| Personal Information | |
| NAME | Neeraj Kumar |
| PRESENT ADDRESS | Indian Institute of Science Education and Research, Kolkata |
| E-115 ICVS Hall, IISER Kolkata Campus | |
| Mohanpur, Nadia - 741 246 | |
| West Bengal, India | |
| MOBILE NO. | +91 8016560258 |
| neerajk095@gmail.com, nk12ms043@iiserkol.ac.in | |
| LANGUAGES | English (fluent), Hindi (native), French (basic, written) |
| NATIONALITY | INDIAN |
| Research Interests | |
| My interests, broadly, lie in Algebra, Topology and Geometry. My studies so far have revolved around Lie and Topological groups, with an interplay of representation theory, differential geometry and algebraic topology. | |
| Educational Qualifications | |
| 2012 - 2017 | Five years Integrated Dual B.S. - M.S. |
| DISCIPLINE | Mathematical Sciences |
| THESIS | The master's thesis was titled Maximal torus in a Lie group and its Weyl group . It was a study of Lie groups- starting from the basics, and up till the maximal torus in compact connected Lie groups. The main result studied was the Conjugation theorem of Maximal Tori, primarily following the text by Theodor Brocker and Tammo tom Dieck on the subject, along with J.P. Serre's articles in Seminaire Sophus Lie}. |
| INSTITUTION | Indian Institute of Science Education and Research, Kolkata, India |
| CGPA | 8.01 (absolute grading & in scale of 10.) |
| SEMESTER GPA | Sem 1: 8.44 Sem 2: 7.89 Sem 3: 7.96 Sem 4: 8.08 Sem 5: 7.71 |
| Sem 6: 7.43 Sem 7: 7.83 Sem 8: 8.33 Sem 9: 8.20 Sem 10: 8.60 | |
| MAJOR COURSES | Linear Algebra, Analysis I, Analysis II (Differentiation, Integration, etc.), Algebra I (Group theory), Analysis III (Metric Space Topology and Calculus in n-dimensional Euclidean space), Topology, Geometry of Curves and Surfaces, Algebra II (Ring, Field and Galois Theory), Analysis IV (Measure Theory), Complex Analysis, Functional Analysis, Algebra III (Commutative algebra), Differential Geometry, Algebraic Topology, Riemannian Geometry, Riemann Surfaces, Partial Differential Equations. |
| OTHER COURSES | Fourier Analysis, Sobolev Spaces: Theory and Applications , Probability and Statistics, Mathematical Statistics I, Graph Theory and Combinatorics, Elementary Number Theory, Advanced Data Structures and Algorithms, Inverse Theory, Numerical Analysis Laboratory, Foundations I and II & Computer Laboratory, Mathematics I (Vector Calculus, Matrices- Linear Algebra, Multiple integration, etc.) & Statistics Laboratory, Mathematics II (Ordinary Differential Equations). |
| 2017 - 2018 | |
| BREAK YEAR | I took a break after completing my MS due to health problems. During the two years of my MS, I was suffering from some problems related to chronic sleep issues, fatigue and a form of IBS (Inflammatory Bowel Syndrome). Although the problem wasn't severe yet its nature was chronic, so I was informed by the doctor that it should be treated slowly over a long treatment gradually. Therefore I took a break from the mid of 2017 to mid of 2018 during which I had the treatment. After that I decided to do a project before applying for a PhD - the details of which are as mentioned below. |
| 2018 - 2019 | |
| PROJECT | Root Systems, Weyl Character Formula and Spin groups. This project followed up on the thesis, studying the representations of compact Lie groups. It began with a recall of representation theory with an introduction to weights and roots. Later, the Root systems were covered in detail, including the Dynkin diagrams and the fundamental groups of compact Lie groups. Finally, the Weyl Character Formula was covered. This was followed by computations for the case of the classical Lie groups using the WCF. Afterwards, Clifford algebras and the Spin groups were studied using the lecture notes by B. Conrad and R. Borcherds and later the text by Brocker and Dieck was followed for the calculation of its maximal torus, Weyl group, root system and, finally the application of WCF to compute its representations. |
