[{"content":" Home/Members/Academic Year 2026-\u0026#39;27 Here is the list of core members of the club for the academic year 2026-\u0026lsquo;27.\nCore Members Daibik Barik (M. Math, 2028) Sushant Aditya (M. Math, 2028) Shameel (M. Math, 2028) Yuvraj Singh Rajpurohit (M. Math, 2028) Aritrabha Majumdar (M. Math, 2028) Srijeet Bhattacherjee (M. Math, 2028) Ahan Chakraborty (B. Stat, 2027) Aishee Bhattacharya (M. Stat, 2028) Somarddha Das (M. Stat, 2027) ","permalink":"https://mathclubisik.github.io/members/ay_2026_27/","title":"Academic Year 2026-'27"},{"content":"\rHome/Activities/Expository Talks/Special Lectures/Special Lectures 2025 Fall 2025 SL2502: Determinantal Point Processes Speaker: Prof. Manjunath Krishnapur (IISc, Bangalore) Abstract: A point process on $\\mathbb{R}^d$ is a random discrete (hence countable) subset. The most well-known example of a point process is the Poisson process which is characterized by complete independence of what happens in disjoint regions of the space. A determinantal point process is different, in that there is inbuilt repulsion between points. Surprisingly many naturally occurring point processes turn out to be determinantal. Examples are eigenvalues of various models of random matrices, uniform spanning trees of a graph, zeros of certain random analytic functions, non-interesecting random walks, etc. This talk will give a brief introduction to determinantal processes. Pre-requisites: Knowledge of Poisson process will be helpful but not necessary. The talk will be aimed at the level of B.Stat 2nd or 3rd year. Resources: Scribbled Notes \u0026amp; Slides. Video: (Not Recorded) Date and Time: Thursday, 23rd October 2025, 7:30 PM - 9:00 PM (IST) Venue: Online (Google Meet) Spring 2025 SL2501: An Introduction to Impartial Games Speaker: Prof. Arnab Chakraborty (ISI, Kolkata) Abstract: Impartial games are where two players alternate moves, and the same set of moves is available to both the players. Typically the player able to move last wins. These are useful things to know when you sit in the back row during a boring lecture. We shall learn about such games (and the some of the math underlying it) by actually playing the games. You\u0026rsquo;ll get to know about exciting games that you have not possibly heard about before! References: Winning Ways for your Mathematical Plays by Elwyn Berlekamp, John Horton Conway, and Richard K. Guy On Numbers and Games by John Horton Conway Surreal Numbers by Donald Knuth Video: (Not Recorded) Date and Time: Thursday, 27th March 2025, 4:30 PM - 6:00 PM (IST) Venue: Room 401, 4th floor, SN Bose Bhavan ","permalink":"https://mathclubisik.github.io/activities/expository_talks/special_lectures/sl_2025/","title":"Special Lectures 2025"},{"content":"\rHome/Activities/Expository Talks/Student Talks/Student Talks 2025 Talks given by students during the year 2025 are listed below.\nFall 2025 EP2508: The Matthew\u0026rsquo;s method for cover times Speaker: Swastika Dey (M. Stat, 2027) Abstract: The cover time of a random walk on a finite graph is the expected time it takes to visit all of the vertices. In this talk, we will introduce the notion of cover time and discuss Matthews’ method, which provides both lower and upper bounds by relating the cover time to hitting time of subsets of the vertices and hitting time of the whole graph respectively. We will illustrate the technique in detail on the complete graph, where the problem reduces to the well-known coupon collector model, yielding a sharp cover time $\\Theta(n \\log n)$. Along the way, we will emphasize proof strategies behind the method. Notes: Available here. Video: [TBA] Date and Time: Saturday, 20th September 2025, 6:00 PM - 7:30 PM Venue: Online (Google Meet) EP2507: Probabilistic Number Theory and the values of Riemann Zeta Function Speaker: Srijeet Bhattacharjee (B. Stat, 2026) Abstract: We will have an introduction to the subject of Probabilistic number theory with some classical results and see how the ideas can be used to demystify the behaviour of Riemann Zeta Function in the critical strip. The main focus would be the proof of Bagchi\u0026rsquo;s theorem (Who was a student of ISI Kolkata) and Selberg\u0026rsquo;s Central Limit Theorem. Notes: Available here. Video: Available here. Date and Time: Sunday, 24th August 2025, 6:00 PM - 7:30 PM Venue: Online (Google Meet) EP2506: Wigner Matrices - The Semicircular Law and its Variants Speaker: Saraswata Sensarma (M. Math, 2026) Abstract: Random Matrix Theory was introduced as a model for studying \u0026ldquo;typical\u0026rdquo; matrices of a given nature. The initial investigations were made by Wishart (1928) for random covariance matrices and Wigner (1955) for random hermitian matrices. Today, RMT boasts connections with topics ranging from integrable particle systems to number theory, with applications in data science, telecommunication, and theoretical physics to name a few.