Curry Leaf, the Math Club of MTTS Alumni, is turning four this year! Join us for an exciting lineup of talks covering a diverse range of mathematical topics. Our speakers will explore minimal surfaces in R^3, computational complexity theory, the fascinating interplay between graphs and matrices,the rigorous mathematics behind differential equations, and more! We'll also be celebrating Professor Kumaresan's 74th birthday and Curry Leaf's 4th anniversary. !
Days
Speakers
Events
In this talk, we present CRRao.jl, a Julia package designed to provide a unified framework for estimating frequentist and Bayesian statistical predictive models. Named after the eminent statistician C. R. Rao, the package offers robust support for linear, logistic, Poisson, and negative binomial regression models, simplifying the process of model estimation with a consistent API. By leveraging Julia's high-performance capabilities, CRRao.jl seamlessly integrates with widely used Julia packages like GLM.jl for frequentist models and Turing.jl for Bayesian inference. This paper describes the architecture of CRRao.jl, its core features, and its role in statistical analysis, emphasizing its flexibility, ease of use, and computational efficiency. Additionally, we discuss the package’s applications in real-world data analysis and propose directions for future enhancements.
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In this talk, we will explore minimal surfaces (surfaces with zero mean curvature) in R^3, which locally minimize area. We will review several methods for constructing minimal surfaces, focusing on the classical approach to their construction. We will also discuss some open problems in the field. Additionally, we will cover triply periodic minimal surfaces (TPMS). Throughout the presentation, various well-known examples will be discussed. If time permits, we will briefly touch on minimal surfaces in other spaces. This talk is aimed at undergraduate and early graduate students.
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Which of the following problems is "harder" to solve? Adding two 5-digit numbers or multiplying them? In general, it seems that multiplying is harder, but is there a way to make this feeling formal? The area of theoretical computer science tries to do just that for any given problem! In this talk, we will look at some examples of such problems and try to see how easy/hard it is to solve them.
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In this lecture, we will discuss some interactions between graphs and matrices. Real valued matrices like adjacency, incidence and Laplacian matrices are associated to a graph. On the other hand, the structure of a matrix is specified at times by combinatorial objects like graphs and digraphs. After some elementary discussions on determinants of matrices, we will explore how determinants, characteristic polynomials and the eigenvalues of the associated matrices are linked to the structure of the graph.
We present some applications (Examples) of ordinary differential equations which models the classical problems like: populations growth, spring-mass-dashpot system etc. Through the examples, we will see the importance of studying problems from engineering and science via rigorous mathematics. We realize that quite often obtaining the solution is not enough to understand the problem, need to mathematically analyze the problem for further understanding. In fact, most of the time, closed form solutions will not be available and hence the need to understand the differential equations qualitatively and otherwise. This requires good knowledge of analysis, linear algebra, functional analysis, geometry etc.
The RSA cryptosystem named after its proposors Ron Rivest, Adi Shamir and Leonard Adleman is a public-key cryptosystem is one of the oldest, popular, and widely used secure cryptosystem. The security of RSA is based on the factoring problem, i.e., factorization of an integer into primes. On the other hand, for its implementation, large primes need to be generated. How to determine whether a large integer chosen is prime or not? In this talk we describe the RSA cryptosystem and discuss a couple of primality tests, one due to Fermat and the other due to Miller-Rabin. We shall see that Fermat's result has limitations and so the property of primes given by Miller-Rabin is preferable. The talk is elementary in nature, suitable for all B.Sc. and M.Sc. students in Mathematics and requires minimal prerequisites like some basic knowledge of number theory (primes and congruences).
On the 16th of October 1843, William Rowan Hamilton wrote down what we would today call the structure constants for a real, 4-dimensional associative algebra with unity. The Quaternion algebra - as Hamilton's invention is now called - was the first example of a noncommutative ring and, in the words of Henri Poincare, catalysed a "revolution in arithmetic which is entirely similar to the one which Lobachevsky affected in geometry". The 181 years since the invention of the Quaternions has seen ring theory, both commutative and noncommutative, develop as a fundamental part of pure mathematics. We will begin this talk by describing the origins of ring theory and discussing some simple examples (including the Quaternions!). We will then touch upon the connections between commutative ring theory and geometry. Time permitting, we will finish by describing some aspects of the theory of noncommutative rings which display behavior not visible in the commutative context.
This talk will discuss some results whose popular proofs inherently rely on the Axiom of Choice. Often such results do not depend on this axiom, and a slight modification to the standard proofs makes them choice-free. Sometimes, a drastically different proof is required to achieve this. However, there are cases where the use of the Axiom of Choice cannot be avoided. Such results depend on, or are sometimes even equivalent to, this axiom. I will discuss all of this, along with some related ideas.
In this talk, I shall discuss the Exhaustion method by Archimedes, both geometrically and analytically, to approximate the area of a circle. Further, it will be depicted that the idea can be extended to approximate the volume of a cylinder. Also, I shall talk about the Darboux and Riemann methods to approximate the area under a curve. To visualize the process of approximation, I shall be using the software – Mathematica.
Anand
Arighna
Bhargav
Bhoomika
Chaitanya
Harinder
Jyoti
Ritoprovo
Soumya
Tamoghna
Uday
