International Conference in honour of Prof. V Kumar Murty

Venue: KSOM, Kozhikode

17 - 21 August, 2016

The Institute organized an International Number Theory Conference on Arithmetic Geometry and L-functions during August 17-21, 2016 to honour Professor V. Kumar Murty who is turning 60 this year(2016). Professor Murty is a leading researcher in Mathematics and  mainly working in the field of Number Theory. He has motivated young minds and helped many young researchers. The organisers are  M.Manickam (KSOM, Kozhikode), B.Ramakrishnan (HRI, Allahabad) and Sanoli Gun (IMSc, Chennai).

The event was supported by KSOM, Kozhikode; HRI, Allahabad and IMSc, Chennai.


List of Speakers

Sl. No. Name
1 S. D. Adhikari , HRI Allahabad                   
2 V. Balaji, CMI Chennai                        
3 R. Balasubramanian, IMSc Chennai    
4 S. Boecherer, University of Mannheim , Germany                  
5 S. Das, IISc Bangalore
6 S. David, University Pierre and Marie Curie , Paris, France                                       
7 A. Dixit, University of Toronto,Canada
8 C. Khare , UCLA Mathematics Department, Los Angeles, CA                         
9 A. Mukhopadhyay, IMSc Chennai
10 M. R. Murty, Queen's University,Canada                  
11 D. S. Nagaraj, IMSc Chennai             
12 M. S. Narashimman, TIFR, Bangalore
13 T. Oda, Tokyo                                     
14 R. Raghunathan, IIT Bombay
15 A. Raghuram, IISER Pune                   
16 C. S. Rajan , TIFR Mumbai
17 B. Sahu, NISER Bhubaneswar
18 A. Sankaranarayanan, TIFR Mumbai
19 N. Saradha, TIFR Mumbai
20 P. Sastry, CMI Chennai
21 J. Sengupta, TIFR Mumbai
22 K. Sinha, IISER Pune
23 V. Srinivas, TIFR Mumbai                 
24 R. Sujatha, University of British Columbia, Canada.                      
25 R. Tandon , University of Hyderabad
26 R. Thangadurai , HRI Allahabad                 
27 A. Vatwani, Queen's University, Canada


List of Participants

Sl. No. Name Institute
1 Abhash Kumar Jha NISER, Bhubaneswar
2 Abhishek T Bharadwaj CMI Chennai
3 Akhilesh P IMSc, Chennai
4 Anup Kumar Singh Harish Chandra Research Institute Allahabad
5 Arpita Kaur Queens University, Canada
6 Arvind kumar HRI, Allahabad
7 Balesh Kumar HRI, Allahabad
8 Biplab Paul IMSc, Chennai
9 Guhan Venkat University College London.
10 Gunja Sachdeva IISER Pune
11 Jaban Meher NISER, Bhubaneswar
12 Jyothsnaa S IMSc, Chennai
13 Makarand Sarnobat IISER Pune
14 Mallesham K HRI, Allahabad
15 Manish Kumar Pandey HRI, Allahabad
16 Moni Kumari NISER, Bhubaneswar
17 P Rath CMI Chennai
18 Pranendu Darbar IMSc, Chennai
19 Praveen I Amritha Viswa Vidyapeetham, Amritha University
20 Rajeev K Amritha University
21 Sagar Shrivastava National Institute of Science Education and Research, Khorda
22 Sameena Kalathodi NIT Calicut
23 Siddhi Pathak Queens University, Canada
24 Srivatsa V Kerala School of Mathematics, Kozhikode
25 Tapas Chatterjee  IIT Ropar
26 Vindhya V Calicut University

