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 |

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

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

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

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

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

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

** **

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

2Vasudevarao Allu and Vibhuti Arora, Bohr-Rogosinski type inequalities for concave univalent functions, Journal of Mathematical Analysis and Applications (Accepted for publication) (2022)

3Vasudeavarao Allu, Vibhuti Arora and Amal Shaji, On the Second Hankel determinant of Logarithmic Coefficients for certain univalent functions, Mediterranean Journal of Mathematics (Accepted for publication) (2022)

4Daoud 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 (Accepted for publication) (2022), DOI: 10.1007/s12220-022-00895-2

5Vasudevarao Allu and Himadri Halder, Operator valued analogues of multidimensional Bohr's inequality, Canadian Mathematical Bulletin (2021) (Accepted for publication), https://doi.org/10.4153/S0008439521001077

6Vasudevarao Allu and Himadri Halder, The Bohr inequality for certain harmonic mappings, Indagationes Mathematicae 33 (2022), 581--597.

7Vasudevarao Allu and Himadri Halder, Bohr phenomenon for certain close-to-convex analytic functions, Computational Methods and Function Theory 22 (2022), 491–517.

8Molla Basir Ahamed and Vasudevarao Allu, Bohr phenomenon for certain classes of harmonic mappings, Rocky Mountain Journal of Mathematics 52(2022), 1205-1225.

9Md 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.

10Vasudevarao 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

11Molla 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.

12Md. 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.

13Vasudevarao Allu and Himadri Halder, The Bohr phenomenon for certain Subclasses of Harmonic Mappings, Bulletin des Sciences Mathématiques 173 (2021), Paper No. 103053, 18 pp., https://doi.org/10.1016/j.bulsci.2021.103053

14Molla Basir Ahamed, Vasudevarao Allu and Himadri Halder, The Bohr Phenomenon for analytic functions on simply connected domains, Annales Fennici Mathematici 47(2021), 103–120.

15Molla 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

16Molla Basir Ahamed, Vasudevarao Allu and Himadri Halder, Improved Bohr inequalities for certain class of harmonic univalent functions, Complex Variables and Elliptic Equations (Accepted for publication) (2021), https://doi.org/10.1080/17476933.2021.1988583

17Vasudevarao Allu and Abhishek Pandey, Support points of some classes of analytic and univalent functions, C. R. Math. Acad. Sci. Paris 359 (2021), 465–473.

18Vasudevarao Allu and Himadri Halder, Bohr radius for certain starlike and convex univalent functions, Journal of Mathematical Analysis and Applications 493(2021), 124519.

19Vasudevarao Allu and Abhishek Pandey, Zalcman Conjecture for certain analytic and univalent functions, Journal of Mathematical Analysis and Applications 492(2020), 124466.

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

21Md. 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.

22Vasudevarao 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.

23Nirupam Ghosh and Vasuevarao Allu, On some subclass of harmonic mappings, Bulletin of the Australian Mathematical Society 101(2020), 130--140.

24Md 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.

25Nirupam Ghosh and A. Vasudevarao, The radii of fully starlikeness and fully convexity of a harmonic operator, Monatshefte für Mathematik 188 (2019) 653--666.

26Nirupam Ghosh and A. Vasudevarao, On some subclass of harmonic close-to-convex mappings, Monatshefte für Mathematik 188(2019), 247--267.

27Vasudevarao Allu, Derek K. Thomas and Nikola Tuneski, On Ozaki close-to-convex functions, Bulletin of the Australian Mathematical Society 99(2019), 89--100.

28Samiran Chakraborty and Allu Vasudevarao, On Stable Functions, Computational Methods and Function Theory 18(2018), 677--688.

29Derek 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

30Md Firoz Ali and A. Vasudevarao, On Certain Families of Analytic Functions in the Hornich Space, Computational Methods and Function Theory 18(2018), 643–659.

31Nirupam Ghosh and A. Vasudevarao, Some basic properties of certain subclass of harmonic univalent functions, Complex Variables and Elliptic Equations 63 (2018), 1687—1703.

32U. Pranav Kumar and A. Vasudevarao, Logarithmic coefficients for certain subclasses of close-to-convex functions, Monatshefte für Mathematik 187(2018), 545--563.

33Md 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.

34Md 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.

35Md Firoz Ali and A. Vasudevarao, Logarithmic coefficients of some close-to-convex functions, Bulletin of the Australian Mathematical Society 95 (2017), 228–237.

36Md 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.

37Nirupam Ghosh and A. Vasudevarao, Coefficient estimates for certain subclass of analytic functions defined by subordination, Filomat 31(11) (2017), 3307-3318.

38A. Vasudevarao, Fekete–Szegö inequality for certain spiral-like functions, C. R. Math. Acad. Sci. Paris 354 (2016), 1065–1070.

39M. Okada, S. Ponnusamy, A. Vasudevarao and H. Yanagihara, Circular symmetrization, subordination and arclength problems on convex functions, Mathematische Nachrichten 289 (2016), 1044–1051.

40Md 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.

41A. Vasudevarao, Fekete-Szegö problem for certain subclasses of univalent functions, Bulletin of the Korean Mathematical Society 52 (6)(2015), 1937–1943.

42Md 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.

