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A quantum analogue of complex plane is the C*-algebra B "generated" by an unbounded operator n satisfying the commutation relation n^{*}n=q^{2}nn^{*} for some real number 0

This series of talks will cover various notions of zeta functions associated to graphs

In this talk, we will give an alternate (and constructive) proof to a result of Luc Tartar which demonstrated the loss of semi-group structure due to the presence of high frequency oscillations in coefficients. The discussions will revolve around (i) the notion of weak convergence in Lp spaces; (ii) the notion of two-scale convergence in the theory of homogenization. Furthermore, we shall discuss some interesting results in the context of (i) structure breaking in other differential equations; (ii) inverse homogenization. We also intend to list some related open problems which are accessible to available techniques.

In this talk, we will address the homogenization of a neutron transport model while the scattering coefficients in the equation exhibit rapid oscillations with respect to the energy variable. It turns out that this problem has very close links to a result of Luc Tartar from late 1980's. Hence we will be revisiting this paper of Luc Tartar. Our discussions will revolve around (i) Laplace transform and Bernstein's theorem from the theory of Regular variation (ii) Nevanlinna-Herglotz function from complex analysis (iii) Two-scale convergence and Young measures from the theory of homogenization. This talk is based on a recent preprint: Harsha Hutridurga, Olga Mula, Francesco Salvarani, Homogenization in the energy variable for a neutron transport model, arXiv:1901.10164 Weblink: https://arxiv.org/pdf/1901.10164.pdf

In this talk, I shall first give an introduction to the subject of dynamical systems. After going through a few concepts that arise in dynamical systems through examples, we see how similar ideas can be interpreted in the context of linear algebra. In particular, we deal with finite dimensional complex vector spaces and end by understanding a simple proof of the Cayley-Hamilton theorem. An interesting aspect of this approach is that we can avoid the machinery of determinants altogether.

I will give an introductory course of 3-4 lectures on the topics mentioned in the title to an audience without any prior knowledge of the subject which is a meeting ground for Differential geometry, Algebraic geometry, and Number theory.

This series of talks will cover various notions of zeta functions associated to graphs.