Time Schedule

09:00 AM : Registration
10:00 AM : Inauguration
10:30 AM - 11:10 AM V Srinivas Chair:
V Kumar Murty
11:15 AM - 11:55 AM M Ram Murty
12:00 PM-12:40 PM N Saradha
02:30PM-03-20PM  TBA Chair:
V Srinivas
03:25PM-04-05PM R Thangadurai
04-30PM-05:00PM Anup Dixit
09:30AM-10:20AM M S Narasimhan Chair:
M Ram Murty
10:25AM- 11:05 AM S Boecherer
11:30AM-12:20PM A Sankaranarayanan
12:25PM-01:05PM C S Rajan
02:30PM-03-20PM A Raghuram Chair:
S Boecherer
03:25PM-04-05PM J Sengupta
04-30PM-05:00PM Soumya Das
09:30AM-10:10AM R Balasubrahmanian Chair:
C S Rajan

10:15AM- 10:55 AM S David
11:30AM-12:10PM S D Adhikari
12:15PM-12:55PM R. Tandon
02:30PM-03-10PM Sujatha Chair:
R Balasubrahmanian

03:15PM-03:55PM Ravi Raghunathan
04-30PM-05:00PM B. Sahu
09:30AM-10:10AM D S Nagaraj Chair:
S David

10:15AM- 10:55 AM Anirban Mukhopadhyay
11:30AM-12:10PM Pramathanath Sastry
12:15PM-12:55PM V Balaji
02:30PM-03-10PM Kaneenika Sinha Chair:
S D Adhikari

03:15PM-03:45PM A Vatwani
4:00 PM Felicitation  
09:30AM-10:10AM M Manickam  
10:20AM-11:00AM V Kumar Murty  

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International Conference on

Venue: KSOM, Kozhikode

13 & 14 February, 2015

Time Schedule

Date 9:30-10:10 10:20-11:00 11:00-11:30 11:30-12:10 12:20-13:00 13:00-14:10 14:10-14:50 15:00-15:40 15:40-16:00 16:00-16:40 16:50-17:30
13-Feb-15 J Sengupta R Raghunathan Tea Break S Boecherer B Heim Lunch Break B Sahu K Senthilkumar Tea Break B Saha V Srivatsa
14-Feb-15 M Manickam U.K Anandavardhanan S Das Saurabh Singh J Mehar Rahothaman    


J Sengupta, TIFR Bombay M Manickam, KSOM Kozhikode
Topic: Determination of GL3 Hecke Eigen forms with respect to central values of L-function Topic: On Taylor coefficients of Jacobi forms of higher degree.
R Raghunathan, IIT Bombay U. K. Anandavardhanan, IIT Bombay
Topic: Convolution of Dirichlet series of low degree Topic: Symplectic local root numbers for GL(2)
S Boecherer, Mannheim S Das, IISc Bangalore
Topic: Quasi modular forms are p-adic Topic: Jacobi forms and Differential operators
B Heim, GVTech, Oman Saurabh Singh, TIFR Bombay
Topic: Jacobi forms, Lifts and Symmetries Topic: On Riesz mean of n/φ(n)
B Sahu, NISER, Bhubaneswar J Mehar, IISc Bangalore
Topic: Construction of Jacobi forms. Topic: On Fourier coefficients of weakly holomorphic quasi modular forms.
K Senthilkumar, IMSc, Chennai R Rahothaman, Sona Engineering College, Salem
Topic: Some remarks on Scharuel's Conjecture Topic: On congruences for modular forms
B Saha, IMSc, Chennai
Topic: On the zeros of weakly holomorphic forms
V Srivatsa, KSOM Kozhikode
Topic: Action of Hecke operators on Poincare Series.


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ICTS Program on
(Sponsord by International Centre for Theoretical Sciences (ICTS), Mumbai)
(International Conference)

Venue: KSOM, Kozhikode

17-26 February, 2014

ORGANIZERS : Rajendra Gurjar, A.J. Parameswaran

Many striking results about the group of automorphisms of affine varieties have been proved in recent years. Similarly, several exciting open problems have been raised which are very good topics for young researchers.

The aim of this program is to bring together several experts in different aspects of the area of automorphism groups of affine varieties, viz. Locally Nilpotent Derivations, Rings of Invariants of finite and continuous Reductive Group Actions on Cn, Theory of Non-complete Algebraic Varieties, Applications of Brauer Groups, etc. We plan to have about five expository lectures each on these topics.

