ISL Advanced Complex Analysis (2013)

Venue:  CU, Rajasthan
Dates: 24th Jun to 13th Jul,2013

 

Convener(s) Speakers, Syllabus and Time table Applicants/Participants

 

School Convener(s)
Name Prof. A. P. Singh     Dr. J. K. Prajapat
Mailing Address Head, Department of Mathematics,
Central University of Rajasthan,
Bandar sindri, kishangarh, 305801
District Ajmer, Rajasthan		 Central University of Rajasthan,
Bandar Sindri, Kishangarh, 305801
District Ajmer, Rajasthan

 

Speakers and Syllabus 

 

Speakers and Syllabus details:

Speaker Dates Lectures Detailed Syllabus
Prof. A. P. Singh (APS)
Central University of Rajasthan
&
Prof. S. P. Goyal (SPG)
Univ. of Rajasthan		 24th - 27th June 2013 12 Fundamental Concepts: Analytic functions, Cauchy Riemann Equations, Cauchy’s Theorems, Cauchy’s integral formula, Applications of Cauchy’s integral formula, Liouvilles theorems, Taylor’s theorem, Laurent theorem, Cauchy Residue theorem, Contour integral, Zeros of holomorphic functions, Rouche’s theorem, Counting of zeros and poles, Complex Dynamics
Prof. Ravi Kulkarni (RSK)
IIT Mumbai		 28th,29th June 2013 6 Schwarz reflexion principle and Riemann mapping theorem: Schwarz reflexion, reflexion across analytic arcs, applications of Schwarz reflexion, Compact space in function spaces, Statement and proof of Riemann mapping theorem, Behaviour of the boundary (Ch. IX, Ch. X of Complex Analysis by Serge Lang)
Prof. A. R. Shastri (ARS)
IIT Mumbai		 1st, 2nd July 2013 6 Analytic Continuation: Definition of the analytic function element, analytic continuation along a curve, the monodormy theorem, idea of Riemann surface, elliptic modular functions and Picard’s theorem, elliptic functions (Ch. X of Function Theory of one complex variables, R. E. Greens & S. G. Krantz)
Prof. S. S. Bhoosnurmath (SSB)
Karnatak University
&
Prof. R. K. Raina (RKR)
MPUAT, Udaipur		 3rd, 4th, 5th, 6th July2013 12 Applications of Maximum modules principle and Jensen’s formula: Jensen’s formula, Picard Borel Theorem, bounds by the real part, Borel Caratheodary theorem, Hadamard three circle theorem, effect of small derivatives (Ch. XII of Complex Analysis by Serge Lang), Nevanlinna Theory
Prof. S. Poonusamy (SP)
IIT Chennai		 8th, 9th July2013 6 Geometric Function Theory: Univalence in complex plane, Area theorem, covering and distortion results, starlike and convex functions, close to convex functions, subordination, application of subordination principle, first and second order differential subordination with applications (Ch. 2 of Univalent functions by P. L. Duren and Ch. 2 of Differentia Subordination by Miller and Mocanu)
Dr. J. K. Prajapat (JKP)
Central University of Rajasthan		 10th, 11th July2013 6 Gamma and Zeta functions: Differentiation Lemma, the Gamma function, Weiresstrass product, the Gauss multiplication formula, the Gauss formula, Mellin transform, Stirling formula, Lerch formula, Zeta functions, Basic Analytic properties of Zeta functions, Prime Number Theorem (Ch. XV, XVI of Complex Analysis by Serge Lang)
Prof. K. Verma (KV)
IISc Bangalore		 12th, 13th July2013 6 Introductions of several complex variables: Holomorphic functions, Polydisc, Cauchy’s integral formula, Cauchy estimates, Taylor series expansion, Principle of analytic continuation, Open mapping Theorem, Maximum principles, Montel’s theorem, Poincare’s theorem, Cartan uniqueness theorem, Fatou Biberbach domains, Domains of holomorphy
(A short introduction of several complex variable by Oliver Knill, 1996 http://www.math.harvard.edu/~knill/teaching/severalcomplex_1996/severalcomplex.pdf)

 

Refrences:

  1. Serge Lang: Complex Analysis, IVth edition, Springer International Edition.
  2. R. E. Greene and S. G. Krantz; Function theory of one complex variables, American Mathematical Society.
  3. S. G. Krantz, Complex Variables, Chapman & Hall
  4. L. V. Ahlfors, Complex Analysis, McGraw Hill.
  5. I. Graham and G. Khor; Geometric function theory in one and higher dimensions, Marcel Dekker.
  6. P. L. Duren, Univalent Functions, Springer-Verlag, New Yark.
  7. S. S. Miller and P. T. Mocanu, Differential Subordinations, Theory and Applications, New York and Basel, Marcel Dekker, 2000.

