IITG Mathematics Seminar Series

Lecture Number: | 316 |

Title: | Spectral Approximation for Self-adjoint Operators, by Truncation |

Speaker: | Prof. Kalyan B. Sinha |

Affiliation: | SERB Distinguished Associate, Theoretical Sciences Unit, JNCASR and NMI Distinguished Associate, IISc |

Date: | 22nd March, 2018 (Thursday) |

Time: | 4:15 PM |

Abstract: Arveson's program of numerical spectral approximation is extended to unbounded self-adjoint operators, with a view for applications to Schrodinger Operators. Several Szego-type theorems are proven for such operators, showing that the empirical density of eigenvalues, under suitable hypothesis on the so-called degree of the operator, converges to the density of the essential spectrum.

Lecture Number: | 315 |

Title: | Two Open Problems in Linear Algebra |

Speaker: | Prof. Michael Karow |

Affiliation: | Institute for Mathematics, TU Berlin, Germany |

Date: | 6th March, 2018 (Tuesday) |

Time: | 4:00 PM |

Abstract: This talk is about two (unrelated) problems. The first concerns the construction of a subspace of maximal dimension on which two Hermitian forms are simultaneously positive definite. The second problem is about estimating the size of pseudospectra of block triangular matrices.

Lecture Number: | 314 |

Title: | Confinement and nonlocal elasticity effects in premelting dynamics |

Speaker: | Dr. Satyajit Pramanik |

Affiliation: | Post-Doctoral Researcher, Nordic Institute for Theoretical Physics, Sweden |

Date: | 22nd February, 2018 (Thursday) |

Time: | 4:00 PM |

Abstract: Abstract: We study the combined effects of non-local elasticity and confinement induced ordering on the dynamics of thermomolecular pressure gradient driven premelted films bound by an elastic membrane. The confinement induced ordering is modeled using a film thickness dependent viscosity (Pramanik & Wettlaufer 2017 *Phys. Rev. E* *96*, 052801). When there is no confinement induced ordering, we recover the similarity solution for the evolution of the elastic membrane, which exhibits an infinite sequence of oscillations (Wettlaufer *et al.* 1996 *Phys. Rev. Lett. **76*, 3602-3605). However, when the confinement-induced viscosity is comparable to the bulk viscosity, the numerical solutions of the full system reveal the conditions under which the oscillations vanish. Implications for general thermomechanical dynamics, frost heave observations, and cryogenic cell preservation are discussed.

Lecture Number: | 313 |

Title: | Finite Element Model Updating : A Wonderful Inverse Eigenvalue Problem |

Speaker: | Prof. Biswa Nath Datta |

Affiliation: | Distinguished Research Professor, Northern Illinois University, USA |

Date: | 20th February, 2018 (Tusday) |

Time: | 4:00 PM |

Abstract: The Finite Element Model Updating concerns updating a finite element generated second-order model of some specified structures in such way that a set of prescribed eigenvalues and eigenvectors are reproduced, the other eigenvalues and eigenvectors remain unchanged and the updated model maintains the same structures as the original model. The problem routinely arises in vibration industries, such as automobile, aerospace, and spacecraft. A properly updated model can be used by the engineers with confidence for future designs and manufacturing.

Mathematically, it is a partially prescribed structured quadratic inverse eigenvalue problem. Since, the problem was formulated in quadratic inverse eigenvalue setting by the speaker in 2001, much research has been done by both mathematicians and engineers, but, unfortunately, the problem still has not satisfactorily been solved. The structure preservation is the most difficult aspect of the problem. Some notable progress has been made in the last few years by the speaker and his collaborators.

This talk will discuss (i) how the problem arises in industries, (iii) mathematical formulation of the problem in the quadratic inverse eigenvalue setting, (iii) mathematical, computational and engineering challenges, (iv) the progress made so far, and (v) the future research

The talk is interdisciplinary blending mathematics, scientific computing, optimization with vibration engineering and structural dynamics , and will be of interests to students, researches and practicing engineers in these disciplines.

Lecture Number: | 312 |

Title: | The Journey of Lagrange and Applications of Euler-Lagrange Equations in Fluid Mechanics. |

Speaker: | Prof. G. P. Raja Sekhar |

Affiliation: | Professor, Indian Institute of Technology, Kharagpur |

Date: | 25th January, 2018 (Thursday) |

Time: | 5:00 PM |

Abstract: This talk introduces in brief the popular contributions of Joseph-Louis Lagrange and his journey. A brief outline on Lagrange's interaction with Euler will be discussed before introducing the Lagrange equations of second kind or Euler-Lagrange equations. A fluid mechanical problem of lifting a large object that is sunken in a fluid and lying in a neutrally buoyant condition on top of a fluid filled anisotropic porous bed will be discussed in detail. The talk introduces the corresponding Euler-Lagrange equations and then mechanics of break -out phenomenon while lifting such an object will be discussed. This problem has direct application in salvaging sunken ships, moving object at offshore, submersible - engineering etc. .

Lecture Number: | 311 |

Title: | Maximum Principle and Harnack's Inequality |

Speaker: | Prof. Mrinal Kanti Ghosh |

Affiliation: | Indian Institute of Science, Bangalore |

Date: | 17th January, 2018 (Wednesday) |

Time: | 4:00 PM |

Abstract: We begin with classical harmonic functions. Using mean value theorem we show how to establish maximum principle and Harnack's inequality for classical harmonic functions. Then we provide a probabilistic approach to these problems. Next we discuss more general uniformly elliptic equations and establish similar results using probabilistic methods. Finally we treat uniformly elliptic systems with weak coupling and establish maximum principle and Harnack's inequality for such systems.

Lecture Number: | 310 |

Title: | In the neighbourhood of Sato-Tate conjecture |

Speaker: | Dr. Sudhir Pujahari |

Affiliation: | Post-Doctoral Fellow, Harish-Chandra Research Institute, Allahabad |

Date: | 4th January, 2018 (Thursday) |

Time: | 3:30 PM |

Abstract: In this talk, we will discuss the distribution of gaps between eigenangles of Hecke operators acting on the space of cusp forms of weight $k$ and level $N$, spaces of Hilbert modular forms of weight $\underline k=(k_1,k_2,\dots,k_r)$ and space of primitive Maass forms of weight $0$. Moreover, we will see a stronger version of multiplicity one theorem for the space of cusp forms of weight $k$ and level $N.$ The last part is a joint work with M. Ram Murty.