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Details |
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| Overview | Bhaskaracharya Pratishthana is organising a Symposium in Mathematics for Mathematics students and teachers on the occasion of the Birth Day of Founder Director Professor Shreeram S. Abhyankar, a world famous Mathematician. Prof. Abhyankar was born on 22nd July 1930 in Ujjain. |
| Venue | Bhaskaracharya Pratishthana |
| Date | Friday, 22nd July 2016 |
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Speakers |
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| Sr. | Name | Affiliation |
| 1 | Professor M. S. Narasimhan | TIFR, Mumbai |
| 2 | Professor M. S. Raghunathan | IIT Bombay |
| 3 | Professor Sudhir Ghorpade | IIT Bombay |
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Programme |
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| Sr. | Time | Speaker | Title | ABSTRACT: |
| 1 |
03:00 PM |
Prof. M. S. Narasimhan | Geometry Beyond Euclid | The talk will deal with some aspects of geometry which have gone beyond Euclid's "Elements". I will treat some concepts and problems that arose in this process and their role in the development of algebraic and differential geometry.The three famous "Greek" problems of antiquity involving constructions with ruler and compass and their relation to algebra and algebraic geometry will be discussed. I will also discuss the "Parallel Postulate" of Euclid and and how it served as a catalyst to the evolution of non-euclidean and Riemannian Geometry. |
| 2 | 04:20 PM to 05:20 PM |
Prof. M. S. Raghunathan | The Inverse and Implicit Function Theorems | The inverse and implicit function theorems are arguably by far the most important and foundational results in Differential Geometry. It is the implicit function theorem that led one to a proper definition of a differentiable manifold. And in general in differential geometry and differential topology it has a central role. In this talk I will give a proof (which is not found in the standard literature) of the inverse function theorem - the implicit function theorem is equivalent to it. I will then go on to define the notion of a differentiable manifold. Time permitting I will give proofs of the Fundamental theorem of algebra and the Brouwer fixed point theorem using the implicit function theorem. |
| 3 | 05.35 PM to 06.35 PM |
Prof. Sudhir Ghorpade | Glimpses of Abhyankar's work on Young tableaux and Determinantal Varieties | Shreeram Shankar Abhyankar (1930–2012) was an extraordinary mathematician and educator, who has contributed significantly to many parts of mathematics and has left a lasting influence on numerous students and peers. In this talk, we will attempt to provide glimpses of major research contributions of Abhyankar, with particular emphasis on the period 1982–1988 during which he worked almost exclusively on enumerative combinatorics on Young tableaux and its applications to determinantal varieties. In particular, we will give a short account of Schubert varieties (in Grassmannians and in flag manifolds) and questions concerning them that led Abhyankar to enumerative combinatorics of Young tableaux. We will outline Abhyankar’s enumerative proof of the straightening law of Doubilet-Rota-Stein and the remarkable consequences of this approach to an explicit determination of the multiplicity and Hilbert function of a class of determinantal varieties. Connections with lattice path combinatorics will be highlighted and we will give a sketch of an alternative proof of Abhyankar’s formula using the counting of families of nonintersecting lattice paths with a given number of turns. If time permits, we will touch upon some of the subsequent developments influenced by Abhyankar’s work on enumerative combinatorics. |
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Registration |
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| 1 | Registration form is closed for 2016 |
| 2 | Please click here for the list of participants |