\nThe semicircular law (SCL) was among the first universality results for random matrices. Proven by Wigner in his seminal paper, this law governs the behavior of the bulk of the eigenvalues of Wigner matrices. In the coming years, several other techniques were introduced for the proof of the SCL, some of which have since been used to prove stronger universality phenomena for the spectrum.\nIn this talk, we wish to give a sketch of Wigner\u0026rsquo;s original proof - which involved the moment method and an inverse moment computation. We briefly discuss some other methods for the proof of SCL, and how they are applicable in a broader setting. We then talk about more intricate universality results - a local variant of the SCL, eigenvalue rigidity and eigenvector delocalisaion (quantum unique ergodicity). We end with some remarks on non-Hermitian Matrices. Pre-requisites: Some results from Probability III will be stated and used. To follow along, a knowlegde of Probability I and some linear algebra would be sufficient. Notes: Available here. Video: Available here. Date and Time: Sunday, 10th August 2025, 6:00 PM - 7:30 PM Venue: Online (Google Meet) EP2505: Random Polynomials Speaker: Srijan Saha (M. Stat, 2027) Abstract: This talk aims to introduce the audience to the fascinating world of random polynomials—polynomials with randomly chosen coefficients. Formally, a random polynomial of degree $n$ is a function $P_n$ defined as $$ P_n(t) = X_0 + X_1 t + \\ldots + X_n t^n,\\quad t\\in\\mathbb{R}, $$ where $(X_0, X_1, \\ldots, X_n)$ are random variables drawn from a specified distribution.\nThe central goal of the talk is to analyze the real zeros of such random polynomials. By reducing this question to a tractable multivariable analysis problem for deterministic polynomials, we can derive the expressions for the expected number of real zeros for random polynomials. Special cases will be highlighted, and we will explore the asymptotic behavior of this expected number as $n \\to \\infty$.\nIn the second part of the talk, I will present a strikingly elegant approach to the same problem using a probabilistic argument inspired by Buffon\u0026rsquo;s needle problem, with tools borrowed from integral geometry.\nThe talk is primarily based on the foundational work of Edelman and Kostlan Notes: [TBA] References: How many real roots does a random polynomial have? \u0026ndash; Alan Edelman and Eric Kostlan Video: (Not Recorded) Date and Time: Tuesday, 29th July 2025, 6:15 PM - 7:15 PM Venue: Room 508, 5th floor, SN Bose Bhavan Spring 2025 EP2504: Ramanujan\u0026rsquo;s Circle Method, and application to Partition Number Speaker: Srijeet Bhattacharjee (B. Stat, 2026) Abstract: Srinivasa Ramanujan was one of the greatest Indian mathematicians, who has left us with a great number of interesting and beautiful results. One of his most famous contribution is the asymptotic expression of the partition number. Few years later, Rademacher gave an exact expression of it, in terms of a series. However, the ingenious \u0026ldquo;Circle Method\u0026rdquo;, that Ramanujan used in the proof, has ever since been refined and applied to a vast plethora of number theoretic problems, and is still heavily being used in modern day research.\nWe would state Ramanujan\u0026rsquo;s version of the Circle Method, and prove Rademacher\u0026rsquo;s Series of Partition Number. Pre-requisites: Some very basic understanding of complex analysis (2nd year onwards have seen this much in the context of Characteristic Functions), however this can be safely ignored. Notes: Available here. Video: (Not Recorded) Date and Time: Tuesday, 1st April 2025, 4:30 PM - 6:00 PM Venue: Room 401, 4th floor, SN Bose Bhavan EP2503: Convergence of random series Speaker: Ayan Ghosh (B. Stat, 2026) Abstract: Discussion on upper and lower bounds on Kolmogorov\u0026rsquo;s maximal inequality, Hence proving Kolmogorov\u0026rsquo;s three series theorem. Discussion on rates of convergence. Finally a theorem (probably by Levy): Convergence of the series $\\sum_{n = 1}^{\\infty} X_n$ in distribution implies almost sure convergence of the series, provided $X_i$\u0026rsquo;s are independent. Video: (Not Recorded) Date and Time: Tuesday, 18th March 2025, 4:30 - 6:00 PM Venue: Room 508, 5th floor, SN Bose Bhavan EP2502: A Short Proof of Kolmogorov\u0026rsquo;s SLLN