The Department of Mathematics, SRM IST, Ramapuram organizes a 10 days International Virtual FDP on “Frontiers of Mathematics” from **17.08.2020 to 26.08.2020 **for faculty members & research Scholors.

**Day – 1**

Resource person: **Dr. Joao Manuel R.S. Tavares**,

Faculdade de Engenharia, da Universidade do Porto, Portugal

Topic: **“Image Analysis by Computer Methods”**

Image Segmentation by threshold, Segmentation of contours in dynamic pedobarography, segmentation of ear structures, segmentation based on deformable templates, segmentation based on active shape models, level set method and machine learning were elucidated. Image tracking and image matching, Registration based on contours matching, optimization and dynamic programming were discussed. Registration of images based on Fourier transform, and iterative search were further interpreted.

There was a tremendous response from participants from all over the world.

**Day 2**

Resource Person: **Dr. Arpita Ghosh**,

Adjunct Researcher, University of Haifa, Israel

Topic: **“Ramsey Theoretic Study in Partial Semi group” **

Dr. Arpita explained the monochromatic colored set, finitely colored set. The algebraic counterpart with the basic definitions of binary associative operation, partial semigroup, matrix multiplication was elucidated. Connection between Ramsey Theory and ultrafilters was explained through Finite sums theorem, Central sets in natural numbers, Central sets in arbitrary semigroups and partial semigroups were further interpreted. Algebraic structures of Os, New Central Sets theorem for commutative Adequate Partial Semigroups, New version of Central sets theorem, JO set were discussed.

**Day 3**

Resource Person: **Dr. K. Kannan,**

Department of Mathematics and Statistics,

University of Jaffna, Sri Lanka

Topic: **“Rapid Decay Property and Invariant Approximation Property”**

Introduction to C* – algebra, uniform Roe algebra, the reduced C* – algebra and some example with C* – algebra were discussed. Left and right regular representations, Uniform Roe algebra, Invariant Approximation Property (IAP), the IAP for direct products with finite group, Property RD and length functions were interpreted. RD and Invariant approximation property, some examples with IAP, Approximation property and Strong Invariant Approximation Property were expounded.

The talk of the resource person was enlightening as the participants were much benefited from it.

**Day 4**

Resource Person: **Mr. Rajagopal Srinivasan**,

Head, TCS, Enterprise Architecture, North America

Topic: **“Math on my Path” **

Mr. Rajagopal discussed his Journey intertwined with Mathematics and Science. Page Rank Algorithm, Discrete Mathematics in Data Science, calculus and optimization for machine learning, basics of linear algebra for machine learning , probability theory, statistics for exploratory data analysis were interpreted. Data knowledge, Basic mathematics, data visualization, machine learning, statistics which are required for the Data Scientist were elucidated. Mathematics in Artificial intelligence involving linear algebra, probability theory and statistics, calculus, algorithms and complexity and others was expounded.

The talk of the resource person brought an insight on how Information Technology with Mathematics can bring sweeping change that goes far beyond what is envisioned.

**Day 5**

**Session – 1**

Resource Person: ** Dr. Manoj Kummini,**

Chennai Mathematical Institute, Chennai

Topic: **“Invariant Theory” **

Dr. Manoj explained Group actions, identity function, composition of functions . The permutation group, the requirement to give group action of set is to give a group homomorphism were discussed. Dihedral group, Groups of algebra automorphisms, k- algebra automorphisms, linear actions, necessary condition for a function on a set of variables to be bijective were interpreted. G- invariant, cyclic group of order 3 acting on C[x,y], Reynolds operator, Hilbert basis theorem were explicated.

The informative talk of the resource person made the session much beneficial.

**Day5 **

**Session – 2**

Resource Person: **Dr. Mathew C. Francis,**

Computer Science Unit, Indian Statistical Unit, Chennai Centre

Topic: **“Graph Colouring” **

Dr. Mathew began his talk with the introduction to graphs, clique, independent set. Graph colouring, vertex colouring, chromatic number, upper bounds for chromatic number were interpreted. High Chromatic graphs, Mycielski’s Construction, Trees in high chromatic graphs were expounded. Famous open problems on colouring- Gyárfás –Sumner Conjecture, Hadwiger’s Conjecture were further discussed.