 

Time Table:

Day Date

Lecture 1

09:30 to 11:00

  

Lecture 2

11:30 to 01:00

   Tutorial or
Guest Lecture
02:00 to 04:00		  
Mon 24 June 2013 APS Tea APS Lunch JKP

Tea

and

Snacks
Tue 25 June 2013 APS APS JKP
Wed 26 June 2013 SPG SPG JKP
Thu 27 June 2013 SPG SPG JKP
Fri 28 June 2013 RSK RSK JKP
Sat 29 June 2013 RSK RSK JKP
Mon 01 July 2013 ARS ARS SKD
Tue 02 July 2013 ARS ARS SKD
Wed 03 July 2013 SSB SSB SKD
Thu 04 July 2013 SSB SSB SKD
Fri 05 July 2013 RKR RKR SKD
Sat 06 July 2013 RKR RKR SKD
Mon 08 July 2013 SP SP SKP
Tue 09 July 2013 SP SP SKP
Wed 10 July 2013 JKP JKP SKP
Thu 11 July 2013 JKP JKP SKP
Fri 12 July 2013 KV KV SKP
Sat 13 July 2013 KV KV SKP

 

Tutorial Assistants:

Sr. Name Affiliation
1 Dr. J. K. Prajapat Central University of Rajasthan
2 Sanjib Kumar Dutta Kalyani University
3 Sanjay Kumar Pant Delhi University

 

 