Speaker: Atmadeep Sengupta (B. Stat, 2026) Abstract: Strong law of large number gives a justification of thumbs rule of average. It states that sample mean converges to original mean almost surely. The original and traditional proof is due to A. N. Kolmogorov. The alternative elementary proof by N. Etemadi bypasses stuffs like maximal inequalities and convergence of random series. In this talk, we will discuss this proof and have some insight on the elegance of the proof. After that, we will have a proof of another statistic, namely median. We will have a short proof of almost sure convergence of sample median to true median, in the case of unique median. Notes: Available here. Video: (Not Recorded) Date and Time: Wednesday, 12th March 2025, 4:30 PM - 5:30 PM (IST) Venue: Room 401, 4th floor, SN Bose Bhavan EP2501: Dirichlet\u0026rsquo;s Theorem of Primes in an Arithmetic Progression Speaker: Srijeet Bhattacharjee (B. Stat, 2026) Abstract: We know that there are infinitely many primes in natural numbers. But are there infinitely many primes in any arithmetic progression? More generally which arithmetic progressions contain infinitely many primes? We would prove Dirihclet\u0026rsquo;s theorem on primes in an arithmetic progression. We will introduce the concepts of Dirichlet characters and Dirichlet $L$-functions, which gave rise to other general $L$-functions and studying their properties is an area of the bulk of active research in Analytic number theory and even connected to the Riemann Hypothesis Notes: Available here. Video: (Not Recorded) Date and Time: Friday, 7th March 2025, 4:30 PM - 5:30 PM (IST) Venue: Room 401, 4th floor, SN Bose Bhavan ","permalink":"https://mathclubisik.github.io/activities/expository_talks/student_talks/st_2025/","title":"Student Talks 2025"},{"content":" Home/Members/Academic Year 2025-\u0026#39;26 Here is the list of core members of the club for the academic year 2025-\u0026lsquo;26.\nCore Members Bikram Halder (M. Math, 2026) Ritabrata Bhattacharyya (M. Math, 2026) Saraswata Sensarma (M. Math, 2026) Sougata Panda (M. Math, 2026) Shriyaa Srivastava (M. Math, 2027) Somarddha Das (B. Stat, 2025) Aishee Bhattacharya (B. Stat, 2026) Srijeet Bhattacherjee (B. Stat, 2026) Ahan Chakraborty (B. Stat, 2027) ","permalink":"https://mathclubisik.github.io/members/ay_2025_26/","title":"Academic Year 2025-'26"},{"content":"\rHome/Activities/Foundational Courses/Foundational Courses 2025 Spring 2025 FC2501: Galois Theory Audience: B. Stat, 2nd year students and seniors Abstract: Given a polynomial of degree $n$, what is the relation between its roots and its coefficients? Is there a formula for finding the roots? Can we construct any polygon using only ruler and compass? This course on Galois theory answers these and many more interesting questions by observing certain beautiful connections within mathematics. Pre-requisites: Basic understanding of Linear Algebra. Additional prerequisites will be developed as needed during the course. Instructors: Saheb Mohapatra (M. Math, 2025) Sourish Goswami (M. Math, 2025) Schedule: 1-hour session, once per week Duration: One semester ","permalink":"https://mathclubisik.github.io/activities/foundational_courses/fc_2025/","title":"Foundational Courses 2025"},{"content":" Home/Members/Academic Year 2024-\u0026#39;25 Here is the list of core members of the club for the academic year 2024-\u0026lsquo;25.\nCore Members Kishalay Sarkar (JRF) Saheb Mohapatra (M. Math, 2025) Aytijhya Saha (M. Stat, 2025) Bikram Halder (M. Math, 2026) Ritabrata Bhattacharyya (M. Math, 2026) Saraswata Sensarma (M. Math, 2026) Sougata Panda (M. Math, 2026) Somarddha Das (B. Stat, 2025) Srijan Saha (B. Stat, 2025) Aishee Bhattacharya (B. Stat, 2026) Srijeet Bhattacherjee (B. Stat, 2026) ","permalink":"https://mathclubisik.github.io/members/ay_2024_25/","title":"Academic Year 2024-'25"},{"content":"\rHome/Activities/Expository Talks/Student Talks/Student Talks 2024 Talks given by students during the year 2024 are listed below.\nFall 2024 EP2403: Representation of Compact Groups and the Peter-Weyl Theorem Speaker: Ritabrata Bhattacharyya (M. Math, 2026) Abstract: In this talk, we\u0026rsquo;ll give a short overview of Representation of Finite Groups and Haar Measure on Locally Compact Groups. Then we\u0026rsquo;ll define unitary representations and develop the language of Representation theory for Compact Groups. For a compact group $G$, we\u0026rsquo;ll give $L^2(G)$, the space of square integrable functions on $G$ a continuous action of $G$ and see how we can decompose it into simpler looking finite dimensional representations of $G$. We\u0026rsquo;ll study certain continuous functions on $G$, called \u0026ldquo;Matrix Coefficients\u0026rdquo;, which arise from various representations of $G$. Then we\u0026rsquo;ll prove the Peter Weyl Theorem which states how $L^2(G)$ decomposes and the space of matrix coefficients is dense in $L^2(G)$. As a consequence, we\u0026rsquo;ll show that for any compact hausdorff group $G$ and any neighborhood $U$ of the identity, we can find a closed normal subgroup $H$ inside $U$ so that $G/H$ can be embedded inside some general linear group $GL_n(\\mathbb{C}).