| CURRENT | After its completion, I was directed by Dr. Datta to study Algebraic topology, with the aim to study Poincare Duality because of its importance in the study of geometry and topology. The book by Allen Hatcher is being followed. The study started with Homology theory- Simplicial, Singular and Cellular homology. It also included some of its classical applications such as Borsuk-Ulam theorem and Lefshetz fixed point theorem. After its completion, the study is moving to Cohomology. |
| Research Experience | |
| AUG. 2011 - JUL. 2012 | Visiting Student Research Programme 2016 |
| SUPERVISOR | Dr. Sandeep Varma, Tata Institute for Fundamental Research (TIFR) Mumbai, India. |
| ABSTRACT | A version of Peter Weyl Theorem for compact quotients. The project was a study of the representations of Topological groups. It starting with the necessary preliminaries, such as a proof of the existence of Haar measure on locally compact topological groups, and the Hilbert space theory. Afterwards, the notes by Paul Garett- Unitary Representations of Topological groups was followed, from the start till the section number 22, where we concluded with the Peter Weyl Theorem- a version for the compact quotients of locally compact topological groups. |
| AUG. 2011 - JUL. 2012 | Student Project 2015 |
| SUPERVISOR | Dr. Neena Gupta, Indian Statistical Institute, Kolkata, India. |
| ABSTRACT | Commutative Algebra. The project was a study in Commutative Algebra, which comprised of the continuation of the Ring theory course from the previous semester, using the text Introduction to commutative Algebra by Atiyah and Macdonald. The topics covered were Rings, Ideals and Module theory. |
| AUG. 2011 - JUL. 2012 | Student Research Fellowship Programme 2014 |
| SUPERVISOR | Prof. A. J. Parameswaran, TIFR Mumbai, India. |
| ABSTRACT | Linear and Homological Algebra. The project involved the study of the linear and abstract algebraic structures with some elements of multilinear algebra following the classic text on the subject Finite Dimensional Vector Spaces by Paul R Halmos and the TIFR pamphlet in mathematics Algebraic Topology. Further, the pamphlet Homological Methods in Commutative Algebra was referred for some applications of linear algebra to Homology such as the Euler Characteristics. |
| Computer Skills | |
| OPERATING SYS. | Microsoft Windows (7, XP) and Linux (Ubuntu, Debian, Fedora). |
| PROGRAMMING LANGS. | C, C++, Python, R. |
| SCRIPTING LANGS. | LaTeX and HTML. |
| SOFTWARES | Octave, Origin and Libre Office. |
| Achievements and Awards | |
| 2012 - 2017 | Awarded INSPIRE Fellowship by the Department of Science and Technology, India. |
| NOV. 2017 | General Graduate Record Examination (GRE) 329 out of 340 (Verbal Reasoning: 163/170, Quantitative Analysis: 166/170). |
| DEC. 2017 | Qualified National Eligibility Test (NET) - All India Rank (AIR) : 73 |
| JAN. 2020 | Test of English as a Foreign Language (TOEFL) 110 out of 120. (Reading: 28/30, Listening: 29/30, Speaking: 27/30, Writing: 26/30). |
| JUN. - JUL. 2016 | Selected for Visiting Student Research Programme 2016 at Tata Institute for Fundamental Research (TIFR) Mumbai. |
| MAY - JUL. 2014 | Selected for Student Research Fellowship Programme 2014 by Indian Academy of Sciences, and assigned an internship at Tata Institute for Fundamental Research (TIFR) Mumbai. |
| 2009 (CLASS X) | All India Rank 15, and State Rank 1, in Junior Mathematics Olympiad organized by Kendriya Vidyalaya Sangathan, New Delhi, India. |
| Extracurricular Interests | |
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| References | |
| NAME | Dr. Swarnendu Datta (Thesis Guide) |
| INSTITUTE | Indian Institute of Science Education and Research, Kolkata, India |
| EMAIL ID | swarnendu.datta@iiserkol.ac.in |
| NAME | Dr. Shibananda Biswas |
| INSTITUTE | Indian Institute of Science Education and Research, Kolkata, India |
| EMAIL ID | shibananda@iiserkol.ac.in |
| NAME | Dr. Sushil Gorai |
| INSTITUTE | Indian Institute of Science Education and Research, Kolkata, India |
| EMAIL ID | sushil.gorai@iiserkol.ac.in |