The plan is to bring together senior mathematicians and students from India and around the world. The expository talks will inform the participants about different ways of attacking problems about automorphism groups of affine varieties, in particular affine space. Similarly, several open problems will be mentioned. There will be four expository talks every day for about five days. In the second part of the program there will be a small research level discussion meeting to bring the participants up-to-date with current research in this area.

Expository talks:


17-02-2014 to 21-02-2014       10:00  to  11:00

Non-Complete Algebraic Varieties 
By R.V. Gurjar and M. Miyanishi

We will give a survey of the basic theory of smooth non-complete algebraic varieties, particularly surfaces, and also mention several important applications of this theory.


17-02-2014 to 21-02-2014       11:30  to  12:30

Locally Nilpotent Derivations
By L. Makar-Limanov and Kayo Masuda

We will give a survey of the basic theory of locally nilpotent derivations on affine domains, and also mention several important applications of this theory.


22, 24, 25 and 26 February, 2014      10:00  to  11:00

Automorphisms and Coordinates of Polynomial and Free Associative Algebras
By Jie-Tai Yu and V. Drensky

In our talks, we shall discuss  the Jacobian conjecture, test elements, concellation conjecture, coordinate classification --Vasselin Drensky
Embedding conjecture, Tame-wild automorphisms including Nagata/Anick Conjecture and related Lifting problem/Stable tameness problems- Jietai Yu.


22, 24, 25 February, 2014        11.30 to 12.30

$Ind$-schemes, quantization, Jacobian and Kontsevich Conjectures. 
By A. Kanel-Belov

The famous Jacobian conjecture and other polynomial authomorphism questions related to quantization  questions. For example, equivalence of Dixmier and Jacobian conjectures was established using quantization ideas (by Tshusimoto and Belov
\& Kontsevich). 
This result raised following 
{\bf Conjecture.( Belov \& Kontsevich)} Does the authomorphism group of Weil algebra $W_n$ naturally isomorphic to
 polynomial  symplectomorphism group of ${\bf C}^{2n}$?

This conjecture is related to $Ind$-scheme automorphism questions using idea of E.Rips. 
Recently $Ind$-scheme automorphism group of polynomial automorphisms was established by A. Belov-Kanel, Jie-Tai Yu . Also was established relations between  Belov \& Kontsevich conjecture and lifting problems (i.e. possibility to lift
authomorphism of polynomial ring to automorphism of free associative algebra). 
Recently by A. Belov-Kanel, Jie-Tai Yu was established impossibility to lift as $z$-authomorphism any $z$-wild

authomorphism of $K[x,y,z]$. 

Conference Talks:


18-02-2014              2:30 to  3:30

Parameswaran. A. J.
Title: On the geometry of regular maps from a pure quasi-projective surface to an affine curve

Abstract. We explore here some consequences of the triviality of the monodromy group, for a class of surfaces of which the mixed  Hodge structure is pure, we extend results of Miyanishi and Sugie, Dimca, Zaidenberg  and Kaliman.

Here we prove the following assertions for a map. Let $X$ be a smooth surface with $H^2(X)$ and  $H^3(X)$ have  pure Hodge structure and $f : X\to C$,  is a  morphism with $C$ affine, the we prove:

(i) Monodromy of $f$ is  trivial then Monodromy of $\bar f$ is trivial and $f$ is simple.
(ii) The monodromy of $f$ is detremined by the monodromy of a simple loop at infinity.
(iii) The number of reducible fibres of $f$ is bounded above by  $\delta -1 + $b_2(X)$
(iv) If the monodromy group is trivial and all fibres are reduced and irreducible then
$f$ is a locally trivial fibration
(v)  If the monodromy group is trivial and all fibres are  irreducible and at least one fibre is non reduced, then the general fible of $f$ is $\bC$ or $\bC^*$ or an elliptic curve where $\bC$   denote the complex plane. 


19-02-2014                2:30 to  3:30

Lenney Makar-Limanov
Title:   An estimate of the degree of the field extension for a Jacobian pair.