$ Pre-requisites: Measure Theory, Point-Set Topology. Some knowledge on Representation of Finite Groups would be helpful, but not necessary. Video: [TBU] Notes: [TBU] Date and Time: Saturday, 26th October 2024, 4:00 PM - 6:30 PM (IST) Venue: Online (Google Meet) EP2402: Extreme Singular Values of Random Matrices Speaker: Saraswata Sensarma (M. Math, 2026) Abstract: Random Matrix Theory (RMT) originated in the late 1940s with Wigner and Eisenbud\u0026rsquo;s efforts to model strong interactions in heavy nuclei. A pivotal advancement occurred in 1973 when Dyson and Montgomery uncovered a connection between the zeros of the zeta function and the eigenvalues of random Hermitian matrices. Since then, RMT has developed significantly and is now connected with numerous mathematical disciplines. Traditionally, RMT examines the limiting distributions of spectral statistics as matrix size increases. However, many practical problems require precise bounds for matrices of a fixed finite size, leading to the development of non-asymptotic random matrix theory, which employs techniques from geometric functional analysis and has applications across theoretical computer science, statistics, and signal processing.\nIn this talk, we will explore bounds on the extremal singular values of square random matrices with independent and identically distributed (iid) entries. We derive bounds for the largest singular value using concentration inequalities and a covering argument. However, this approach is insufficient for the smallest singular value. For this, we employ geometric methods developed by Rudelson and Vershynin, which involve analyzing weighted sums of iid random variables. This will involve a brief detour into Littlewood-Offord Theory, and its recent advancements by Tao and Vu. We will also see some generalizations of these ideas to other setups. The emphasis throughout will be on the proof techniques, given their broad applicability. Pre-requisites: Probability, Linear algebra Video: Available here Notes: Available here Date and Time: Saturday, 28th September 2024, 6:00 PM - 7:30 PM (IST) Venue: Online (Google Meet) EP2401: On Dirichlet\u0026rsquo;s Problem on the Circle Speaker: Nilaksh Pundir (M. Math, 2025) Abstract: Given an $L^1$ function on a circle, it can be shown that its Poisson integral defines a harmonic function on the unit disc. This then relates to the Dirichlet problem on the circle, which asks whether a function on the circle can be \u0026ldquo;extended\u0026rdquo; to a harmonic function on the unit disc. It is known that for continuous functions, this gives a complete solution to the Dirichlet problem. In the case of $L^1$ functions, we will see that convergence of the Poisson integral depends on the path you take to reach the boundary. We will also define the Hardy-Littlewood maximal function on the circle and study the method of maximal functions. Pre-requisites: Basic measure theory Video: (Not Recorded) Date and Time: Thursday, 26th September 2024, 4:00 PM - 5:30 PM (IST) Venue: 508, 5th floor, SN Bose Bhavan ","permalink":"https://mathclubisik.github.io/activities/expository_talks/student_talks/st_2024/","title":"Student Talks 2024"},{"content":"\rHome/Activities/Foundational Courses/Foundational Courses 2024 Fall 2024 FC2403: Metric Spaces and Topology Audience: B. Stat, 2nd year students and seniors. Abstract: This series of lectures will serve as an introduction to topology. Starting with the Euclidean spaces, we will introduce the notion of metric spaces and important properties such as continuity, convergence, compactness, connectedness, and so on. We then define Topological spaces by abstracting out the notion of open sets, and use those to generalize the concepts discussed in the previous talks. These ideas will enable us to discuss results for normed linear spaces. Pre-requisites: Knowledge of elementary real analysis should be sufficient to follow every detail of this course. Instructors: Mayank Jangid (M. Math, 2026) R. Vedanta (M. Math, 2026) Schedule: Lectures: All sessions will be held from 9:00 PM. Sunday, 