Seminars and Colloquia by Series

Tuesday, November 7, 2017 - 13:00 , Location: Skiles 006 , Günter Stolz , University of Alabama, Birmingham , , Organizer: Michael Loss
Tuesday, November 7, 2017 - 10:00 , Location: Skiles 006 , Yulia Karpeshina , University of Alabama, Birmingham , , Organizer: Michael Loss
  Existence of ballistic transport for Schr ̈odinger operator with a quasi- periodic potential in dimension two is discussed. Considerations are based on the following properties of the operator: the spectrum of the operator contains a semiaxis of absolutely continuous spectrum and there are generalized eigenfunctions being close to plane waves ei⟨⃗k,⃗x⟩ (as |⃗k| → ∞) at every point of this semiaxis. The isoenergetic curves in the space of momenta ⃗k corresponding to these eigenfunctions have a form of slightly distorted circles with holes (Cantor type structure). 
Friday, October 27, 2017 - 15:00 , Location: Skiles Room 202 , Rafael Benguria , Catholic University of Chile , , Organizer: Michael Loss
During the last few years there has been a systematic pursuit for sharp estimates of the energy components of atomic systems in terms of their single particle density. The common feature of these estimates is that they include corrections that depend on the gradient of the density. In this talk I will review these results. The most recent result is the sharp estimate of P.T. Nam on the kinetic energy. Towards the end of my talk  I will present some recent results concerning geometric estimates for generalized Poincaré inequalities obtained in collaboration with C. Vallejos and H. Van Den Bosch. These geometric estimates are a useful tool to estimate the numerical value of the constant of Nam's gradient correction term.
Tuesday, March 28, 2017 - 15:00 , Location: Skiles 005 , Alissa Geisinger , University of Tuebingen, Germany , , Organizer: Michael Loss
We consider the two-dimensional BCS functional with a radial pair interaction. We show that the translational symmetry is not broken in a certain temperature interval below the critical temperature. For this purpose, we first introduce the full BCS functional and the translation invariant BCS functional. Our main result states that theminimizers of the full BCS functional coincide with the minimizers of the translation invariant BCS functional for temperatures in the aforementioned interval. In the case of vanishing angular momentum our results translate to the three dimensional case. Finally, we will explain the strategy and main ideas of the proof. This is joint work with Andreas Deuchert, Christian Hainzl and Michael Loss.
Tuesday, March 14, 2017 - 15:00 , Location: Skiles 005 , Tobias Ried , Karlsruhe Institute of Technology , , Organizer: Michael Loss
We study regularity properties of weak solutions of the homogeneous Boltzmann equation. While under the so called Grad cutoff assumption the homogeneous Boltzmann equation is known to propagate smoothness and singularities, it has long been suspected that the non-cutoff Boltzmann operator has similar coercivity properties as a fractional Laplace operator. This has led to the hope that the homogenous Boltzmann equation enjoys similar smoothing properties as the heat equation with a fractional Laplacian. We prove that any weak solution of the fully nonlinear non-cutoff homogenous Boltzmann equation (for Maxwellian molecules) with initial datum $f_0$ with finite mass, energy and entropy, that is, $f_0 \in L^1_2(\R^d) \cap L \log L(\R^d)$, immediately becomes Gevrey regular for strictly positive times, i.e. it gains infinitely many derivatives and even (partial) analyticity.This is achieved by an inductive procedure based on very precise estimates of nonlinear, nonlocal commutators of the Boltzmann operator with suitable test functions involving exponentially growing Fourier multipliers.(Joint work with Jean-Marie Barbaroux, Dirk Hundertmark, and Semjon Vugalter)
Monday, November 14, 2016 - 15:00 , Location: Skiles 005 , Tobias Kuna , Unisrsity of Reading, UK , Organizer: Federico Bonetto
The discrete truncated moment problem considers the question whether given a discrete subsets $K \subset \mathbb{R}$ and a sequence of real numbers one can find a measure supported on $K$ whose (power) moments are exactly these numbers. The truncated moment is a challenging problem. We derive a minimal set of necessary and sufficient conditions. This simple problem is surprisingly hard and not treatable with known techniques. Applications to the truncated moment problem for point processes, the so-called relizability or representability problem are given. The relevance of this problem for statistical mechanics in particular the theory of classic liquids, is explained. This is a joint work with M. Infusino, J. Lebowitz and E. Speer.
Friday, April 15, 2016 - 14:05 , Location: Skiles 006 , Alex Grigo , The University of Oklahoma , , Organizer: Federico Bonetto
In this talk we will consider a few different mathematical models of gas-like systems of particles, which interact through binary collisions that conserve momentum and mass. The aim of the talk will be to present how one can employ ideas from dynamical systems theory to derive macroscopic properties of such models.
Friday, October 16, 2015 - 14:00 , Location: Skiles 006 , Ben Webb , Brigham Young University , Organizer: Federico Bonetto
We consider the motion of a particle on the two-dimensional hexagonal lattice whose sites are occupied by flipping rotators, which scatter the particle according to a deterministic rule. We find that the particle's trajectory is a self-avoiding walk between returns to its initial position. We show that this behavior is a consequence of the deterministic scattering rule and the particular class of initial scatterer configurations we consider. Since self-avoiding walks are one of the main tools used to model the growth of crystals and polymers, the particle's motion in this class of systems is potentially important for the study of these processes.
Tuesday, February 17, 2015 - 14:05 , Location: Skiles 005 , Almut Burchard , University of Toronto , Organizer: Michael Loss
Two-point symmetrizations are simple rearrangementsthat have been used to prove isoperimetric inequalitieson the sphere. For each unit vector u, there is atwo-point symmetrization that pushes mass towardsu across the normal hyperplane.How can full rotational symmetry be recovered from partialinformation? It is known that the reflections at d hyperplanes in general position generate a dense subgroup of O(d);in particular, a continuous function that is symmetric under thesereflections must be radial. How many two-point symmetrizationsare needed to verify that a function which increases under thesesymmetrizations is radial?  I will show that d+1 such symmetrizationssuffice, and will discuss the ergodicity of the randomwalk generated by the corresponding folding maps on the sphere.(Joint work with G. R. Chambers and Anne Dranovski).
Friday, November 14, 2014 - 14:00 , Location: Skiles 005 , Jean Savinien , University of Lorraine, Metz, France , Organizer: Federico Bonetto
We build a family of spectral triples for a discrete aperiodic tiling space, and derive the associated Connes distances. (These are non commutative geometry generalisations of Riemannian structures, and associated geodesic distances.) We show how their metric properties lead to a characterisation of high aperiodic order of the tiling. This is based on joint works with J. Kellendonk and D. Lenz.