List of Colloquia hosted in the recent past by the Dept. of Mathematics, RKMVERI, Belur Math Campus.


Sl. No. Speaker Institute Date Details
1. Prof. Sourav Sen Visiting Fellow, Tata Institute, Mumbai 11 Jan, 2023 Title: Tameness of degree functions
Click here for the abstract


Sl. No. Speaker Institute Date Details
1. Prof. Thangadurai HRI Prayagraj 17 Oct, 2022 Title: Trace of powers of algebraic numbers

We shall discuss a sufficient condition for classifying algebraic integers. One such condition is dealing with the trace of powers of algebraic numbers. We start from scratch and introduce the problem. We discuss some elementary results and at the end, we state our results.

2. Prof. S.M. Srivastava 28 Sep, 2022 Title: A Result on Zeroes of Holomorphic Functions

This talk is aimed at M.Sc. students in mathematics. However, I hope all mathematicians will find the result interesting and surprising. We shall require only preliminary results from Complex Analysis and General Topology which I am assuming that all of you know. The result has a beautiful and surprising connection with Set theory. I will present the requisite background from Set theory. The problem to be discussed here was asked by Wetzel in Ann Arbor Problem Book and the famous mathematician Paul Erdős gave the surprising and beautiful answer.

3. Prof. Anirban Mukhopadyay IMSC Chennai 22 Aug, 2022 Title: Poissonian pair correlation

For a sequence of reals in [0,1], pair correlation statistics studies the distribution of their gaps. Most arithmetically interesting sequence is expected to have a gap distribution similar to a random sequence. Such results are known in many cases for almost all sequences, although proving for most individual sequences remains challenging. In this lecture, we will survey some of the results including a joint work with Tanmoy Bera and Mithun Das where we look
at these questions in higher dimensions.

4. Prof. Rebeya Basu IISER Pune 7 Jun, 2022 Title: Linear algebra and K-theory

In this talk we will discuss the interplay between linear algebra and classical K-theory. The talk will be accessible to graduate students. Basic knowledge in linear algebra, rings and module theory will be enough.

5. Prof. V. Muruganandam IIT Pallkad 11 May, 2022 Title: The Legacy of Harish-Chandra : A bird’s eye view
6. Prof. V. Muruganandam IIT Pallkad 5 May, 2022 Title: Thematic lectures on exponential map in analysis and geometry
7. Prof. Oliver Ramare Aix-Marseille University, France 9 Apr, 2022 Title: Peg Solitaire

Peg Solitaire is an old board game that has existed in several countries under different names. It’s mathematical understanding at the beginning of the 18th century by a report of Leibniz, and continued later, a most notable step having been achieved by a group led by Conway in the sixties. We will present a unified and gentle introduction to the subject ; on our journey, we will encounter vector spaces and modules in dimension 33 and 37, the finite field F_2, some colourings, the integer points in a polyhedron and the simplex algorithm.


Sl. No. Speaker Institute Date Details
1. Prof. Anish Ghosh TIFR, Mumbai 11 Nov, 2021 Title: Is the square root of 2 very different from the cube root of 2?

It is a remarkable fact that one can understand properties of numbers using “chaotic” dynamical systems. I will illustrate this principle with several examples and in doing so, try and answer the question in the title.

2. Prof. Malabika Pramanik University of British Columbia, Vancouver 8 Oct, 2021 Title: So, you think you can solve x+y=z
Click here for the abstract
3. Prof. TSSRK Rao CARAMS, Manipal Academy of Higher Education 24 Sep, 2021 Title: Birkhoff-James orthogonality in spaces of operators

Birkhoff-James orthogonality is one very successful extension of the orthogonality notion in a Hilbert space. A challenging problem is to understand this in concrete Banach spaces. Motivated by the seminal work of R. Bhatia and P. Semrl, that interprets this orthogonality for individual operators on Hilbert spaces, we derive results in the context of Banach spaces, on operators that are Birkhoff-James orthogonal to a class of operators. This is linked to a hard minimax problem in convex optimization and is partly solved here, using techniques from Geometry of Banach spaces.

4. Sudhir Pujahari University of Warsaw 27 Aug, 2021 Title: Distribution of moments of trace of Frobenius in arithmetic progressions and holomorphic projection
Click here for the abstract
5. Prof. Liangyi Zao University of New South Wales in Sydney, Australia 20 Aug, 2021 Title: Moments of central values of quartic Dirichlet L-functions

I will present an asymptotic formula for the moments of the central values of quartic Dirichlet L-functions. A corollary of the result is a quantitative non-vanishing theorem for these L-values. One of the key inputs is a large sieve type inequality for quartic Dirichlet characters. This is joint work with P. Gao.