11th August 2024 (Mayank Jangid) - Notes \u0026amp; Video Saturday, 17th August 2024 (R. Vedanta) - Notes \u0026amp; Video Sunday, 18th August 2024 (Mayank Jangid) - Notes \u0026amp; Video Spring 2024 FC2402: Measure Theory and Probability Audience: B. Stat, 2nd year students and seniors Abstract: We will study measures and their properties. Starting with a relatively abstract yet motivated setup, we will try to study measures, the Lebesgue Integration Theory, some major results, product measures and the Radon-Nikdoym Theorem. This would be followed by some convergence issues and probability theoretic applications. Pre-requisites: Metric Topology, Probability and Riemann Integration. Instructors: Rishiraj Baul (M. Math, 2025) Soham Mallick (M. Stat, 2025) Schedule: Lectures: All sessions will be held from 4:30 PM. [TBA] FC2401: Group Theory Audience: B. Stat, 1st year students Abstract: This course will be an introduction to the theory of groups, specifically its role in the study of symmetry. We will also be discussing the axiomatic foundations of group theory as well as some number theory. Pre-requisites: None Instructor: Snehinh Sen (M. Math, 2024) Schedule: Lectures: All sessions will be held from 4:30 PM, unless otherwise mentioned. [TBA] ","permalink":"https://mathclubisik.github.io/activities/foundational_courses/fc_2024/","title":"Foundational Courses 2024"},{"content":" Home/Members/Academic Year 2023-\u0026#39;24 Here is the list of core members of the club for the academic year 2023-\u0026lsquo;24.\nCore Members Kishalay Sarkar (JRF) Saheb Mohapatra (M. Math, 2025) Aytijhya Saha (M. Stat, 2025) Aman Singh (M. Math, 2024) Snehinh Sen (M. Math, 2024) Sonali Priyadarshini Behara (M. Math, 2024) Aniruddhan Ganesaran (M. Stat, 2024) Archisman Mukherjee (B. Stat, 2024) Srijan Saha (B. Stat, 2025) Somarddha Das (B. Stat, 2025) ","permalink":"https://mathclubisik.github.io/members/ay_2023_24/","title":"Academic Year 2023-'24"},{"content":"\rHome/Activities/Expository Talks/Special Lectures/Special Lectures 2023 Fall 2023 SL2302: Linear Algebra over Rings Speakers: Prof. Mrinal Kanti Das (ISI, Kolkata) Abstract: Let $R$ be a commutative ring with 1. A row vector $u= (a_1,\\cdots,a_n)\\in R^n$ is called unimodular if there is another row vector $v = (b_1,\\cdots,b_n)\\in R^n$ such that $uv^T=1$. In other words, $a_1b_1+\\cdots a_nb_n=1$. Take any matrix $M \\in SL_n(R)$. The first row of $M$ is a unimodular row. Now let us ask this intriguing question: Let $u$ be a unimodular row. Is it the first row of a matrix in $ SL_n(R)$? We shall explore this question in detail, and if possible, will talk about some recent research as well. Video: (Not Recorded) Date and Time: Monday, 25th September 2023, 5:30 PM - 7:00 PM (IST) Venue: $L^{\\infty}$-seminar room, 5th floor, Kolmogorov Bhavan SL2301: Weierstrass Approximation Through Bernstein Polynomials: When Probability Helps Analysis Speaker: Prof. Parthanil Roy (ISI, Bangalore) Abstract: In this lecture, a probabilistic proof of Weierstrass approximation theorem will be presented. Basic probability theory needed for the proof will be developed in a self-contained manner. The statement and motivation of the approximation theorem will also be discussed from the viewpoint of real analysis. This lecture will explain, among other things, how inter-dependent the two subjects (probability theory and real analysis) are. Special care will be taken so that this lecture is accessible to everyone. Slides: Available here Notes: Available here Video: (Not Recorded) Date and Time: Wednesday, 30th August 2023, 4:30 PM - 6:00 PM (IST) Venue: $L^{\\infty}$-seminar room, 5th floor, Kolmogorov Bhavan ","permalink":"https://mathclubisik.github.io/activities/expository_talks/special_lectures/sl_2023/","title":"Special Lectures 2023"},{"content":" Home/Members/Academic Year 2022-\u0026#39;23 The club started in the spring semester of the academic year 2022-\u0026lsquo;23 under the leadership of Snehinh Sen. The core team and active contributors of the club during this period were involved in organizing talks, foundational courses, and lecture series. The club\u0026rsquo;s activities were well-received by the students, and it helped in fostering a sense of community among the math and stat majors.\nCore Members Snehinh Sen (M. Math, 2024) Sonali Priyadarshini Behara (M. Math, 2024) Aytijha Saha (M. Stat, 2025) Archisman Mukherjee (B. Stat, 2024) Saptashwa Baisya (B. Stat, 2025) Active Contributors Rishiraj Baul (M. Math, 2024) Soham Mullick (M. Stat, 2024) Ritabrata Karmakar (M. Stat, 2024) Samprit Chakraborty (M. Stat, 2025) Koustav Mallick (B. Stat, 2024) Somarddha Das (B. Stat, 2025) Soupayan Dasgupta (B. Stat, 2025) Apart from the core team and active contributors, the club had regular participants who attended most of the lectures actively.