Abstract:  Yitang Zhang who became famous recently for the brake-through on the twin prime conjecture wrote his PhD thesis in 1991 on the Jacobian Conjecture. In his thesis he proved that for a Jacobian pair $f, \ g$ the degree $[\C(x, y) : \C(f, g)]$ of the field extension does not exceed the minimum
of $\deg(f), \ \deg(g)$. In my talk I'll show how to get a somewhat better estimate.


20-02-2014                   2:30 to  3:30

S.M. Bhatwadekar
Title: Projective modules over the kernel of a locally nilpotent derivation on an affine space.

Abstract: Let $k$ be an algebraically closed field of characteristic zero, $D$ be a locally nilpotent derivation on the polynomial algebra  $k[X_1, \cdots , X_n]$ and $A$ be the kernel of $D$. In this set up a  question of Miyanishi asks whether finitely generated projective modules  over $A$ are free. Note that for $n = 3$ , by a result of Miyanishi,  the kernel $A$ is a polynomial algebra in two variables over $k$ and hence an  answer to the question is affirmative.
In my talk I will address this question for $n = 4$.


20-02-2014                   4.00 to  5.00

Fang Li
Title: Representation rings of Nakayama truncated algebras.

Abstract: Nakayama truncated algebras can be viewed as a finite dimensional Hopf algebra,
by using covering quiver and weight sequence. With this view-point, we investigate a class of Nakayama truncated algebras
and obtain
the precise characterization of their Green rings. More consideration is shown a little, too.


21-02-2014                   2:30 to  3:30

Neena Gupta
Title: On the affine threefold $x^my= F(x, z, t)$.

Abstract:  Let $k$ be any field.
In this talk we shall consider rings of the form $A=k[X,Y,Z,T]/(X^mY-F(X,Z,T))$, $m > 1$, and present
several equivalent criteria for such a ring $A$ to satisfy:
(i) $A[W] \cong k[X_1, X_2, X_3, X_4]$.
(ii) $A \cong k[X_1, X_2, X_3]$.
For instance, a necessary and sufficient condition for the above ring $A$   to be a polynomial ring is that $F(0, Z, T)$ is a variable in $k[Z, T]$.
Another equivalent condition is that $A$ is a UFD, $\K_1(A)=k^*$ and a certain invariant called ``Derksen invariant'' is trivial.  
It follows from these criteria that when ch $k>0$, there exists an infinite family of non-isomorphic rings which satisfy (i) but violates (ii); in particular, {\it $\A^3_k$ is not cancellative when ch $k>0$}.
Note that the rings of the above type $A$ include Asanuma's candidates for a counter-example
to the Linearisation/Cancellation Conjecture 
in positive characteristic as well as the Russell-Koras' threefold.


24-02-2014                          2:30 to  3:30

Alok Maharana
Title: Complements of multi-sections on Hirzebruch surfaces. 

Abstract: Motivated from a theorem of Danilov-Gizatullin that isomorphism class of the complement
of an ample section on a Hirzebruch surface depends only on the self-intersection of the section,
we explore the isomorphism classes of the complements of multi-sections on Hirzebruch surfaces.


25-02-2014           2:30 to  3:30

Krishanu Dan
Title: Null Correlation Bundle on Projective Three Space.

Abstract: Null Correlation bundle is a rank 2 stable vector bundle on P^3 which, when restricted to a hyperplane is not stable, only semi-stable. It is unique (up to translation by automorphisms of P^3 and tensoring by line bundles) with respect to this property. We will give an alternate construction of this bundle. It is a joint work with Prof. D. S. Nagaraj.

Workshop and Conference in Honour of KALYAN B SINHA - 70th Birthday

Operator & Spectral theory, Operator algebras, Non-commutative Geometry & Probability

(Partially supported by The Institute of Mathematical Sciences, Chennai)
(International Conference)

Venue: KSOM, Kozhikode

07-14 February, 2014

Featured Topics

Spectral Theory of Operators, Non commutative Probability Theory, Operator Systems and Choquet Theory, Operator Algebras.,
Geometric and Singular Analysis.