6. Monika Zheng PhD Scholar, University of Memphis 13 Aug, 2021 Title: Numerical index of a Banach space
Click here for the abstract
7. Prof. B. Poggi University of Minnesota 16 Jul, 2021 Title: The landscape function and the exponential decay of solutions to Schrödinger operators with electric or magnetic potentials

In the first half of the last decade, Marcel Filoche and Svitlana Mayboroda observed that a certain solution to an elliptic PDE problem (the landscape function) can be effectively used to numerically predict the localization of eigenfunctions to Schrödinger operators with electric potentials exhibiting randomness. This localization phenomenon through disorder is known as Anderson localization, for which Phillip Anderson won the Nobel prize in physics in 1977. In this talk, we will introduce recent mathematical results showing the exponential decay given by the landscape function, for fundamental solutions, Lax-Milgram solutions, and eigenfunctions for Schrödinger operators; in particular, we will see that the landscape function generalizes previous tools used to study the exponential decay of solutions to Schrödinger operators when the potentials are regular.

8. Prof. R.B. Bapat ISI, Delhi 15 Jul, 2021 Title: Combinatorial applications of some topological theorems

The Brouwer’s Fixed Point Theorem and the Borsuk-Ulam Theorem are important theorems in Topology with many applications. Brouwer’s Fixed Point Theorem asserts that a continuous function from a compact convex set to itself has a fixed point. We will describe equivalent versions of the theorem including Sperner’s lemma which is purely combinatorial. The Borsuk-Ulam Theorem states that any continuous function from the n-dimensional sphere to the n-dimensional euclidean space must map two antipodal points to the same point. Lovasz used the theorem to settle a long-standing conjecture about the chromatic number of a certain graph, called the Kneser graph. We will present this proof after introducing the necessary background.

9. Prof. Jörn Steuding University of Würzburg, Germany 9 Jul, 2021 Title: Value distribution of L-functions

The distribution of values of L-functions plays a central role in analytic number theory. One aspect is a remarkable approximation property, called universality, first discovered by Voronin in the 1970s: appropriate shifts of the Riemann zeta-function approximate any analytic non-vanishing target function. This result has been generalized in various ways. In this talk we shall discuss applications of “joint universality” (simultaneous approximation) to the distributions of zeros.

10. Prof. Peng Gao Beihang University, Beijing, China 2 Jul, 2021 Title: Bounds for moments of central values of families of Dirichlet L-functions

Moments of central values of families of L-functions are important subjects in analytic number theory. In this talk, I will explain two powerful principles in the study of sharp bounds for these moments: the upper bounds principal of Radziwill and Soundararajan and the lower bounds principal of Heap and Soundararajan. As an application, we will use these principles to obtain sharp bounds for moments of central values of the quadratic family of Dirichlet L-functions.

11. Prof. Beata Randrianantoanina Miami University, Ohia, USA 28 May, 2021 Title: On the Banach-Mazur rotation problem
Click here for the abstract
12. Prof. Sudeshna Basu RKMVERI 7 May, 2021 Title: Linear Hahn-Banach type Extension Operators in Banach Algebras of Operators

The notion of linear Hahn-Banach extension operator was first studied in detail by Heinrich and Mankiewicz(1982) . Previously, Lindenstrauss (1966) studied similar versions of this notion in the context of non-separable reflexive Banach spaces. Subsequently, Sims and Yost (1989) proved the existence of linear Hahn-Banach extension operators in a purely Banach space theoretical set up. In this paper, we study similar questions in the context of Banach modules and module homomorphisms, in particular, Banach algebras of operators on Banach spaces. Based on Dales, Kania, Kochanek, Koszmider and Laustsen (2013), and also Kania and Laustsen(2017) , we give complete answers for reflexive Banach spaces and the non-reflexive space constructed by Kania and Laustsen from the celebrated Argyros-Haydon space with very few operators.

13. Fernanda Botelho University of Memphis 30 Apr, 2021 Title: Contractive Projections and Lifting of Operators on Banach Spaces
Click here for the abstract
14. Dijana Ilisevic University of Zagreb, Croatia 16 Apr, 2021 Title: On isometries on some Banach spaces and their spectrum

Isometries are maps between metric spaces which preserve distance between elements. In this talk we first recall the structure of (surjective) linear isometries on some important Banach spaces. Basic introductory material will be followed by recent results related to the following problem: when is a given finite set of modulus one complex numbers the spectrum of a linear isometry on a complex Banach space? Necessary conditions on such a set will be presented. Since sufficient conditions are related to the structure of specific Banach spaces, some particular cases will be considered and insightful examples will be given.


