no. 1, Paper No. 22, 17, https://doi.org/10.1007/s00009-021-01934-y

21Molla Basir Ahamed and Vasudevarao Allu, Bohr-Rogosinski inequalities for certain fully starlike harmonic mappings, Bulletin of the Malaysian Mathematical Sciences Society 45 (2022), 1913--1927.

22Md. Firoz Ali, A. Vasudevarao and H. Yanagihara, An application of Schur algorithm to variability regions of certain analytic functions-I. Computational Methods and Function Theory 22 (2022), 35--54.

23Vasudevarao Allu and Himadri Halder, The Bohr phenomenon for certain Subclasses of Harmonic Mappings, Bulletin des Sciences Mathématiques173 (2021), Paper No. 103053, 18 pp., https://doi.org/10.1016/j.bulsci.2021.103053

24Molla Basir Ahamed, Vasudevarao Allu and Himadri Halder, The Bohr Phenomenon for analytic functions on simply connected domains, Annales Fennici Mathematici 47(2021), 103--120.

25Molla Basir Ahamed, Vasudevarao Allu, and Himadri Halder, Bohr radius for certain classes of close-to-convex harmonic mappings, Analysis and Mathematical Physics 11 (2021), no. 3, Paper No. 111, 30 pp. doi:10.1007/s13324-021-00551-y

26Vasudevarao Allu and Abhishek Pandey, Support points of some classes of analytic and univalent functions, C. R. Math. Acad. Sci. Paris 359 (2021), 465--473.

27Vasudevarao Allu and Himadri Halder, Bohr radius for certain starlike and convex univalent functions, Journal of Mathematical Analysis and Applications 493(2021), 124519.

28Vasudevarao Allu and Abhishek Pandey, Zalcman Conjecture for certain analytic and univalent functions, Journal of Mathematical Analysis and Applications 492(2020), 124466.

29 Md. Firoz Ali, Vasudevarao Allu and Nirupam Ghosh, A convolution property of univalent harmonic right half mappings, Monatshefte für Mathematik 193(2020),729-736.

30Md. Firoz Ali, A. Vasudevarao and H. Yanagihara, On a class of univalent functions defined by a differential inequality, Journal of Ramanujan Mathematical Society 35 (2020), 217-226.

31Vasudevarao Allu, Janusz Sokol and Derek K Thomas, On a close-to-convex analogue of certain starlike functions, Bulletin of the Australian Mathematical Society 102(2020), 268-281.

32Nirupam Ghosh and Vasuevarao Allu, On some subclass of harmonic mappings, Bulletin of the Australian Mathematical Society 101(2020), 130--140.

33Md Firoz Ali and Vasudevarao Allu, Coefficient estimates and integral mean estimates for certain classes of analytic functions, C. R. Math. Acad. Sci. Paris 357 (2019), 436-442.

34Nirupam Ghosh and A. Vasudevarao, The radii of fully starlikeness and fully convexity of a harmonic operator, Monatshefte für Mathematik 188 (2019) 653--666.

35Nirupam Ghosh and A. Vasudevarao, On some subclass of harmonic close-to-convex mappings, Monatshefte für Mathematik 188(2019), 247--267.

36Vasudevarao Allu, Derek K. Thomas and Nikola Tuneski, On Ozaki close-to-convex functions, Bulletin of the Australian Mathematical Society 99(2019), 89--100.

37Samiran Chakraborty and Allu Vasudevarao, On Stable Functions, Computational Methods and Function Theory 18(2018), 677--688.

38Derek K. Thomas, Nikola Tuneski and Allu Vasudevarao, Univalent Functions: A Primer, De Gruyter Studies in Mathematics, 69, De Gruyter, Berlin, Boston, 2018, xiii+252 pp, ISBN 978-3-11-056096-1

39Md Firoz Ali and A. Vasudevarao, On Certain Families of Analytic Functions in the Hornich Space, Computational Methods and Function Theory 18(2018), 643--659.

40Nirupam Ghosh and A. Vasudevarao, Some basic properties of certain subclass of harmonic univalent functions, Complex Variables and Elliptic Equations 63 (2018), 1687â€”1703.

