MHRD Scheme on Global Initiative on Academic Network (GIAN)
Presents a Course on
QUASICONFORMAL MAPPINGS AND THEIR APPLICATIONS
December 11-16, 2017
Venue: Indian Institute of Technology Indore (IIT Indore)
This course will, for the most
part, focus on the following:
- notion of quasiconformality;
- theory of quasiconformal and related mappings;
- applications to composition operators and to eigenvalue estimates.
The value of quasiconformal mappings for the study of PDE's in the plane
was recognized already at the early stages of the theory. Only quite recently
it was observed that the techniques also apply for Calderon's inverse
conductivity problem (that forms the basis for computer tomography).
Generalizations of quasiconformal mappings have also been applied in nonlinear
elasticity. Most recently, quasiconformal mappings have turned out to be of
value in eigenvalue estimates for the Neumann (p-)Laplacian via composition
operators.
The relevant themes from quasiconformal mappings and their applications will be introduced to the
participants through a series of lectures and tutorials by the International faculty.
The tutorial hours will mostly consist of problem discussion sessions.
Examinations for interested student participants will be conducted over the weekend
and course credit will be given to them.
These lectures are intended to serve as a catalyst for gaining basic/fundamental knowledge
and for generating new ideas for further collaborative activities in quasiconformal mappings and related topics.
The program will provide an opportunity for fruitful interaction among researchers from India and
from several other countries. Interaction with subject experts will also put special emphasis on
exposure of PhD students and postdoctoral fellows to the latest trends.
Click here for the course brochure
Click here to know about GIAN
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The primary objectives of the course are as follows:
1. Exposing young participants to the fundamentals of Quasiconformal Mappings
and their Applications.
2. Building in confidence and capability amongst the participants in the area of
Quasiconformal Mappings and their Applications.
3. Providing exposure to problems and their solutions, through live discussions.
4. Enhancing the capability of the participants to identify recent research topics
for further studies and research.
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Day 1: December 11, 2017 (Monday)
Lecture 1 (9:30-10:30): Definition of quasiconformal mappings
Lecture 2 (11:00-12:00): Examples of quasiconformal mappings
Tutorial 1 (15:00-17:00): Problem solving session with examples: based on Lecture 1 and Lecture 2
Day 2: December 12, 2017 (Tuesday)
Lecture 3 (9:30-10:30): Regularity properties
Lecture 4 (11:00-12:00): Mapping theorems
Tutorial 2 (15:00-17:00): Problem solving session with examples: based on Lecture 3 and Lecture 4
Day 3: December 13, 2017 (Wednesday)
Lecture 5 (9:30-10:30): Generalizations of quasiconformality I
Lecture 6 (11:00-12:00): Generalizations of quasiconformality II
Tutorial 3 (15:00-17:00): Problem solving session with examples: based on Lecture 5 and Lecture 6
Day 4: December 14, 2017 (Thursday)
Lecture 7 (9:30-10:30): Invariant function spaces
Lecture 8 (11:00-12:00): Applications to eigenvalue estimates: Neumann-(p-) Laplacian
Tutorial 4 (15:00-17:00): Problem solving session with examples: based on Lecture 7 and Lecture 8
Day 5: December 15, 2017 (Friday)
Tutorial 5 (10:00-12:00): Problem solving session with examples: based on Lectures 1-8
Day 6: December 16, 2017 (Saturday)
Examination for Student Participants (10:00-12:00)
There will be
Special Sessions for limited invited and contributed talks
on recent developments in the area of Geometric Function Theory.
Interested participants can send their talk details (in the form of a PDF file consisting of title, abstract, author(s),
affiliation, address, email)
with type of presentations
(i.e. invited talk/contributed talk)
by email to
"swadesh[at]iiti.ac.in" latest by November 22, 2017 (extended). Accepted abstracts for contributed talks
will be notified by email on November 23, 2017 (extended).
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Professor Pekka Koskela
is currently working as a professor at University of Jyväskylä, Finland.
He worked as a faculty at University of Michigan for three years starting from 1992. He has been
appointed as a fellow in 1994 and a senior fellow in 1998 and in 2003 by Academy of Finland.
He has also served as a visiting faculty in several institutions like Universidad Autonoma
de Madrid in 1995, Universite Cergy-Pontoise in 1998 and Centre de Recerce Matematica in 1999.