Selected Applicants
Sr. SID Full Name Gender Affiliation State Position in College/ Univ. Univ/ Institute M.Sc./M.A. Year of Passing M.Sc./ M.A Ph.D. Degree Date
1 3059 Mr. Aryan Kanjibhai Patel Male M.N.College,Visnagar Gujarat Asst. Prof. Sardar Patel Univ., Vallabh Vidyanagar 2006  
2 3152 Mr Sarbeswar Barik Male Hi-Tech Institute of Technology Orissa Asst. Prof. Berhampur Univ. 2002  
3 3154 Mr. Navneet Mittal Male ICG-The IIS Univ. , Jaipur Rajasthan Asst. Prof. Central Univ. of Rajasthan 2012  
4 3160 Dr. Deepak Bansal Male Goverment College Of Engineering And Technology Rajasthan Asst. Prof. Mohan Lal Sukhadia Univ. 2001 18 Jan 2008
5 3162 Mr. Piyush Goyal Male S.C.D. Govt College for Boys, Ludhiana Punjab Lecturer Panjab Univ., Chandigarh 2011  
6 3220 Mr Manas Gajare Male K.T.H.M. College, Nashik Maharashtra Asso. Prof. KTHM College, Nashik 2012  
7 3262 Mr Samten Tamang Male Univ. of Kalyani, Kalyani. West Bengal Asst. Prof. Univ. of North Bengal 2007  
8 3273 Mr. Dilip Chandra Pramanik Male Univ. of North Bengal. West Bengal Asst. Prof. Univ. of North Bengal 2008  
9 3295 Mr. Bipul Pal Male Univ. Of Kalyani West Bengal Ph.D. Student Univ. OF Kalyani 2008  
10 3333 Mr. Pulakesh Sen Male Employed In D.N.C. College Under The Univ. Of Kalyani West Bengal Asst. Prof. IIT, Kharagpur 2001  
11 3379 Mr Kshittiz Chettri Male Sikkim Govt. College Under Sikkim Univ. Sikkim Asst. Prof. Sikkim Manipal Univ. 2006  
12 3473 Mr. Raj Kumar Garg Male Sant Longowal Institute of Engineering & Technology Punjab Ph.D Guru Nanak Dev Univ. , Amritsar 2007  
13 3479 Ms. Sarika Verma Female Sant Longowal Institute of Engineering & Technology Punjab Asst. Prof. Punjab Univ. Chandigarh, M.Sc. 2007  
14 3491 Ms Jyoti Thorwe Female Shivaji Univ. ,Kolhapur. Maharashtra Asst. Prof. Pune Univ. , Pune 2008  
15 3523 Ms. Deepti Lohia Female Guru Nanak College For Girls Punjab Asst.Prof. M.Sc 2007  
16 3535 Dr. Ratan Kumar Dutta Male Patulia High School West Bengal Asst. Teacher Univ. of Kalyani 2004 30 Aug 2011
17 3541 Mr. Sudip Mazumder Male Bengal College of Engineering and Technology, Durgapur West Bengal Asst. Prof. Burdwan Univ. 2006  
18 3546 Mrs. Mamta Amol Wagh Female Deen Dayal Upadhyaya College, Univ. Of Delhi Delhi Asst. Prof. Dr. B. R. Ambedkar Univ. , Agra 2007  
19 3563 Dr. Shalini Shekhawat Female Swami Keshwanand Institute of Technology, Management & Gramothan Rajasthan Lecturer Univ. of Rajasthan 2006 11 Nov 2010
20 3575 Mr. Sanjay Lamba Male Swami Keshvanand Institute of Technology, Management and Gramothan Rajasthan Lecturer Central Univ. of Rajasthan 2012  
21 3576 Dr. Vishal Saxena Male Global Institute Of Technology, Jaipur Rajasthan Asst. Prof. Univ. of Rajasthan 2005 21 Apr 2012
22 3580 Prof. Abhishek Mukherjee Male Kalna College West Bengal Asst. Prof. M.Sc. 2007  
23 3589 Mr. Sukhdev Singh Male Lovely Professional Univ. Punjab Lecturer Panjab Univ. , Chandigarh 2008  
24 3618 Mr Suhail Gulzar Mattoo Male Kashmir Univ. Jammu and Kashmir Ph.D Scholar Kashmir Univ. 2007  
25 3632 Mr Sajad Hussain Ahangar Male Univ. of Kashmir, Srinagar Jammu and Kashmir Ph.D. Scholar Univ. of Kashmir 2007  
26 3642 Mr. Subhabrata Patra Male Bengal College of Engineering & Technology. West Bengal Asst. Prof. Guru Ghasidas Univ. 2008  
27 3645 Dr. Reema Jain Female SKIT(VIT Campus) Rajasthan Professor M.Sc. 1999 15 Feb 2006
28 3646 Mr Imrul Kaish Male Berhampore college West Bengal Asst. Prof. Univ. of Kalyani 2007  
29 3648 Mr Faroz Ahmad Bhat Male Univ. of kashmir Jammu and Kashmir Ph.D Kashmir Univ. 2007  
30 3654 Mr. Girish Dhondiram Shelake Male Willingdon College Maharashtra Asst. Prof. Shivaji Univ. , Kolhapur 2004  
31 3656 Mr. Yogesh Kumar Bansal Male Rajasthan Institute Of Engineering And Technology Rajasthan Asst. Prof. Central Univ. of Rajasthan 2012  
32 3659 Dr. Sanjay Kumar Male Central Univ. of Jammu Jammu and Kashmir Asst. Prof. Univ. of Jammu 2003 19 Jul 2009
33 3665 Mr. Bipendra Singh Rawat Male Dept. of Mathematics & Statistics, Gurukul Kangari Univ. Uttarakhand/ Uttaranchal Asst. Prof. HNBGU Srinagar 2009  
34 3666 Dr. Dheerendra Bahadur Singh Male Dept. of Mathematics & Statistics, Gurukul Kangari Univ. Uttarakhand/ Uttaranchal Asst. Prof. BHU Varanasi 2005 17 Jan 2012
35 3681 Mr Tumiki Naveen chandar Raju Male Govt. Degree College, Jammikunta Andhra Pradesh Asst. Prof. Univ. Of Hyderabad / Campus 2001  
36 3688 Mr Sushil Kumar Goswami Male Bharati Vidhyaopeeth College Of Engineering Delhi Asst. Prof. Dr. B. R. Ambedkar Univ. , Agra 2001  
37 3696 Dr Praveen Agarwal Male Anand International College of Engineering, Jaipur Rajasthan Assoc. Prof. Rajasthan Univ. 2000 24 Apr 2006
38 3702 Dr. Narinder Sharma Male Govt. Degree College Ramnagar Jammu and Kashmir Asst. Prof. Univ. of Jammu 2004 31 Oct 2012
39 3722 Mr. Pabitra Debnath Male St. Xavier's College (Autonomous), Kokata West Bengal Asst. Prof. I.I.T Kanpur 2004  
40 -- Mr. Suresh Kumar S Male SRM University Tamil Nadu Asst. Prof. I.I.T Madrass 2004  
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