TEW Complex Analysis (2013)
|Venue:||Vivekananda Mahavidhyalaya, Burdwan-713103|
|Dates:||27th - 31st Dec|
Supported by the ARSI Foundation
|Convener(s)||Speakers, Syllabus and Time table||Applicants/Participants|
|Name||Biswajit Mitra||Krishnendu Gongopadhyay|
|Mailing Address||Vivekananda Mahavidhyalaya, Burdwan-713103
IISER Mohali, Sector 81, SAS Nagar, P. O. Manauli, Punjab 140306
Proposed Scientific Plan
In the proposed TEW, our theme would be Complex Analysis (from a geometric viewpoint). We propose to have three mini-courses in this program consisting of around 4 lectures, each of 1.5 hrs duration. The rest of the time will be devoted to group discussions and tutorial. The aim of this course would be to depict a flow of ideas along with absolute mathematical precision wherever possible. We hope the courses will provide a geometric realization of several topics of complex analysis to the audience.
Later in the summer or winter of 2014, we plan to have a follow up of this workshop with advanced courses followed by a mini-conference consisting of survey talks that will connect the subject to cutting edge research.
Syllabus of the Workshop.
The syllabus of the workshop has been designed in a way so that the major part of the workshop will be devoted to foundational aspects of complex analysis. A salient feature of the proposed workshop is that besides foundational aspects, the participants will also be exposed to some advanced topics like Mobius geometry or Introductory Complex Dynamics. These topics are mostly missing in the syllabus of colleges/universities though they are foundational to learn many modern aspects of Mathematics. In addition to the mini-courses, we shall also have two survey talks on the last day of the program. The survey talks will be given by known experts in the subject from the region. In the following we summarize the syllabus of the courses, along with the names of the speakers for the respective courses. We have also mentioned the number of contact hours for each course.
- Course Title: Arithmetic of Complex Numbers. (3 hrs)
Speaker: Brundaban Sahu (NISER Bhubaneswar)
Course outline: (i) Arithmetic of complex numbers, Exponential functions, Holomorphic functions, Harmonic Functions, Relation between holomorphic and harmonic functions. (ii) The Exponential and complex trigonometric functions, Polynomials, Logarithmic function, Power series.
- Course Title: Geometric Complex Analysis (7 hrs)
Speaker: Kingshook Biswas (RKMVU Belur)
Course Outline: Complex Integration: Cauchy’s theorem, Cauchy’s formula, General contour integration; Application of Cauchy’s formula: zeros of a holomorphic function. Liouville’s theorem; Maximum modulus principle. Isolated Singularities, Riemann’s removable singularity theorem, Residue theorem, Poles and essential singularity, Meromorphic function, Analytic continuation.
- Course Title: Mobius Geometry (4.5 hrs)
Speaker: Krishnendu Gongopadhyay (IISER Mohali)
Course outline: Ideas of conformal transformation, Euclidean similarity geometry using complex numbers, introduction to hyperbolic plane, Mobius groups (groups of Mobius transformations of the sphere), action of Mobius transformations on hyperbolic plane, Algebraic classification of Mobius transformations; Finite groups of Mobius transformations.
- Course Title: Dynamics on the Riemann Sphere (3 hrs)
Speaker: Tarakanta Nayak (IIT Bhubaneswar)
Course outline: Rational functions on the sphere, The Fatou and the Julia set of rational functions, Classification of Fatou components, Properties of the Julia sets, Critical values and their dynamical importance, Iteration of Transcendental map, Baker domains, Wandering domains, Singular values and their importance, Some open questions.
On the last day, there will be two survey talks:
(i) Title: Survey on Nevanllina Theory.
Speaker: Indrajit Lahiri (Kalyani University, WB)
(ii) Title: Characterization of maximal ideals in the ring of entire functions.
Speaker: K. C. Chattopadhyay (Burdwan University, WB)
Participants who would be provided local hospitality would be strictly Under-Graduate College teachers. Preferences will be given to UG-teachers from the region. However, if there are slots, we may include a few more from neighboring places of West Bengal. We are expecting around 35 College Teachers to participate. If there are more than 35 participants, we may ask each participants for some registration fees, if any, that would be required. Some local doctoral and post doctoral students may also be included in the workshop. However, it will be made clear to them that the RMS-TEW is primarily for UG-college teachers.
