The Department of Mathematics, School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore, is organizing the "Pre-Conference Symposium - 36th Annual Ramanujan Mathematical Society Conference (RMS 2021)" on August 4, 2021.

Number Theory

Convener: Dr. Thangadurai, HCRI, Allahabad

  • Prof. Akshaa Vatwani, -IIT Gandhi Nagar
  • Prof. Aparmeyo Pal, - HRI, Prayagraj
  • Prof. Biswajyoti Saha, - IIT Delhi
  • Prof. K. Senthil Kumar - NISER, Bhubaneshwar
  • Prof. Kasi Viswanadham - IISER, Berhampur
  • Prof. Mohan Chintamani - University of Hyderabad

Discrete Mathematics

Convener: Dr. Aparna Lakshmanan, CUSAT

  • Prof. Csilla Bujtás, - University of Ljubljana, Slovenia .
  • Prof. Subrahmanyam Kalyanasundaram, IIT Hyderabad
  • Prof. Sukanta Pati, - IIT Guwahati
  • Prof. Vinayak Joshi, Savitribai Phule - Pune University, Pune.
  • Prof. Harishchandra Ramane, Karnataka University, Dharwad.

 

Functional Analysis

Convener: Dr. M. Thamban Nair, IIT-M

  • Prof. C.R. Jayanarayanan - IIT Palakkad
  • Prof. E.K. Narayanan - IISc Bengaluru 
  • Prof. Sameer Chavan - IIT Kanpur
  • Prof. Santanu Dey - IIT Bombay
  • Prof. D. Sukumar - IIT Hyderabad
  • Prof.  Kiran Kumar V. B. - CUSAT

Complex Analysis

Convener: Prof. Sushil Gorai, IISER Kolkata.

  • Diganta Borah, IISER Pune
  • Sabyasachi Mukherjee, TIFR Mumbai
  • Pranav Haridas, Kerala School of Mathematics
  • D. K. Thomas, Swansea University, UK
  • Vikramjeet Singh Chandel, HRI Allahabad
  • Jiri Lebl, Oklahoma State University, USA

Complex Analysis
Prof. Sushil Gorai
IISER Kolkata
Differential Equations Prof. Bal Kaushik
IIT Kanpur
Discrete Mathematics Prof. Aparna Lakshmanan
CUSAT
Functional Analysis Prof. M. T. Nair
IIT Madras

Number Theory
Prof. R. Thangadurai
HCRI, Allahabad

Register Online

Note: There is no registration fee for participants.

Number Theory

Convener: Dr. Thangadurai, HCRI, Allahabad

Faculty Coordinators: Dr. J. Mahalakshmi and Dr. Santhakumar

Time Speaker Title Link
10.00 a.m – 10.50 a.m Prof.G. Kasi Viswanadham,
IISER,  Berhampur.
On Desingularized Multiple Zeta Functions Click Here to Join
11.00 a.m – 11.50 a.m Prof. Mohan Chintamani,
Central University of Hyderabad, Hyderabad.
On Weighted Zero-Sum Constants
12.00 p.m – 12.50 p.m Prof. Aprameyo Pal,
Harish-Chandra Research Institute (HRI), Prayagraj.
p-adic Galois-representations and multivariable $(varphi, Gamma)$-modules
02.00 p.m – 02.50 p.m Prof. K. Senthil Kumar,
NISER, Bhubaneshwar
Linear dependence of quasi-periods over the rationals.
03.00 p.m – 03.50 p.m Prof. Akshaa Vatwani,
IIT-Gandhi Nagar  
Limitations to equidistribution in arithmetic progressions

Discrete Mathematics

Convener: Dr. Aparna Lakshmanan, CUSAT

Faculty Coordinators: Dr. J. Geetha and Dr. L. Govindarao

Time Speaker Title Link
10.00 a.m – 10.50 a.m Prof. Subrahmanyam Kalyanasundaram,
IIT Hyderabad.
Conflict-Free Coloring in Open Neighborhoods Click Here to Join
11.00 a.m – 11.50 a.m Prof. Sukanta Pati,
IIT Guwahati.
Laplacian Matrices and Algebraic Connectivity
12.00 p.m – 12.50 p.m Prof. Vinayak Joshi
Savitribai Phule Pune University, Pune.    
Zero-divisor graphs of ordered sets and its applications to graphs associated with  algebraic structures
02.00 p.m – 02.50 p.m Prof. Harishchandra Ramane,
Karnataka University, Dharwad.
Complementary Equienergetic Graphs
03.00 p.m – 03.50 p.m Prof. Csilla Bujtás,
University of Pannonia, Hungary.
3/5- and 1/2-Conjectures on the Domination Game

Functional Analysis

Convener: Dr. M. Thamban Nair, IIT-M

Faculty Coordinators: Dr. V. Pragadeeswar and Dr. Poonguzali G

Time Speaker Title Link
10.00 a.m – 10.50 a.m Prof. C.R. Jayanarayanan
IIT Palakkad
On Best Approximations in Banach Spaces Click Here to Join
11.00 a.m – 11.50 a.m Prof. E.K. Narayanan
IISc Bengaluru 
Heckman-Opdam Hypergeometric Functions
12.00 p.m – 12.50 p.m Prof. Sameer Chavan
IIT Kanpur
The Cauchy Dual Subnormality Problem
via De Branges-Rovnyak Spaces
02.00 p.m – 02.50 p.m Prof. Santanu Dey
IIT Bombay
The Order-n Minors of Certain (n+kn Matrices
03.00 p.m – 03.50 p.m Prof. D. Sukumar
IIT Hyderabad
An Expedition From Spectrum To Condition Spectrum
4.00 p.m- 4.45 p.m Prof. V.B. Kiran Kumar
CUSAT
Discrete Borg-Type Theorems