\nRegular Participants (B. Stat, 2024) Aritra Ghosh, Swpnomoy Samadder, Swapnaneel Bhattacharya (B. Stat, 2025) Koustav Goswami, Rupsa Ray, Shambo Saha, Shreetama Bhuniya, Suvankar Saha, Swagato Das, Swastika Dey, Urjit Paul Chowdhury ","permalink":"https://mathclubisik.github.io/members/ay_2022_23/","title":"Academic Year 2022-'23"},{"content":"\rHome/Activities/Foundational Courses/Foundational Courses 2023 Fall 2023 FC2305: Random Walks and Mixing Times (continued into the next semester) [TBA]\nFC2304: Complex Analysis [TBA]\nSpring 2023 FC2303: Measure Theory and Probability Audience: B. Stat, 2nd year students and seniors Abstract: We will study measures and their properties. Starting with a relatively abstract yet motivated setup, we will try to study measures, the Lebesgue Integration Theory, some major results, product measures and the Radon-Nikdoym Theorem. This would be followed by some convergence issues and probability theoretic applications. Pre-requisites: Metric Topology, Probability and Riemann Integration. Instructors: Rishiraj Baul (M. Math, 2024) Soham Mallick (M. Stat, 2024) Schedule: All sessions will be held from 6:30 PM Lectures: Monday, 13th March 2023 Wednesday, 15th March 2023 Wednesday, 22nd March 2023 Monday, 27th March 2023 Wednesday, 29th March 2023 Monday, 3rd April 2023 Monday, 10th April 2023 Monday, 17th April 2023 FC2302: Metric Spaces and Topology Audience: Everyone Abstract: We will cover the very basics of metric spaces and generalise the notion of sequences and continuity. We will also discuss some introductory notions from Point Set Topology. Pre-requisites: None Instructors: Koustav Mallick (B. Stat, 2024) Sonali Priyadarsini Behara (M. Math, 2024) Schedule: All sessions will be held from 4:30 PM Lectures: Thursday, 23rd March 2023 Thursday, 30th March 2023 Thursday, 13th April 2023 Tuesday, 18th April 2023 Problem Sessions: Thursday, 6th April 2023 Thursday, 20th April 2023 Advanced Topic Session: Tuesday, 25th April 2023 FC2301: Group Theory Audience: B. Stat, 1st year students Abstract: This course will be an introduction to the theory of groups, specifically its role in the study of symmetry. We will also be discussing the axiomatic foundations of group theory as well as some number theory. Pre-requisites: None Instructor: Snehinh Sen (M. Math, 2024) Schedule: All sessions will be held from 4:30 PM, unless otherwise mentioned Lectures: Thursday, 9th March 2023 (Online, from 5:30 PM) Tuesday, 21st March 2023 Tuesday, 28th March 2023, Problem Session: Wednesday, 5th April 2023 Advanced Topic Session: Tuesday, 11th April 2023 ","permalink":"https://mathclubisik.github.io/activities/foundational_courses/fc_2023/","title":"Foundational Courses 2023"},{"content":" ","permalink":"https://mathclubisik.github.io/calendar/","title":"Calendar"},{"content":"[TBA]\n","permalink":"https://mathclubisik.github.io/activities/reading_groups/summer/summer_2023/","title":"DGRP Summer 2023"},{"content":"\rHome/Activities/Reading Groups/DGRP Summer Activities/DGRP Summer 2024 [TBA]\nTopics in Number Theory (Details to be provided later; this group was headed by Snehinh Sen (M. Math, 2024))\nDifferentiable Manifolds and Differential Forms (Started but did not progress much)\nCommutative Algebra This reading group is led by Saheb Mohapatra (M. Math, 2025), who is the best guide.\n","permalink":"https://mathclubisik.github.io/activities/reading_groups/summer/summer_2024/","title":"DGRP Summer 2024"},{"content":"[TBA]\nAnalytic Number Theory A reading course with some classes.\n","permalink":"https://mathclubisik.github.io/activities/reading_groups/winter/winter_2023/","title":"DGRP Winter 2023"},{"content":"\rHome/Activities/Reading Groups/DGRP Winter Activities/DGRP Winter 2024 Knot Theory What is a knot and what makes it safe when tied up? We\u0026rsquo;ll be exploring questions of this kind through in this winter group. We plan to rigorously understand what define a \u0026lsquo;knot\u0026rsquo;; \u0026lsquo;knotting\u0026rsquo; and \u0026lsquo;unknotting\u0026rsquo;. To study knots we would like to develop tools like Alexander and Jones Polynomials. Finally if time permits, we might try to touch up on bits \u0026amp; pieces of Khovanov Homology that will put knot theory in perspective with the way it interacts with topology.