C3

TBC

Einstein’s theory of general relativity reshaped our understanding of the universe. Instead of thinking of gravity as a force, Einstein showed it is the bending and warping of space and time caused by mass and energy. This radical idea not only explained how planets orbit stars, but also opened the door to astonishing predictions. In this seminar we will explore some of its most fascinating consequences from the expansion of the universe, to gravitational waves, and the existence of black holes.

The electrochemical processes in electrolytic cells are the basis for modern energy technology such as batteries. Electrolytic cells consist of an electrolyte (an salt dissolved in solution), two electrodes, and a battery. The Poisson–Nernst–Planck equations are the simplest mathematical model of steady state ionic transport in an electrolytic cell. We find the matched asymptotic solutions for the ionic concentrations and electric potential inside the electrolytic cell with mass conservation and known flux boundary conditions. The mass conservation condition necessitates solving for a higher order solution in the outer region. Our results provide insight into the behaviour of an electrochemical system with a known voltage and current, which are both experimentally measurable quantities.

With the classification theory of simple and nuclear C*-algebras of real rank zero advanced to a level which may very well be final, it is natural to wonder what happens when one allows ideals, but not too many of them. Contrasting the simple case, the K-theoretical classification theory for real rank zero C*-algebras with finitely many ideals is only satisfactorily developed in subcases, and in many settings it is even unclear and/or disputed which flavor of K-theory to use.

Restricting throughout to the setting of real rank zero, Søren Eilers will compare what is known of the classification of graph C*-algebras and of approximately subhomogeneous C*-algebras, with an emphasis on what kind of conclusion can be extracted from restrictions on the complexity of the ideal lattice. The results presented are either more than a decade old or joint with An, Liu and Gong.

An epsilon-representation of a discrete group G is a map from G to the unitary group U(n) that is epsilon-multiplicative in norm uniformly across the group. In the 1980s, Kazhdan showed that surface groups of genus at least 2 are not uniform-to-local stable in the sense that they admit epsilon-representations that cannot be perturbed, even locally (on the generators), to genuine representations.
 

In this talk, Marius Dadarlat of Purdue University will discuss the role of bounded 2-cohomology in Kazhdan's construction and explain why many rank-one lattices in semisimple Lie groups are not uniform-to-local stable, using certain K-theory properties reminiscent of bounded cohomology.

We present Gromov's celebrated reconstruction theorem in Lorentzian geometry and show two applications. First, we introduce several notions of convergence of (isomorphism classes of) normalized bounded Lorentzian metric measure spaces, for which we describe several fundamental properties. Second, we state a version within the spacetime reconstruction problem from quantum gravity. Partly in collaboration with Clemens Sämann (University of Vienna).

We study the fixed points of the Berezin transform on the Fock-type spaces F^{2}_{m} with the weight e^{-|z|^{m}}, m > 0. It is known that the Berezin transform is well-defined on the polynomials in z and \bar{z}. In this talk from Ghazaleh Asghari from Reading University, we focus on the polynomial fixed points and we show that these polynomials must be harmonic, except possibly for countably many m \in (0,\infty). We also show that, in some particular cases, the fixed point polynomials are harmonic for all m.