Complex Analysis

Convener: Prof. Sushil Gorai, IISER Kolkata

Faculty Coordinators: Dr. Biswambhar Rakshit and Dr. Ramesh Babu

Time Chair Speaker Title Link
10:00 am – 10:50 am Prof. S. Ponnusamy Prof. Diganta Borah, IISER Pune Title: Narasimhan-Simha type metrics on strongly pseudoconvex domains in Cn
Abstract: For a bounded domain D in Cn, denote by KD the Bergman kernel on the diagonal and consider the reproducing kernel Hilbert space of holomorphic functions on D that are square integrable with respect to the weight KD−d, where d is a nonnegative integer. The corresponding weighted kernel KD,d transforms appropriately under biholomorphisms and hence produces an invariant Khler metric on D. This class of metrics is known as the Narasimhan-Simha type metrics on D, and in this talk, we will attempt to study them in much the same way as the Bergman metric has been with a view towards identifying properties that are common to this family. When D is strongly pseudoconvex, we will use the scaling principle to obtain the boundary asymptotics of these metrics and several invariants associated with them. This is joint work with Kaushal Verma.


Abstract

Click Here to Join
11:10 am – 12:00 Noon Prof. Gautam Bharali Prof. Sabyasachi Mukherjee Title: Conformal welding and combination theorems in holomorphic dynamics
Abstract: A welding homeomorphism is a homeomorphism of the circle that captures how the interior and the exterior of a Jordan curve fit together conformally. Characterizing welding homeomorphisms is an important open question in geometric function theory. After reviewing some classical results in this direction, we will discuss recent developments motivated by combination problems in holomorphic dynamics.


Abstract

12:20 pm – 1:10 pm Prof. Sabyasachi Mukherjee Prof. Pranav Haridas Title: Proper holomorphic self-maps of certain quasi-balanced domains in C3
Abstract: One of the first results in the study of proper holomorphic self maps is Alexander’s theorem which states that such maps of the unit ball in Cn are necessarily automorphisms of the unit ball. A generalization of Alexander’s theorem to strictly pseudoconvex domains was later proved by Pinchuk. It has been a folklore conjecture that Alexander’s theorem is true for pseudoconvex domains with smooth boundaries in Cn. In this talk, we will explore the journey of this conjecture in various cases over the ages and then answer the conjecture in the special case of certain smoothly bounded pseudoconvex quasi-balanced domains of finite type in C3.


Abstract

1:10 pm – 4:30 pm: Break
4:30 pm – 5:20 pm Prof. S. Ponnusamy Prof. D. K. Thomas Title: Successive coefficients of univalent functions - Some open problems
Abstract: An up-to-date summary of most of the important results concerning bounds for successive coefficients of univalent functions and subclasses is given, together with some significant open problems.


Abstract

5:40 pm – 6:30 pm Prof. Kaushal Verma Prof. Vikramjeet Singh Chandel Title: On a spectral version of Cartans theorem
Abstract: H.Cartan in 1931 proved the following theorem: every holomorphic self-map of a bounded domain (in the complex Euclidean space) that has a fixed point so that the derivative of the holomorphic map at the fixed point is identity has to be the identity map on the given bounded domain. Later, in 1970, S.Kobayashi generalized the above theorem to its strongest form; namely, one could replace bounded domains by Kobayashi hyperbolic complex manifolds in the above theorem. To illustrate to a reader unfamiliar with this topic, any planar domain that misses at least two distinct points in the complex plane is Kobayashi hyperbolic.
For a given domain Ω in the complex plane, we consider the matricial domains Sn(Ω) consisting of those n×n complex matrices whose spectrum is contained in Ω. The domains Sn(Ω) are not Kobayashi hyperbolic for any Ω and any n≥ 2. In this talk, we present results about holomorphic self-maps of Sn(Ω) in the spirit of Cartan’s Theorem. Our first result is: let Ψ be a holomorphic self-map of Sn(Ω) such that Ψ(A) = A and the derivative of Ψ at A is identity for some A ∈ Sn(Ω), then if A is either diagonalizable or non-derogatory then for most domains Ω, Ψ is spectrum-preserving on Sn(Ω). If time permits, we shall present another result; namely, for an arbitrary matrix A, Ψ is spectrum-preserving on a certain analytic subset of Sn(Ω).


Abstract

7:00 pm – 7:50 pm Prof. Sivaguru Ravisankar Prof. Jiri Lebl Title: Segre-degenerate points form a semi-analytic set
Abstract: The Segre variety is a useful tool for studying the geometry of real-analytic objects in complex space. The tool was originally developed for CR submanifolds, but it can be useful for singular objects as well, although there are caveats. Most importantly, the Segre variety need not be of constant dimension as one moves from point to point. However, one can semi-analytically stratify a real-analytic subvariety by the dimension of the Segre variety. In particular, the Segre-degenerate points form a semi-analytic set (not necessarily a subvariety).


Abstract

Event Details
Date: 
2021-08-04 09:00 to 17:00
ORGANIZED BY:
Department: 
Mathematics
School: 
School of Engineering
Campus: 
Coimbatore
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