41U. Pranav Kumar and A. Vasudevarao, Logarithmic coefficients for certain subclasses of close-to-convex functions, Monatshefte für Mathematik 187(2018), 545--563.

42Md Firoz Ali, D. K. Thomas, and A. Vasudevarao, Toeplitz determinants whose elements are the coefficients of analytic and univalent functions, Bulletin of the Australian Mathematical Society 97(2)(2018), 253--264.

43Md Firoz Ali and A. Vasudevarao, On logarithmic coefficients of some close-to-convex functions, Proceedings of the American Mathematical Society 146(3)(2018), 1131--1142.

44Md Firoz Ali and A. Vasudevarao, Logarithmic coefficients of some close-to-convex functions, Bulletin of the Australian Mathematical Society 95 (2017), 228--237.

45Md Firoz Ali and A. Vasudevarao, On Coefficient Estimates of Negative Powers and Inverse Coefficients for Certain Starlike Functions, Proceedings of the Indian Academy Of Science (Math. Sci.) 127(3)(2017), 449--462.

46Nirupam Ghosh and A. Vasudevarao, Coefficient estimates for certain subclass of analytic functions defined by subordination, Filomat 31(11) (2017), 3307-3318.

47A. Vasudevarao, Fekete–Szegö inequality for certain spiral-like functions, C. R. Math. Acad. Sci. Paris 354 (2016), 1065--1070,

4847) M. Okada, S. Ponnusamy, A. Vasudevarao and H. Yanagihara Circular symmetrization, subordination and arclength problems on convex functions, Mathematische Nachrichten 289 (2016), 1044--1051

49Md Firoz Ali and A. Vasudevarao, Coefficient inequalities and Yamashitas conjecture for some classes of analytic functions, Journal of the Australian Mathematical Society 100(1) (2016), 1-20.

50A.Vasudevarao, Fekete-Szegö problem for certain subclasses of univalent functions, Bulletin of the Korean Mathematical Society 52 (6)(2015), 1937--1943

51Md Firoz Ali and A. Vasudevarao, Integral Means and Dirichlet integral for certain class of analytic function, Journal of the Australian Mathematical Society 99(3)(2015), 315--333.

52A. Vasudevarao, An Arclength problem for some subclasses of m-fold symmetric functions, Mathematica (Cluj) 56(79)(2014), 182-192.

53A. Vasudevarao, An arclength problem for some subclasses of univalent functions, The Journal of Analysis 22 (2014), 145-149.

54A. Vasudevarao, Region of variability for some subclasses of univalent functions, Springer Proc. Math. Stat. 91 (2013), 151--170,

55A. Vasudevarao and Hiroshi Yanagihara, On the growth of analytic functions in the class ${mathcal U}(lambda )$, Computational Methods and Function Theory 13(4) (2013), 613--634.

56S. Ponnusamy, A. Vasudevarao and M. Vuorinen, Region of variability for exponentiall convex functions, Complex Analysis and Operator Theory 5(3) (2011), 955--966.

57S. Ponnusamy and A. Vasudevarao, Region of variability for functions with positive real part, Annales Polonici Mathematici 99(3)(2010), 225--245.

58S. Ponnusamy, A. Vasudevarao and H. Yanagihara, Region of variability for close-to-convex functions-II, Applied Mathematics and Computation 215(3)(2009), 901--915.

59S. Ponnusamy, A. Vasudevarao and M. Vuorinen, Region of variability for certain classes of univalent functions satisfying differential inequalities, Complex Variables and Elliptic Equations 54(10)(2009), 899--922.

60S. Ponnusamy, A. Vasudevarao and M. Vuorinen, Region of variability for spirallike functions with respect to a boundary point, Colloquium Mathematicum 116(1)(2009), 31--46.

61S. Ponnusamy, A. Vasudevarao and H. Yanagihara, Region of variability of univalent functions $ f(z)$ for which $ zf'(z)$ is spirallike, The Houston Journal of Mathematics 34(4) (2008), 1037--1048.

62S. Ponnusamy, A. Vasudevarao and H. Yanagihara, Region of variability for close-to-convex functions, Complex Variables and Elliptic Equations 53(8)(2008), 709 -- 716.