International Advisory Committee Invited Speakers

R Balasubramanian - IMSc Chennai
Furutani Kenro - Tokyo University of Science, Japan
Gadadhar Misra - IISc Bangalore
Michael Demuth - Tech Univ. of Clausthal, Germany
Rajeeva Karandikar - CMI Chennai
Rahul Roy - ISI Delhi
V. S. Sunder - IMSc Chennai


L.Accardi (Rome, Italy)
Stephen Barreto (PCCE, Goa)
Wolfram Bauer (Gottingen, Germany)
Belton, Alexander (Lancaster University, UK)
Rajarama Bhat (ISI, Bangalore)
R.Bhatia(ISI, Delhi)
Tirthanakar Bhattacharyya (IISc, Bangalore)
Partha Chakraborty (IMSc., Chennai)
M.Demuth (University of Clausthal, Germany)
M. Dritschel (University of Newcastle-upon-Tyne, UK)
F.Fagnola (Milan, Italy)
D.Goswami (ISI, Kolkata)
Jaeseong Heo (Hanyang University, Seoul, South Korea)
Un Cig Ji (Chungbuk University, Korea)
Kiran Kumar (KSOM, Kozhikode)
Hyunho Lee (University of Ulsan, Ulsan, Korea)
Martin Lindsay (University of Lancaster, UK)
Joseph Mathew (KSOM, Kozhikode)
A.Mohapatra (University of Goa)
Mahendra Nadkarni (Center for Excellence for Basic Sciences, Bombay University)
K.R.Parthasarathy (ISI, Delhi)
S Pramod (Hindustan Institute of Technology, Coimbatore)
B.S.Rajput (Tennessee at Knoxville, US)
Rahul Roy (ISI Delhi)
Yuri Safarov (Kings College, London)
R. Srinivasan (CMI, Chennai)
V.S. Sunder (IMSC Chennai)
Joachim Toft (Institutionen för datavetenskap, Sweden)
Stephen Wills (School of Mathematical Sciences, UCC, Cork, Ireland)
Organising Committee

M. Krishna -IMSc, Chennai
M. Manickam - KSOM, Kozhikode
M N N. Namboodiri - CUSAT, Kochi
A K.Vijayarajan - KSOM, Kozhikode


Programme Schedule

Analytic and Algebraic Geometry related to bundles

International Conference


Venue: KSOM, Kozhikode

25 - 29 March, 2013



Parameswaran A J (TIFR)
Indranil Biswas (TIFR)

Local Organiser

 Kerala School of Mathematics


Supported by
 National Centre for Mathematics

List of speakers & Participants:

1. Tomas Gomez, ICMAT, Madrid 
2. Marina Logares, ICMAT, Madrid 
3. J. Hurtubise, McGill University 
4. F. Schaffhauser, University of Los Andes, Bogota 
5. ALessia Mandini, IST, Lisbon 
6. A. Dhillon, University of Western Ontario 
7. Matthias Stemmler, Marburg University 
8. D. S. Nagaraj, IMSc 
9. V. Balaji, CMI 
10. S. Mehrotra, CMI 
11. Arijit Dey, IIT Madras 
12. Venkata Balaji, IIT Madras 
13. N. Raghavendra, HRI 
14. S. Amrutiya, IMSc 
15. S. Kannan, CMI 
16. Jonathan Sanchez, Universidad Complutense de Madrid 
17. K. Verma, IISc 
18. Archana Moyre, CMI 
19. Chanchal Kumar, IISER, Mohali 
20. F. Campana, Institut Elie Cartan, Nancy 
21. M. Verbitsky, Laboratory of Algebraic Geometry, Moscow 
22. V. Mathai, Adelaide University 
23. Francois Machu, University of Western Ontario 


Time Table


11.00 -11.30

11.30 - 12.30

12.30 -2.30

02.30 - 03.30

3.30 - 4.00

04.00 - 05.00



Tea Break

F. Campana


Lunch Break

Stemmler, M.