43A. Vasudevarao, An Arclength problem for some subclasses of m-fold symmetric functions, Mathematica (Cluj) 56(79)(2014), 182-192.

44A. Vasudevarao, An arclength problem for some subclasses of univalent functions, The Journal of Analysis 22 (2014), 145-149.

45A. Vasudevarao, Region of variability for some subclasses of univalent functions,Springer Proc. Math. Stat. 91 (2013), 151–170.

46A. 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.

47S. Ponnusamy, A. Vasudevarao and M. Vuorinen, Region of variability for exponentiall convex functions, Complex Analysis and Operator Theory 5(3) (2011), 955--966.

48S. Ponnusamy and A. Vasudevarao, Region of variability for functions with positive real part, Annales Polonici Mathematici 99(3)(2010), 225--245.

49S. Ponnusamy, A. Vasudevarao and H. Yanagihara, Region of variability for close-to-convex functions-II, Applied Mathematics and Computation 215(3)(2009), 901--915.

50S. 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.

51S. 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.

52S. 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.

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

54S. Ponnusamy and A. Vasudevarao, Region of variability of two subclasses of univalent functions, The Journal of Mathematical Analysis and Applications 332 (2007), 1323--1334.

1Participated “The Current Developments in Mathematics (CDM) conference”, jointly hosted by Harvard University and the Massachusetts Institute of Technology (MIT) (through virtual mode), from 2022-03-18 to 2022-03-19.

2Invited talk: Bohr radius for Banach spaces on simply connected domains, Computational Methods in Function Theory (CMFT), The Federico Santa María Technical University in Valparaíso, Chile, January 10-14, 2022.

3Plenary talk “Bohr phenomenon for harmonic Bloch functions on simply connected domains” (with Himadri Halder) at VIII International Conference of Mathematics and Computer Science "Congressio Mathematica", University of Warmia and Mazury in Olsztyn, Poland, during September 19–25, 2022.

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

5Plenary talk “ The Bohr phenomenon for certain analytic and univalent functions” at the VI Conference of Mathematics and Computer Science, "Congressio Mathematica", University of Warmia and Mazury in Olsztyn, Poland, during November 21-22; 28–29, 2020.

6Plenary talk “ On the Third Logarithmic Coefficient of Close-to-convex Functions” (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 23–25, 2018.

7Short Communication “Certain subclasses of harmonic univalent mappings” (with Nirupam Ghosh) in Short Communication at International Congress of Mathematicians (ICM 2018), Rio de Janeiro (Brazil) during August 1–9, 2018.

8Invited talk “On the Growth of Some Subclasses of the Class of Univalent Functions” at International Symposium in Geometric Function Theory and Applications at Isik University, Turkey during August 26-September 4, 2013.

9Invited talks “On region of variabilities for family of analytic functions” at the Department of Applied Sciences, Yamaguchi University, Ube, Japan during December 19–23, 2011.

10Short Communication “ Region of variability for spirallike functions with respect to a boundary point” at International Congress of Mathematicians (ICM 2010) at Hyderabad, August 19–27, 2010.

11Invited talk “ Region of variability for functions with positive real part” at ICM 2010-Satellite Conference: International Workshop on Harmonic and Quasiconformal Mappings (HQM2010) at IIT Madras, August 09-17, 2010.

12Invited talk : “Region of variability for functions with positive real part” in Helsinki Analysis seminar at Department of Mathematics and Statistics, University of Helsinki, Finland on September 28, 2009.

13Invited talk “Region of variability and Fekete Szeg¨o problem for exponentially convex univalent functions” in Helsinki Analysis seminar at Department of Mathematics and Statistics, University of Helsinki, Finland on September 14, 2009.

14Invited talk “Region of variability for exponentially convex univalent functions” at International conference on Complex Analysis and Related Topics, 12th Romannian-Finnish Seminar at University Turku, Finland, August 17-21, 2009.

15Invited talk “Region of variability for exponentially convex univalent functions” in Turku Analysis seminar at Department of Mathematics, University of Turku, Finland on August 07, 2009.

16Invited talk “Certain classes of univalent functions and radius problems” in Turku Analysis Seminar at Department of Mathematics, University of Turku, Finland on January 30, 2008.

17Invited talk “Region of variability for certain classes of univalent functions satisfying differential inequalities” 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 “Annual Foundation School – I (AFS-I)” at the Department of Mathematics, NIT Durgapur, during December 12, 2022 to January 7, 2023.

3Invited talk “Bohr and Rogosinski inequalities for operator valued holomorphic functions” In the Symposium “Complex Analysis” 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 22-12–2022.

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 coeﬃcients 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: “Region of variability for certain subclasses of univalent functions” (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: Post-Doctoral Fellow at **ISI Bangalore**)

3) **Dr. Himadr Halder **(2022) (IIT Bhubaneswar) (Defended Ph.D. thesis on 26-10-2022)

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 July 2021

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

1) **Dr. Molla Basir Ahamed** ( Institute Post Doctoral Fellow) (Sept 2020 to May 2021)

(Present Status: Assistant Professor at **Jadavpur University**)

2) **Dr. Vibhuti Arora** (Institute Post Doctoral Fellow) (July 2021 to July 2022)

(Present Status: Assistant Professor at **NIT Calicut)**

**Ongoing: 2****Completed: 13**

- Completed: 4

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

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