63S. Ponnusamy and A. Vasudevarao, Region of variability of two subclasses of univalent functions, The Journal of Mathematical Analysis and Applications 332 (2007), 1323--1334.

1
Prof. Bhavanari Satyanarayana, Prof. Sreedharamalle Sreenadh and Prof. Thota Srinivas Endowment lecture “ On Bohr phenomenon in Geometric Function Theory” at 32nd Annual congress of Andhra Pradesh and Telangana Society for Mathematical Sciences (APTSMS) & International Conference on Computational Modeling in Science and Engineering (ICCMSE-2023), NIT Warangal, 28--30th October 2023.

2Invited talk "On Bohr Inequality for Operator-valued Analytic Functions" at the 29th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications (The 29th ICFIDCAA–2023) organized by Department of Mathematics Ramanujan School of Mathematical Sciences Pondicherry University, August 21-25, 2023.

3Invited talk "On Bhor phenomenon" at International Workshop on Geometric Function Theory (IWGFT 2023), Organized by
Department of Mathematics, IIT Madras, August 18-20, 2023

4Participated â€œThe Current Developments in Mathematics (CDM) conferenceâ€, jointly hosted by Harvard University and the Massachusetts Institute of Technology (MIT) (through virtual mode), from 2022-03-18 to 2022-03-19.

5Invited talk: Bohr radius for Banach spaces on simply connected domains, Computational Methods in Function Theory (CMFT), The Federico Santa MarÃa Technical University in ValparaÃso, Chile, January 10-14, 2022.

6Plenary talk â€œBohr phenomenon for harmonic Bloch functions on simply connected domainsâ€ (with Himadri Halder) at VIII International Conference of Mathematics and Computer Science "Congressio Mathematica", University of Warmia and Mazury in Olsztyn, Poland, during September 19â€“25, 2022.

7 Invited Talk: The Bohr phenomenon for Banach Spaces at Wuerzburg Complex Analysis Seminar, University of Wuerzburg, Germany on February 4th, 2022.

8Plenary talk â€œ The Bohr phenomenon for certain analytic and univalent functionsâ€ at the VI Conference of Mathematics and Computer Science, "Congressio Mathematica", University of Warmia and Mazury in Olsztyn, Poland, during November 21-22; 28â€“29, 2020.

9Plenary talk â€œ On the Third Logarithmic Coefficient of Close-to-convex Functionsâ€ (with Md Firoz Ali and D.K. Thomas) at V International Conference of Mathematics and Computer Science "Congressio Mathematica", University of Warmia and Mazury in Olsztyn, Poland, during September 23â€“25, 2018.

10Short Communication â€œCertain subclasses of harmonic univalent mappingsâ€ (with Nirupam Ghosh) in Short Communication at International Congress of Mathematicians (ICM 2018), Rio de Janeiro (Brazil) during August 1â€“9, 2018.

11Invited talk â€œOn the Growth of Some Subclasses of the Class of Univalent Functionsâ€ at International Symposium in Geometric Function Theory and Applications at Isik University, Turkey during August 26-September 4, 2013.

12Invited talks â€œOn region of variabilities for family of analytic functionsâ€ at the Department of Applied Sciences, Yamaguchi University, Ube, Japan during December 19â€“23, 2011.

13Short Communication â€œ Region of variability for spirallike functions with respect to a boundary pointâ€ at International Congress of Mathematicians (ICM 2010) at Hyderabad, August 19â€“27, 2010.

14Invited talk â€œ Region of variability for functions with positive real partâ€ at ICM 2010-Satellite Conference: International Workshop on Harmonic and Quasiconformal Mappings (HQM2010) at IIT Madras, August 09-17, 2010.

15Invited talk : â€œRegion of variability for functions with positive real partâ€ in Helsinki Analysis seminar at Department of Mathematics and Statistics, University of Helsinki, Finland on September 28, 2009.

16Invited talk â€œRegion of variability and Fekete SzegÂ¨o problem for exponentially convex univalent functionsâ€ in Helsinki Analysis seminar at Department of Mathematics and Statistics, University of Helsinki, Finland on September 14, 2009.