Tea Break

J. Sanchez


 Tomas Gomez

Arijit Dey

P. Sankaran


D. S. Nagaraj

S. Amrutiya

Chanchal Kumar


S. Kannan

V. Balaji

Y. Pandey







Vector Bundles

International Conference


Venue: KSOM, Kozhikode

02 - 06 April, 2012


Programme Committee

Parameswaran A J (TIFR)
Indranil Biswas (TIFR)

Local Organizing Committee 

 M. Manickam ( KSOM)
Joseph Mathew (KSOM)

A. K. Vijayarajan (KSOM)   

List of speakers & Participants:

N. Mohan Kumar               Washinton Univ. St. Luis, USA
S. M. Bhatwadekar           Bhaskaracharya Prathishtan, Pune
V. Srinivas                        TIFR Mumbai
Raja  Sreedharan            TIFR Mumbai,
P. Purnaprajna                 Kensas University, USA
G. Ravindra,                     Washinton Univ. St. Luis
D. S. Nagaraj,                  IMSc. Chennai
Ravi Rao                          TIFR, Mumbai
S Ramanan                     CMI, Chennai
Szpiro                              CUNY, USA
David Wright                    Washinton Univ. St. Luis
Marina Logares                ICMAT, Madrid, Spain
Tomas Gomez                 ICMAT, Madrid, Spain
M. P. Murthy                     Univ. Chicago,  USA
J. Zhang,                          Uni. Albani,  USA
Beheshti,                          Washinton Univ. St. Luis, USA
Christopher Peterson        Colostate Univ.,  USA
R. R.  Simha                     University of  Mumbai
R. C. Cowsik                      Mumbai Univ.
Norbert Hoffmann               Freie  Universitat  Berlin, Germany
S. Subramanian                 TIFR, Mumbai
CS Rajan                           TIFR Mumbai
B. Sury                              ISI  Bangalore
Amarthya Kumar Dutta       ISI Kolkotha.
John Loftin                      Rutgers University, USA


The Conference was sponsored by National Board for Higher Mathematics (NBHM)


Mathematics in Ancient Times

International Conference


Venue: KSOM, Kozhikode

29 August - 1 September 2010


This was a satellite conference of ICM 2010 and featured talks on the mathematics in various ancient cultures, including many on Indian mathematics covering various periods from the Vedic times to the Kerala mathematics. A half-day tour also organised to places of interest around Kozhikode (Calicut) related to the history of Kerala mathematics.

Organizing Committee

Kim Plofker(Chair),
S.G. Dani (Convener), P. P. Divakaran, 
Clemency Montelle,
A. J. Parameswaran (Director, KSOM)
Local Organizing Committee 

A. J. Parameswaran (Chair, Director, KSOM), 
K. V. Jayakumar    (Executive Director, CWRDM),
T. Thrivikraman (Formerly of CochinUniversity), 
  P. T. Ramachandran (University  of  Calicut), 
Joseph Mathew (KSOM), A. K. Vijayarajan (KSOM)   

List of speakers:

1. Mohammad Bagheri, University of Tehran, Iran

2. Bhagyashree Bavare, CBS, Mumbai, India
3. Pierre-Sylvain Filliozat, France
4. Jens Hoyrup, Roskilde University Centre, Roskilde, Denmark
5. Norbert Schappacher, Uni. Strassburg, France
6. Takanori Kusuba, Osaka University of Economics, Osaka, Japan
7. V. Madhukar Mallayya, Mar Ivanios College, Trivandrum, India
8. Clemency Montelle, Uni. Canterbury, New Zealand
9. David Mumford, Brown University, USA
10. Francois Patte, University of Paris V, Paris, France
11. Kim Plofker, Union College, NY, USA
12. K. Ramasubramanian, Indian Institute of Technology, Mumbai, India
13. Alexei Volkov, University of Montreal, Montreal, Canada
14. Michio Yano, Kyoto Sangyo University,Kyoto, Japan

Special presentation by Bill Casselman, with photographs of ancient artifacts.

Click here for Abstract                    


@2010 Kerala School of Mathematics