The talk of the resource person was enlightening making the session beneficial to the participants.

**Day – 6**

Resource person: **Dr. Srinivasarao Thota**, Department of Applied Mathematics,

School of Applied Natural Sciences, Adama Science and Technology University, Ethiopia

Topic: **“Grobner Bases: An Introduction and some Applications”**

Dr. Srinivasarao Thota began his talk with the introduction to power product, Affine n- space, Ideals, Hilbert Basis Theorem for one variable, Ideal Membership, Term order. Gröbner Basis, S- Polynomials, Buchberger Theorem, Reduced Gröbner Basis and some applications of Gröbner basis were discussed. The 3-Color Problem, Automatic Geometric Theorem proving, other applications were elucidated.

The talk of the resource person made the session successful with the participants gaining knowledge over the topic.

**Day 7 **

** **

Resource Person: **Dr. Neelesh S. Upadhye, **Department of Mathematics, Indian Institute of Technology, Madras

Topic: **“Stein Method for Stable Distributions”**

Dr. Neelesh S. Upadhye began his talk introducing the Central Limit Theorem, Berry- Esseen Theorem, an outline to Stein’s method for Standard Normal and Infinitely Divisible distributions. Stable distributions, self- decomposable property, Metrics, Function spaces, Stein’s method in nutshell were interpreted. Stein Operators for Infinitely Divisible distributions, Stein Operator for non- Gaussian Stable distributions, Bounds on the solution to the Stein Equation and applications were explained in detail.

The thought- provoking talk of the resource person through which the participants were benefited made the session of the FDP fruitful.

**Day 8**

Resource Person: **Dr. S. Dheva Rajan, **Department of Mathematics, Al Musanna College of Technology, Al Mussana, Sultanate of Oman, Oman

Topic:** “R for Statisticians- An Introduction”**

Dr. S. Dheva Rajan began his talk listing the popular companies using R, the versions of R, the applications of R, downloading and installation of R were further explained. R Script, Environment, Command Prompt and Access were interpreted. Finding the mean, median, mode, compositions and representation of distributions in R were demonstrated. Creation of Histogram, analysis of Correlation and Regression, 3D Scatter plot and animations in R were explicated.

The session of the FDP was successful by the edifying talk of the resource person, providing greater knowledge and understanding on the topic through which the participants were benefited.

**Day 9**

Resource Person: **Dr. B.V. Senthil Kumar,** Department of Information Technology, Nizwa College of Technology, Oman

Topic:** “Applications of Fourier Series and Fourier Transforms”**

Dr. B.V. Senthil Kumar began his talk with a detailed introduction to Fourier series. Periodicity of the function, the Fourier Series of the wave form, Parseval’s formula, the real life application of RMS value in electrical engineering were demonstrated. Solving a linear differential equation with a periodic forcing function via Fourier series, Continuous and discrete signals, Time – Frequency Analysis, Frequency domain analysis were expounded. Mathematical explanation and applications of Fourier Transform, Convolution of two functions were further interpreted.

The informative talk of the resource person made the session of the FDP successful with the participants much benefited from it.

**Day 10**

Resource Person: **Dr. V. Krishnamoorthy,** Arba Minch University, Sawla Campus, Ethiopia

Topic: **“Some aspects of Intuitionistic Fuzzy sets” **

Dr. V. Krishnamoorthy began his talk with an introduction to Fuzzy sets. The difference between IFS and the other fuzzy set extensions, Fuzzy sets and Intuitionistic Fuzzy sets, some operators of IFS, some basic definitions related to IFS were interpreted. Ideal and Fuzzy left(righ Some results based on Normal IF-h-ideal of Г- hemiring, strong intuitionistic fuzzy graphs, applications of IFS were explicated.

The session of the FDP was fruitful with the enlightening talk of the resource person, benefiting the participants.