The objective is same as that of the proposed RMS-TEW. That is (i) to promote student-initiative activities at the UG-PG levels. (ii) To increase the knowledge of the fundamentals of the college teachers, unity of mathematics, and problem-solving abilities. Emphasis will be given on basic examples.
The program will be largely interactive. The process of learning is described as "1/4th from teacher's teaching, 1/4th from one's own efforts, 1/4th from discussion with the like-minded people, and 1/4th from sleeping over the material for a long time". The program will follow the second and third steps in this process.
|Sr.||SID||Full Name||Affiliation||State||Position in College/ University
||University/ Institute M.Sc./M.A.||Year of Passing M.Sc./M.A||Ph.D. Degree Date|
|1||4879||Mr. Sujit Kumar Ghosh||Scottish Church College, Kolkata||West Bengal||Assistant Professor||University of Calcutta||2002||--|
|2||4882||Ms. Debanjana Basu||Scottish Church College, Kolkata||West Bengal||Assistant Professor||University of Calcutta||2006||--|
|3||4819||Mr. Arindam Das||NIT Rourkela, Rourkela||Orissa||MSc student||Appeared/ Awaiting Result||--|
|4||4846||Mr. Gopal Datt||Department of Mathematics, University of Delhi, Delhi||Delhi||PhD||University of Delhi||2009||--|
|5||4573||Dr. Khushwant Singh Chahal||IISER Mohali, Sas Nagar Mohali||Punjab||Post Doctorate Fellow||Guru Nanak Dev University||2007||17 Jun 2013|
|6||4677||Dr. Sunil Kumar Maity||The University of Burdwan, Burdwan||West Bengal||Assistant Professor||Calcutta University||2001||7 Sep 2006|
|7||4570||Dr Bibhas Chandra Saha||Chandidas Mahavidyalaya, Bolpur||West Bengal||Assistant Professor||University of Burdwan||1995||7 Feb 2010|
|8||4815||Mr. Zafar Iqbal||St. Mary's Technical Campus Kolkata, Barasat||West Bengal||Assistant Professor||University of North Bengal||2011||--|
|9||4645||Mr. Manojit Maity||Boral High School, Kolkata||West Bengal||Asst. Teacher||University of Calcutta||2003||--|
|10||4686||Mr Manas Ranjan Mishra||O.P.Jindal Institute of Technology, Raigarh||Chhattisgarh||Assistant Professor||Sambalpur University||2004||--|
|11||4877||Ms. Sarani Chakraborty||Directorate of Distance Education, University of North Bengal, Siliguri||West Bengal||Assistant Professor||UNIVERSITY of KALYANI||2003||--|
|12||4710||Mr. Shubhashish Das||University of Kalyani, Kalyani||West Bengal||PhD||TIFR-CAM, BANGALORE||2012||--|
|13||4709||Mr. Harekrishna Daripa||Bengal College Of Engineering And Technology, Durgapur||West Bengal||Assistant Professor||INDIAN SCHOOL OF MINES||2012||--|
|14||4928||Mr. Sumanta Das||Burdwan University, Burdwan||West Bengal||Msc.student||Burdwan University||Appeared||--|
|15||4808||Mr Samten Tamang||University of Kalyani, Kalyani||West Bengal||Assistant Professor||University of North Bengal||2007||--|
|16||4907||Mr. Arup Kumar Mondal||The University of Burdwan, Bardhaman||West Bengal||MSc Student||University of Burdwan||Appeared/ Awaiting Result||--|
|17||4946||Dr Tapan Saha||Presidency University, Kolkata||West Bengal||Assistant Professor||Rajabazar Science College, University of Calcutta||2002||7 Jul 2010|
|18||4940||Mr. Palash Goswami||Michael Madhusudan Memorial College, Durgapur||West Bengal||Assistant Professor||Burdwan University||2000||--|
|19||4930||Mr. Gobinda Chandra Panda||Mahavir Institute of Engg. and Technology, Bbsr||Assistant Professor||Sambalpur University||2005||--|