Apart from this, he has held many positions like Chairman of the Department of Mathematics and
Statistics of University of Jyväskylä and Chairman of the instruction subcomission (ICMI) of
the National Committee of Mathematics, 2005-2012. He is one of the leading mathematicians in
the field "Geometric analysis and Geometric function theory". He is well-known for his pioneer
work on quasiconformal mappings and for several other works on mapping theory. He has published about
170 publications (MathSciNet) with about 3600 citations, including the second most cited
publication published in 2000, in all of Mathematics, and the eighth most cited published in 1998.
He is also a coauthor of two monographs: "Lectures on mappings of finite distortion"
in Lecture Notes in Mathematics, 2014, and "Sobolev spaces on metric spaces: An approach
based on upper gradients", Cambridge University Press, 2015.
He has given many invited talks in
conferences including an invited talk in the analysis session of ICM 2010 and
a plenary talk at the American
Mathematical Society 2008 Fall Eastern Section meeting. He has been awarded with two prizes,
Väisälä prize in 2001 and Magnus Ehrnrooth prize in 2012. He has been an
editorial board member for various
international journals including Acta Mathematica and Conformal Geometry & Dynamics.
He has also served as a referee for 95 different journals, including the leading journals Acta Math.,
Annals of Math., Invent. Math. and J. Amer. Math. Soc. and further Ann. Probab., Arch. Ration. Mech. Anal.,
Comm. Pure Appl. Math., Duke Math. J., Geom. Funct. Anal., J. Diff. Geom. He has supervised twenty
students so far for their PhD degree.
For more details, please visit:
http://users.jyu.fi/~pkoskela/
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Dr. Swadesh Kumar Sahoo
received his PhD degree from IIT Madras in 2008 and is currently
working as an Associate Professor in the Discipline of Mathematics, School of Basic Sciences of IIT Indore. He was heading the Discipline of Mathematics from June 20, 2012 until September 24, 2015. His current administrative responsibility also includes Head, School of Basic Sciences at IIT Indore.
His broad area of research is geometric function theory.
He works on problems in the theory of univalent functions, special functions,
quasiconformal mappings,
and hyperbolic-type geometry.
He has already supervised three students for their PhD degree and is currently
supervising
three more Ph.D. students.
He has the total of 25 publications
(MathSciNet) in reputed
international journals with 51 citations. He received a research grant from National Board
for Higher Mathematics (NBHM) for the
period 2016-2019.
He has been collaborating with researchers from India, Japan, China, United States, and Finland.
He has successfully organised three international symposia and has been
involved in several national and international events.
He has participated and delivered a series of invited talks in several
scientific events held in India, Japan, China, United States, and Ukraine.
He has also served as
a co-editor for special volumes of several conference proceedings.
For more details, visit
http://iiti.ac.in/people/~swadesh/
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The above fees include meals (breakfast, lunch, and dinner in students dinning), instructional materials, and 24 hours internet facility.
The participants will be provided with accommodation on payment basis. Charges for accommodation are provided below.
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Registration and Accommodation |
We request the participants to first register at the GIAN portal given at the following link and
then based on their selection, register at the GIAN portal of IIT Indore.
(Alternatively, one can request for participation by sending an email to
swadesh[at]iiti[dot]ac[dot]in along with a short CV of the applicant.
After hearing from the organizers about their selection, they can proceed to register at the GIAN portal of IIT Indore.)
Deadline for registration is November 30, 2017.
Click here for registration at the GIAN portal.
Click here for registration at the IITI GIAN portal
(Please mention NEFT/UTR/Online Transaction Reference Number alongwith the date of transferred amount in the appropriate box.)
Bank Details for Fund Transfer or e-payment:
Name of Account Holder: IIT Indore
Name of Bank: Canara Bank
Branch: IIT Indore, Simrol Campus Branch
Account Number: 1476101027440
Account Type: Saving A/c
Bank IFS Code: CNRB0006223
Bank SWIFT Code: CNRBINBBISG
Credit Card payment option is also available at the link
"https://epayments.iiti.ac.in/". At this link please fill-up with "gian_qcma-your name" for Reference Number
and fill-up the amount and then proceed to pay. After the payment is successful, please DO NOT forget to save and send
the transaction reference page in PDF by email to "swadesh[at]iiti.ac.in".
Accommodation:
The participants may be provided with hostel accommodation, depending on availability, on payment basis.
Few rooms in Institute Guest House may also be available on payment basis.
The outstation participants who require accommodation should send their request
(with choice of accommodation) to swadesh[at]iiti[dot]ac[dot]in
with the subject "Request for Accommodation" latest by November 30, 2017. The rates for accommodation charges are
Institute Hostel accommodation (sharing basis): ₹ 250 per night.
Institute Guest House (Executive Suite): ₹ 2, 000 per night (per unit/room).
Accommodation charges do not include meals expenses.
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