17Invited talk â€œRegion of variability for exponentially convex univalent functionsâ€ at International conference on Complex Analysis and Related Topics, 12th Romannian-Finnish Seminar at University Turku, Finland, August 17-21, 2009.

18Invited talk â€œRegion of variability for exponentially convex univalent functionsâ€ in Turku Analysis seminar at Department of Mathematics, University of Turku, Finland on August 07, 2009.

19Invited talk â€œCertain classes of univalent functions and radius problemsâ€ in Turku Analysis Seminar at Department of Mathematics, University of Turku, Finland on January 30, 2008.

20Invited talk â€œRegion of variability for certain classes of univalent functions satisfying differential inequalitiesâ€ at Finnish Mathematical Days 2008 at Helsinki University of Technology, Helsinki, Finland, January 3-4, 2008.

1Invite talk "Bohr radius for certain classes of analytic and harmonic mappings" at IIT Tirupathi on 18-11-2022.

2Invited lectures at â€œAnnual Foundation School â€“ I (AFS-I)â€ at the Department of Mathematics, NIT Durgapur, during December 12, 2022 to January 7, 2023.

3Invited talk â€œBohr and Rogosinski inequalities for operator valued holomorphic functionsâ€ In the Symposium â€œComplex Analysisâ€ of 37th Annual Conference of Ramanujan Mathematical Society during 06 - 08, December 2022.

4Invited Talk: On logarithmic coefficients problem for univalent functions, One Day International Symposium on Mathematical Analysis on the occasion of National Mathematics Day (134th Birth Anniversary of Srinivasa Ramanujan) Amity University, Haryana 22-12â€“2022.

5Participated 36th Annual Conference of Ramanujan Mathematical Society from 2021-08-04 to 2021-08-07 (Attend through Virtual conference mode)

6Invited talk: Bohr radius for certain classes of analytic and harmonic mappings, Faculty Development Program(FDP) on Mathematical Approaches in Science and Engineering?, Koneru Lakshmaiah Education Foundation (deemed to be University), 11-02-2021

7Participated 35th Annual Conference of Ramanujan Mathematical Society from 2020-12-28 to 2020-12-30 (Attend through Virtual conference mode)

8Participated 35th Ramanujan Mathematical Society (RMS) Pre-Conference Symposium on Complex Analysis organised by Central University, Rajasthan from 2020-12-27 to 2020-12-27 (Attend through Virtual conference mode)

9Invited talk: On logarithmic coeï¬ƒcients of some close-to-convex functions at International Webinar on Recent Trends in Geometric Function Theory & Applications (RTGFTA-2020), September 18-21, 2020 KIIT Deemed to be University, Bhubaneswar.

10Talk: â€œRegion of variability for certain subclasses of univalent functionsâ€ (Awarded for the Best Paper Presentation Award)at , 22nd Annual conference of Ramanujan Mathematical Society at the Department of Mathematical and Computational Sciences, National Institute of Technology Surathkal, India during June 6-8, 2007.

1) **Dr. Md. Firoz Ali** (2017) (IIT Kharagpur)

(Present Status: Assitant Professor at **NIT Durgapur**)

2) **Dr. Nirupam Ghosh** (2019) (Jointly with Prof. G.P. Raja Sekhar) (IIT Kharagpur)

(Present Status: Assitant Professor at **IIEST Shibpur**)

3) **Dr. Himadr Halder **(2022) (IIT Bhubaneswar)

1) **Mr. Abhishek Pandey **(**PMRF**) Joined in January 2020

2) **Mr. Amal Shaji ** (**CSIR**) Joined in January 2021

3) **Mr. Rohit Kumar **(**CSIR**) Joined in January 2021

4) **Mr. Subhadip Pal** (**DST-Inspire**) Joined in January 2021

5) **Mr. Shobhit Kumar **(**CSIR**) Joined in July 2021

6) **Mr. Alan P. Jose** (**CSIR)** Joined in January 2022

1. Reviewer of Mathematical Reviews of American Mathematical Society (Since 2009); 2. Reviewer of Zentralblatt (Since 2010)

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