|20||4910||Mr. Jeet Sarkar||The University of Burdwan, Burdwan||West Bengal||The University of Burdwan||Appeared/ Awaiting Result||--|
|21||4927||Mr Sukhendu Pal||Bahara Adarsha Vidyapith, Kandi||West Bengal||Teacher||Visva Bharati University||1997||--|
|22||4898||Mrs. Paulomi Chattopadhyay||Academy of Technology, Adisaptagram||West Bengal||Assistant Professor||University of Burdwan||2001||--|
|23||4897||Dr. Arindam Sarkar||Kandi Raj College, Kandi||West Bengal||Assistant Professor||University of Kalyani||1995||31 Jan 2007|
|24||4591||Mr. Bipul Pal||University of Kalyani, Kalyani||West Bengal||Ph.D. Student||University of Kalyani||2008||--|
|25||4571||Mr. Soham Dasgupta||Syamsundar College, Burdwan||West Bengal||Ex Student of Math(Hons.)||University of Madras||Appeared/ Awaiting Result||--|
|26||4936||Mr. Haradhan Kundu||The University of Burdwan, Burdwan||West Bengal||SRF(CSIR)||The University of Burdwan||2010||--|
|27||4860||Mr. Apurba Banerjee||The University Of Burdwan, Burdwan||West Bengal||Junior Research Fellow||The University of Burdwan||2009||--|
|28||4638||Mr Dinesh Kumar||Deen Dayal Upadhyaya College, University of Delhi, New Delhi||Delhi||Guest||M.Sc Maths, Hindu College, University of Delhi||2009||--|
|29||--||Mridani Acharya||Dept of Math, Rabindra Bharati Univ||West Bengal||Ex-student||
Rabindra Bharati Univ. MSc Math
|30||--||Mr.Bibhas Mondal||Dept of Math, Surendra Nath college, Kolkata-09||West Bengal||Assistant Professor|| M.Sc Math,
|31||4900||Dr. Ananta Patra||Dr. Meghnad Saha College, Uttar Dinajpur||West Bengal||Assistant Professor||Burdwan University||2002||4 Feb 2013|
|32||4913||Mr . Suhas Basu||Kalyani Govt. Engg. College, Kalyani||West Bengal||Part Time lecturer||University of Kalyani||2008||--|
|33||--||Mr. Rajib Mukherjee||Dept of Mathematics, K.N. College, Berhampur||West Bengal||Assistant Professor||
Kalyani University MSc Math
|34||--||Mr. Subhashish Roy||
Dept of Mathematics, Visva Bharati Univ
|West Bengal||Assistant Professor||
Burdwan University MSc Math
|35||4830||Mr. Imrul Kaish||Berhampore College, Berhampore||West Bengal||Assistant Professor||University of Kalyani||2007||--|
|36||4642||Mr. Chandan Kumar Mondal||University Of Hyderabad, Hyderabad||Andhra Pradesh||MSc student||University Of Hyderabad||Appeared/ Awaiting Result||--|
|37||4601||Ms. Nourin Firdousi||University of Burdwan, Burdwan||West Bengal||MSc student||University of Burdwan||Appeared/ Awaiting Result||--|
|38||4902||Ms. Anita Paul||University of Burdwan, Burdwan||West Bengal||B.Ed Student||University of Burdwan||2012||--|
|39||4829||Dr. Sudip Kumar Pal||University of Kalyani, Kalyani||West Bengal||Post Doctoral Research Fellow||Jadavpur University||2008||10 Sep 2012|
|40||4873||Mr. Ayan Mukherjee||Guskara Mahavidyalaya, Guskara||West Bengal||Guest Lecturer||Burdwan University||2011||--|
|41||4894||Mr. Ramkrishna Thakur||Bidhannagar College, Kolkata||West Bengal||Assistant Professor||Calcutta University||2005||--|
|42||--||Lakshi Kanta Dey||
Dept of Mathematics. National Inst of Tech, Durgapur
|West Bengal||Assistant Professor||
Jadavpur University M.Sc Math
|43||4813||Mr. Soumyadip Mondal||University of Burdwan, Bardhaman||West Bengal||MSc Student||University of Burdwan||Appeared/ Awaiting Result||--|
|44||4713||Mr. Souradip Chatterjee||University Of Hyderabad, Hyderabad||Andhra Pradesh||MSc Student||University Of Hyderabad||Appeared/ Awaiting Result||--|
Dept of Mathematics.
Banaras Hindu Univ, M.Sc Math