\nReferences: No strict choices but some options are: Knotes Knotes \u0026ndash; Justin Roberts Knots and Links \u0026ndash; Dale Rolfsen Knot theory and its applications \u0026ndash; Kunio Murasugi Group Leader: Prognadipto Majumder (M. Math 2026) Commutative Algebra and Algebraic Geometry of Curves Algebraic Geometry is the study of geometric objects, especially locus of zeroes of multivariate polynomials, using methods from algebra. Apart from having several applications in fields like number theory, complex geometry, and mathematical physics, it is also a very rich and thriving field on its own. It is closely related to the more abstract field of Commutative Algebra, which, as the name suggests, is a systematic study of commutative rings and objects related to them (like ideals, modules, algebras, etc.). In this group, we will try to learn the foundations of Commutative Algebra with a very clear focus on its geometric applications. We will mostly focus on curves, especially in the projective setup, and try to prove some fascinating results pertaining to them after developing the necessary algebra. Time permitting, and modulo some assumptions, we will also try to prove Fermat’s Last Theorem for $\\mathbb{C}[t]$ (with appropriate interpretation).\nNote: Even though Commutative Algebra is and would be very important for our considerations, we will only be learning the relevant parts for the sake of the geometry. If people are interested, I would be happy to provide references and meet separately to discuss more algebra. However, for the sake of this group, commutative algebra would mostly be the “language” for us to study algebraic curves.\nPre-requisites: A working understanding of rings and fields (at the level of Algebraic Structures course in ISI Kolkata) is very important. Geometric ideas about curves and their tangents are also helpful. Projective Geometric intuition, though not necessary, might be helpful. Same goes for module theory. Primary References: No strict choices but some options are: Algebraic Curves \u0026ndash; William Fulton Elementary Algebraic Geometry \u0026ndash; Kenneth Kendig Group Leader: Snehinh Sen (M. Math 2024) ","permalink":"https://mathclubisik.github.io/activities/reading_groups/winter/winter_2025/","title":"DGRP Winter 2024"},{"content":" LS2301: Rings and Dimensions Speaker: Snehinh Sen (M. Math, 2024) Abstract: [TBA] Date and Time: [TBA] Venue: [TBA] Videos: (Not Recorded) ","permalink":"https://mathclubisik.github.io/activities/lecture_series/ls_2023/","title":"Lecture Series 2023"},{"content":"Here are a few guidelines you need to follow. To present a talk, fill the form given on the website with the following details:\nYour name. An email id that you check regularly so that we can contact you. Your batch and roll number. A tentative topic for the talk .We request that the topics you choose should be such, that most of the the talk is accessible at the undergraduate level. A small description of your tentative topic. Is it an expository talk or a lecture series. (An Expository Talk would be a single session for about 60-90 minute and a lecture series would be about two to three sessions, adjustable, of about one hour.) Also, it would be helpful if you can mention tentative pre-requisites of the talk, though this field is not compulsory. After we receive your form, we will go through it and contact you back through the mail id mentioned. We will pick few options for a tentative date and let you know. Following that, you have to choose a date and send your final topic, abstract and pre-requisite (this time compulsory). We shall finalise the same and post it on our website.\nIf you are interested to give a talk or a lecture series, fill the following form and we will get back to you as soon as possible.\nGoogle Forms ","permalink":"https://mathclubisik.github.io/participate/present_talks/","title":"Present Talks"},{"content":"\rHome/Participate/Submit Articles and Notes We encourage you to write articles and notes throughout your time at ISI. If you are interested and do not mind, feel free to contact us and send us your articles/notes. We shall post the same in our website to give easy access to every student of ISIB and beyond. Right now, we shall be accepting the following:\nArticles (pre-print/published) and Expository Notes. Additional Notes based on topics of interest (includes alternate proofs, some extra topic, etc.). Interesting Problems with attempts at solution (\\(\\LaTeX\\) typed or links, former preferred). Here are a few Guidelines you need to follow. Guidelines for submitting articles or notes To submit any article or notes on some interesting mathematical topic that you may wish to be put up on the website, write a mail to the official club email address mathclub.isical@gmail.com with the subject \u0026ldquo;Submission of article for club website\u0026rdquo;. Please include with the mail, your name, title of the article, a brief abstract of the article, and the mathematical topics it covers. In case your article is already uploaded on some site such as arXiv or ResearchGate, it suffices to share the link of your article. If not, we request you to send a pdf file of your article, preferably written using \\(\\LaTeX\\).