Sl. No. Speaker Institute Date Details
1. Prof. J.K. Verma IIT Bombay 12 Mar, 2020 Title: An algorithmic proof of the Stanley-Schriver Theorem


Sl. No. Speaker Institute Date Details
1. Dr. Rabeya Basu IISER, Pune 26 Nov, 2019 Title: Classical K-theory and some results related to Serre’s problem on projective modules.
2. Prof. Somnath Jha IIT, Kanpur 18 Nov, 2019 Title: p^r companion modular forms
3. Prof. Satadal Ganguly ISI, Kolkata 6 Nov, 2019 Title: A modular analogue of a problem of Vinogradov
4. Prof. K. N. Raghavan IMSC, Chennai 21 Aug, 2019 Title: Symmetric functions: on their multiplicative structure
5. Prof. Yuval Ginosar University of Haifa, Israel 16 Oct, 2019 Title: Tile the group
6. Dr. Moni Kumari TIFR, Mumbai 25 Sep, 2019 Title: Modular forms and the parity of j-function
7. Prof. Ravi Raghunathan IIT, Bombay 23 Sep, 2019 Title: What are $L$-functions and why should we care?
8. Prof. R. Thangadurai HRI, Prayagraj 19 Sep, 2019 Title: Distribution of Residues Modulo $p$
9. Prof. C.S. Rajan TIFR, Mumbai 13 Sep, 2019 Title: An introduction to p-adic numbers
10. Prof. Goutam Mukherjee ISI, Kolkata 31 Jul, 2019 Title: Free actions of finite groups on spheres.
11. Prof. Ashish Gupta RKMVERI 24 Jul, 2019 Title: Hamilton’s Quaternions and Central Simple Algebras
12. Prof. Manish Mishra IISER, Pune 9 Mar, 2019 Title: Self-dual cuspidal representations
13. Prof. Mahan Mj. TIFR 7 Mar, 2019 Title: What is hyperbolic geometry?
14. Prof. Atul Dixit IIT, Gandhinagar 6 Mar, 2019 Title: On values of the Riemann zeta function at odd positive integers
15. Prof. Stephan Baier RKMVERI 13 Feb, 2019 Title: The circle method and its application to the ternary Goldbach problem
16. Prof. Stephan Baier RKMVERI 12 Jan, 2019 Title: Diophantine approximation with Gaussian primes II
17. Prof. R. Thangadurai 12 Jan, 2019 Title: Digits and Transcendence II
18. Prof. S A Katre 12 Jan, 2019
19. Prof. Mahesh Nerurkar 12 Jan, 2019
20. Prof. Sanoli Gun 12 Jan, 2019 Title: On Euclidean ideal classes
21. Prof. Shanta Laishram 11 Jan, 2019 Title: Some Diophantine Equations involving Lucas sequences II
22. Prof. Purusottam Rath 11 Jan, 2019 Title: Distinguishing algebraic numbers and algebraic integers.
23. Prof. Kingshook Biswas 11 Jan, 2019 Title: Moebius rigidity results for negatively curved manifolds
24. Prof. El Houcein El Abdalaoui 11 Jan, 2019 Title: Erdős-Newman-Littlewood flat polynomials problems and Riemann hypothesis
25. Prof. R. Balasubramanian 11 Jan, 2019
26. Prof. S G Dani 11 Jan, 2019
27. Prof. S G Dani 10 Jan, 2019
28. Prof. R. Balasubramanian 10 Jan, 2019
29. Prof. Shanta Laishram 10 Jan, 2019 Title: Some Diophantine Equations involving Lucas sequences I
30. Prof. Mahesh Nerurkar 10 Jan, 2019 Title: Topological Dynamics IV
31. Prof. Sayani Bera 9 Jan, 2019 Title: Dynamics of polynomial shift-like maps
32. Prof. Purusottam Rath 9 Jan, 2019 Title: Distribution modulo one and Diophantine approximation II
33. Prof. Mahesh Nerurkar 9 Jan, 2019 Title: Topological Dynamics III
34. Prof. El Houcein El Abdalaoui 9 Jan, 2019 Title: Sarnak Möbius disjointness conjecture and dendrites II
35. Prof. Biplab Paul 8 Jan, 2019 Title: Multiplicity one theorem for Hecke eigenforms
36. Prof. Purusottam Rath 8 Jan, 2019 Title: Distribution modulo one and Diophantine approximation II
37. Prof. Mahesh Nerurkar 8 Jan, 2019 Title: Topological Dynamics II
38. Prof. El Houcein El Abdalaoui 8 Jan, 2019 Title: Sarnak Möbius disjointness conjecture and dendrites I
39. Prof. Purusottam Rath 7 Jan, 2019 Title: Distribution modulo one and Diophantine approximation I
40. Prof. Dibyendu De 7 Jan, 2019 Title: A variant of density Carlson-Simpsion Theorem
41. Prof. Mahesh Nerurkar 7 Jan, 2019 Title: Topological Dynamics I
42. Prof. Abhishek Bharadwaj 5 Jan, 2019 Title: On a Question of Baker over Number Fields
43. Prof. Stephan Baier RKMVERI 5 Jan, 2019 Title: Diophantine approximation with Gaussian primes I
44. Prof. Jyothsnaa 4 Jan, 2019 Title: Primitive roots for Piatetski Shapiro primes
45. Prof. Jaitra Chattopadhyay 4 Jan. 2019 Title: Bi-quadratic fields having a non-principal Eu-clidean ideal class
46. Prof. Sampa Dey 4 Jan, 2019 Title: Statistics of moduli space of vector bundles on curves
47. Prof. R. Thangadurai 4 Jan, 2019 Title: Digits and Transcendence I
48. Prof. Bidisha Roy 3 Jan, 2019 Title: On zero-sum subsequences in a finite abelian pgroup
49. Prof. Subha Sarkar 3 Jan, 2019 Title: On fractionally dense sets
50. Prof. Sukumar Das Adhikari RKMVERI 3 Jan, 2019 Title: Some Ramsey-type theorems in combinatorial number theory


