IST Complex Analysis (2015) - Speakers and Syllabus

Speakers

  • Kaushal Verma, Indian Institute of Science, Bangalore
  • Vinayak Sholapurkar, Sir Parashurambhau College, Pune
  • Sameer Chavan, Indian Institute of Technology, Kanpur
  • Diganta Borah, Indian Institute of Science Education and Research, Pune

Course Associates

  • Sayani Bera, Indian Institute of Science, Bangalore
  • Geetanjali Phatak, Sir Parashurambhau College, Pune

Syllabus:

  • Module 1. Complex differentiation, power series, exponential and logarithm, complex line integrals, Cauchy-Goursat theorem on triangle, Cauchy’s integral formula, power series representation, zeros of holomorphic functions, Morera’s theorem, Runge’s theorem
  • Module 2.  Riemann sphere, linear fractional transformations, conformal mappings, harmonic functions, Poisson integral formula, characterisation of harmonic functions, Schwarz reflection principle.
  • Module 3.  Homotopy version of Cauchy’s theorem, branches of logarithm on simply connected domains,singularities, residue theorem, argument principle, Rouche’s theorem, open mapping theorem, maximum modulus principle, Schwarz lemma and the automorphisms of the disc.
  • Module 4. Subharmonic functions, Harnack’s principle, Dirichlet problem, Perron Method, Riemann mapping theorem.

Abstract of the Lectures:

    Prof. V. M. Sholapurkar: Cauchy’s theorem on triangle and local properties of holomorphic functions, e.g. Cauchy’s integral formula, power series representations etc. The lectures will cover Module 1.
    Dr Diganta Borah: Geometric properties of holomorphic functions, e.g. conformality and basic properties of harmonic functions. The lectures will cover Module 2.
    Dr. Sameer Chavan: The homotopy version of Cauchy’s theorem, Residue theorem and its consequences. The lectures will cover Module 3.
    Prof. Kaushal Verma: Perron’s method for solving Dirichlet problem and proof of the Riemann mapping theorem based on the original ideas of Riemann. The lectures will cover Module 4.

References

  • Complex Analysis, Stein and Shakarchi, Princeton University Press, 2006.
  • Complex Analysis, Gamelin , UTM, Spinger Verlag, New York, 2001
  • Functions of One Complex Variable, Conway, 2nd edition GTM 11, Springer Verlag, 1973

 First Week: 16th to 21th November, 2015

Day

9:30-11:00

11:00-11:30

11:30-1:00

1:00-2:30

2:30-3:30

3:30-4:00

4:00-5:00

5:00-5:30

Mon

VS

Tea

DB

Lunch

GP/SB/VS

Tea

GP/SB/DB

Snacks

Tue

VS

Tea

DB

Lunch

GP/SB/VS

Tea

GP/SB/DB

Snacks

Wed

VS

Tea

DB

Lunch

GP/SB/VS

Tea

GP/SB/DB

Snacks

Thu

VS

Tea

DB

Lunch

GP/SB/VS

Tea

GP/SB/DB

Snacks

Fri

VS

Tea

DB

Lunch

GP/SB/VS

Tea

GP/SB/DB

Snacks

Sat

VS

Tea

DB

Lunch

GP/SB/VS

Tea

GP/SB/DB

Snacks

Second Week: 23rd to 28th November, 2015

Day

9:30-11:00

11:00-11:30

11:30-1:00

1:00-2:30

2:30-3:30

3:30-4:00

4:00-5:00

5:00-5:30

Mon

SC

Tea

KV

Lunch

GP/SB/SC

Tea

GP/SB/KV

Snacks

Tue

SC

Tea

KV

Lunch

GP/SB/SC

Tea

GP/SB/KV

Snacks

Wed

SC

Tea

KV

Lunch

GP/SB/SC

Tea

GP/SB/KV

Snacks

Thu

SC

Tea

KV

Lunch

GP/SB/SC

Tea

GP/SB/KV

Snacks

Fri

SC

Tea

KV

Lunch

GP/SB/SC

Tea

GP/SB/KV

Snacks

Sat

SC

Tea

KV

Lunch

GP/SB/SC

Tea

GP/SB/KV

Snacks

SC: Sameer Chavan
KV: Kaushal Verma
VS:Vinayak Sholapurkar
DB: Diganta Borah
SB: Sayani Bera
GP: Geetanjali Phatak

 Notes:

  1. The email Id for any correspondence regarding this IST is bhaskaraprim@gmail.com

  2. Date and time of the special lecture will be announced in due course

  3. The accommodation for participants is planned at Gokhale Institute near Bhaskaracharya Pratishthan.

  4. The time table is tentative in nature and there could be some changes at a later date.

  5. The allocation of the accommodation will be on first come first serve basis.