Quolloquium Series Fall 2017

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The "Quolloquium" series is a set of talks at the colloquium level intended to update the local mathematics community on the topics discussed at QMath13, an international conference that took place at Tech in October, 2016.   Qmath13 broadly covered the mathematical aspects of quantum mechanics, including such fields as models with randomness, quantum information, many-body theory, and models on graphs and similar structures, as well as an open-ended topic of current mathematical problems in theoretical physics.  It is taking place at approximately two-week intervals in Fall Semester, 2017 and may extend into Spring Semester, 2018.

Series: Math Physics Seminar
Title: Isoperimetric inequalities for convex cones
Speaker: Lotfi Hermi Florida International University lhermi@gmail.com
We use the weighted isoperimetric inequality of J. Ratzkin for a wedge domain in higher dimensions to prove new isoperimetric inequalities for weighted Lp-norms of the fundamental eigenfunction of a bounded domain in a convex cone-generalizing earlier work of Chiti, Kohler-Jobin, and Payne-Rayner. We also introduce relative torsional rigidity for such domains and prove a new Saint-Venant-type isoperimetric inequality for convex cones. Finally, we prove new inequalities relating the fundamental eigenvalue to the relative torsional rigidity of such a wedge domain thereby generalizing our earlier work to this higher dimensional setting, and show how to obtain such inequalities using the Payne interpretation in Weinstein fractional space. (Joint work with A. Hasnaoui)


Series: Math Physics Seminar
Title: Semiclassical Spectral Estimates with Renainder Terms
Starting from the classical Berezin- and Li-Yau-bounds onthe eigenvalues of the Laplace operator with Dirichlet boundaryconditions I give a survey on various improvements of theseinequalities by remainder terms. Beside the Melas inequalitywe deal with modifications thereof for operators with and withoutmagnetic field and give bounds with (almost) classical remainders.Finally we extend these results to the Heisenberg sub-Laplacianand the Stark operator in domains.
Vieri Mastropietro (Universita' di Milano, Italy)
will visit the SoM from November 26 to December 2. He will give a seminar on November 27. Exact time, title and abstract: TBA

Ian Jauslin (IAS, Princeton)
approximate dates November 27 to November 29/30. He will also give a seminar on November 27. Exact time, title and abstract: TBA


  • Workflow Status: Published
  • Created By: sbarone7
  • Created: 11/01/2017
  • Modified By: sbarone7
  • Modified: 11/27/2017


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