\nYour submission will be reviewed by the appropriate club members, after which you shall be contacted by the club regarding any minor revisions, if needed, within a few days. Once accepted, your article or notes will be put up on the site under Articles section, in pdf form, or the link as submitted by you. We are looking forward to your submissions\nGuidelines for submitting Problem specific notes or problem collections To submit any problem collection or problem specific notes or any interesting original problem that you may wish to be put up on the website, write a mail to the official club email address mathclub.isical@gmail.com with the subject \u0026ldquo;Submission of Problem note for club website\u0026rdquo;. In case it is a problem collection already uploaded on some site or blog, it suffices to share the link of the site. If not, we request you to send a pdf file of your problem note, preferrably written using \\(\\LaTeX\\). It is highly recommended, that you share some of your own progress or thoughts on the problem(s), as well.\nInstead, if you want to post puzzles or questions for weekly contests, visit the following page.\nWe are looking forward to your submissions!\n","permalink":"https://mathclubisik.github.io/participate/submit_articles_and_notes/","title":"Submit Articles and Notes"},{"content":"\rHome/Participate/Submit Doubts Here are a few Guidelines you need to follow\nTo submit a question, use the form given on the website. We\u0026rsquo;ll try to get back to you as soon as possible. See if your question is more suitable for a StackExchange post or office hours of your instructor We encourage you to try these avenues first but feel free to send your doubts our way.\nFill the form with the following details:\nYour name and email id (one that you check regularly), so that we may contact you. The question and your current understanding of the problem at hand, possibly including ways in which you tried to tackle the problem (try to be as specific as possible). Doing this may clear the doubt! (Try to use \\(\\LaTeX\\) to typeset the math, which is highly recommended, or use clear handwriting for the sake of our mental health) Source of the doubt (if it\u0026rsquo;s a line in a book or lecture notes, a screenshot or pdf). We will try to get back to you as soon as possible, addressing the doubt the best we can, possibly with a reference that we think may help clear the doubt and/or posting the same on our website where participants and members can try it together.\nIf you are interested to submit a doubt, fill the following form and we will get back to you as soon as possible.\n","permalink":"https://mathclubisik.github.io/participate/submit_doubts/","title":"Submit Doubts"},{"content":"\rHome/Participate/Submit Problems If you want to submit questions for weekly contests, general collection on website or which are of puzzle type, it is highly encouraged! We would love to have such puzzles and questions from you. However, along with the question, you should also have a solution ready.\nHere are a few Guidelines you need to follow:\nGuidelines You would need a typed (preferably \\(\\LaTeX\\)ed) document with (if possible) the source file containing the problem and the solution to the question.\nHere are a few things to keep in mind:\nTry to be as descriptive as possible while writing the solutions and questions. For example, defining or referencing non-standard definitions or notations, avoiding unobvious step jumps, etc. After your document is ready, fill in the submission portal form with necessary details. Make sure to give us references or sources if any. After submission, we will go through the problem and store it for future usage. (Your name will be mentioned). If we see there is some unclarity in the question or in the proof, we will contact you regarding the same, so please submit an active email account in the form for this purpose. If you are interested to submit a question for the website, fill the following form and we will get back to you as soon as possible.\n","permalink":"https://mathclubisik.github.io/participate/submit_problem/","title":"Submit Problems"}]