IITG Mathematics Seminar Series
| Lecture Number: | 380 |
| Title: | An overview on metric fixed point theory |
| Speaker: | Professor Mantu Saha |
| Affiliation: | The University of Burdwan, West Bengal |
| Date: | 08th June, 2023 (Thursday) |
| Time: | 04:00 PM (Venue: Seminar Room, Department of Mathematics) |
Abstract: The main objective of our discussion is to focus on the survey of literature of metric fixed-point theory for a class of contractive mappings on metric spaces. The mappings under consideration might be of either continuous or discontinuous nature. Some existential criteria of fixed points with its uniqueness property of such mappings will come into our discussion. Examples and counter examples will be given in support of our results. The motivation of our discussion is to give emphasis on some applications of fixed point theorems for a class of such contractive mappings over a metric space.
| Lecture Number: | 379 |
| Title: | Modeling Long Term Return Distribution and Nonparametric Market Risk Estimation |
| Speaker: | Prof. Santanu Dutta |
| Affiliation: | Department of Mathematical Sciences, Tezpur University |
| Date: | 14th March, 2023 (Tuesday) |
| Time: | 04:00 PM (Venue: Seminar Room, Department of Mathematics) |
Abstract: The log-return of an asset is the change in the asset price, measured in natural logarithmic scale, over a certain time period. We introduce a mathematical model for long term asset return. This model is a generalization of the well-known random walk model and provides the mathematical basis for normal approximation and i.i.d. bootstrap
approximation of the long-term return distribution and its quantiles. Our results yield estimators of long-term value at risk (VaR) and median shortfall (MS) which are well-known measures of market risk. Extensive simulations suggest that the proposed estimators outperform a number of existing estimators of VaR and MS especially over a time horizon of at least one year. Unconditional backtest by Kupiec (J. Derivat. 3, 73–84 1995) based on the annual returns of the Nifty 50 index of the national stock exchange in India, crude oil and gold prices suggests that the proposed model yields reliable estimates of the one-year Value-at-Risk and Median-Shortfall for these assets.
| Lecture Number: | 378 |
| Title: | On the abc Conjecture and some of its consequences. |
| Speaker: | Prof. Michel Waldschmidt |
| Affiliation: | faculty member at CNRS, University of Paris-Sud and University of Paris VI |
| Date: | 27th February, 2023 (Monday) |
| Time: | 11:30 PM (Venue: Seminar Room, Department of Mathematics) |
Abstract: We explain the statement of the abc Conjecture proposed by Oesterlé and Masser in the mid 80's and we give a collection of easy to state consequences of this conjecture. It will not include an introduction to the Inter-universal Teichmüller Theory of Shinichi Mochizuki.
| Lecture Number: | 377 |
| Title: | Asymptotic Analysis of an eigenvalue problem on long cylinders |
| Speaker: | Dr. Prosenjit Roy |
| Affiliation: | Associate Professor, Department of Mathematics & Statistics, IIT Kanpur |
| Date: | 24th January, 2023 (Tuesday) |
| Time: | 04:00 PM (Venue: Seminar Room, Department of Mathematics) |
Abstract: The asymptotic behavior of the eigenvalue of an elliptic operator, defined on cylindrical domains whose length tends to infinity, will be investigated in this talk. We will see that the limit problem can be identified with an appropriate problem defined on a lower dimensional set, namely the cross-section of the cylinder. The talk will be kept at an elementary level and will be accessible to graduate students.