NCMW - Quasiconformal mappings and Holomorphic Dynamics

Speakers and Syllabus

 

Name of the Speaker with affiliation

No. of Lectures

Detailed Syllabus

Kingshook Biswas,
ISI Kolkata

4

Uniformization of Riemann Surfaces:
Riemann surfaces,maps between Riemann surfaces,Riemann mapping theorem, the uniformization theorem, Implication of uniformization for compact surfaces.

Sudeb Mitra,
City University of New York

6

 Quasiconformal Mappings:
Geometric introduction to Quasiconformal mappings, outline of the proof of the Measurable Riemann mapping theorem, Ahlfors–Bers theorem, Quasiconformal motions

Sabyasachi Mukherjee, TIFRMumbai

4

 Holomorphic Dynamics in dimension one:
Fatou-Julia sets, dynamics of rational maps, Sullivan's no wandering theorem, Straightening theorem for polynomial-like maps, the Mandelbrot set and uniformizations of hyperbolic components, J-stability and Holomorphic motion

Sushil Gorai,
IISER Kolkata

4

 Basic SCV and Slodkowski's theorem for holomorphic motion:
Basic notions of several complex variables, holomorphic convexity, domains of holomorphy, polynomial convexity, polynomial hull, automorphisms of complex Euclidean spaces.
Construction of polynomial hulls and their relation with holomorphic motion, Slodkowski's proof of extension of holomorphic motion.

Krishnendu Gongopadhyay, IISER Mohali

1

Quasiconformal maps on Heisenberg groups:
We will give a brief overview of the Korányi-Reimann theory of quasiconformal mappings on the Heisenberg group following the survey arXiv: 1510.02369.

 

References:

  1. Lars V Ahlfors, Lectures on Quasiconformal Mappings Second Edition; with additional chapters by C.J. Earle and I. Kra, M. Shishikura, and J. H. Hubbard; American Mathematical Society; 2006.
  2. L. V. Ahlfors and L. Bers, Riemann’s mapping theorem for variable metrics, Ann. of Math. (2) 72 (1960), 385–404.
  3. L. Bers, Quasiconformal Mappings, With Applications to Differential Equations, Function Theory and Topology; Bulletin of the AMS, Vol 83, Number 6, 1977.
  4. C. J. Earle, Some Remarks On The Beltrami Equation, MATH. SCAND. 36 (1975), 44–48.
  5. Dynamics in one complex variable, John Milnor, Princeton University Press; 3rd edition (22 January 2006).
  6. Quasiconformal mappings on the Heisenberg group: An overview, arXiv: 1510.02369

 

Time Table

 Time Table:

Duration of each lecture 1.5 hrs and tutorial 1 hour

  10:00-11:30 Tea 11:45-1:15 Lunch Break
1:15-2:30		 2:30-4:00 Tea 4:30-5:30
(Discussion Sessions)
Mon SMi   SMu        KB   SMu+AB
Tue SMi   SG KB   SMi+NC
Wed SMi   SG KB   Special Lecture:
4:30-6:00 KG
Thurs SMi   SMu KB   KB+AP
Fri SMi   SMu SG   SG+SM
Sat SMi   SG SMu   SMi+NC

Speakers with affiliations :
SMi: Prof. Sudeb Mitra - City University of New York
KB: Dr. Kingshook Biswas- ISI Kolkata
SG: Dr. Sushil Gorai - IISER Kolkata
SMu: Dr. Sabyasachi Mukherjee - TIFR Mumbai
KG: Prof. Krishnendu Gongopadhyay -IISER Mohali

Tutors with affiliations :
NC: Dr. Nishan Chatterjee - Naba Barrackpur Prafulla Chandra Mahavidyalaya
AB: Mr. Anubrato Bhattacharyya - Presidency University
SM: Mr. Subhamoy Mondal - Presidency University
AP: Mr. Arkajit Palchaudhury - ISI Kolkata.

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