Sl. No. Speaker Institute Date Details
1. Prof. Michel Waldschmidt Sorbonne University, Paris 27 Nov, 2018 Title: On the Landau-Ramanujan constant
2. Prof. A B Raha ISI, Kolkata 20 Nov, 2018 Title: An elementary proof of Real Stone-Weierstrass Theorem
3. Prof. Olivier Ramare University of Marseille 2 Nov, 2018 Title: Products of primes in arithmetic progressions
4. Prof. Jugal Verma IIT Bombay 1 Sep, 2018 Title: Counting roots of multivariate polynomial systems using volumes of Newton polytopes
5. Prof. Sukumar Das Adhikari RKMVERI 21 Aug, 2018 Title: Some algebraic methods in zero-sum problems
6. Dr. Bidyut Sanki IMSc Chennai 25 Jul, 2018 Title: Embedding of metric graphs on hyperbolic surfaces
7. Prof. Jyoti Sengupta TIFR, Mumbai 18 Jul, 2018 Title: A case of simultaneous nonvanishing of automorphic L functions
8. Dr. Arijit Gangopadhyay School of Mathematical Sciences, Tel Aviv University, Israel 11 Jul, 2018 Title: Diophantine approximation in function field of positive characteristic
9. Dr. Mallesham ISI, Kolkata 8 Jul, 2018 Title: Primes in sumsets
10. Dr. Ratna Pal Department of Mathematics, IISER Pune 6 Jul, 2018 Title: A rigidity theorem for Henon maps
11. Anirban Mukhopadhyay IMSc 19 April, 2018 Title: How uniform is Uniform distribution
12. Prof. Partha Sarathi Chakraborty IMSc 17 April, 2018 Title: Haar measure on SO(n)
13. Prof. C. S. Rajan TIFR 10 April, 2018 Title: Numbers of the form $x^2+ny^2$, and an introduction to quadratic reciprocity.
14. D. S. Ramana HRI 16 March, 2018 Title: Additive Energy of Dense Sets of Primes
15. Prof. T. Asanuma 6 Mar, 2018 Title: Jacobian Conjecture
16. Prof. S.M. Srivastava ISI, Kolkata 21 Feb, 2018 Title: A cute result of Erdos on Analytic Functions
17. Prof J. K. Verma IIT Mumbai 30 Jan, 2018 Title: Cartan-Dieudonne Theorem


Sl. No. Speaker Institute Date Details
1. Prof. Michel Waldschmidt University of Paris 6 7 Dec, 2017 Title: Representation of integers by binary cyclotomic forms
2. Vijay M. Patankar JNU 10 Nov, 2017 Title: Factorization of Abelian Varieties modulo primes