seminars:colloquium:y2019-2020
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| + | ====== Colloquium 2019-2020====== | ||
| + | Unless stated otherwise, colloquia are scheduled for Thursdays 4:15-5:15pm in WH-100E with refreshments served from 4:00-4:15 pm in WH-102. | ||
| + | |||
| + | Organizers: [[people: | ||
| + | and [[people: | ||
| + | |||
| + | |||
| + | ------ | ||
| + | |||
| + | ==== Spring 2020 ==== | ||
| + | |||
| + | **Friday January 31, 4: | ||
| + | |||
| + | <WRAP box 90%> | ||
| + | // | ||
| + | Many infinite discrete groups fail to have nice properties only | ||
| + | because of obstructions that disappear on passage to a finite-index | ||
| + | subgroup. Examples of such properties include superrigidity of | ||
| + | representations of linear groups and nilpotence of groups of polynomial | ||
| + | growth. The collection of all finite-index subgroups of a fixed group | ||
| + | Gamma has algebraic and geometric structures that can reflect properties | ||
| + | of Gamma. We will discuss some of these structures, including the abstract | ||
| + | commensurator of Gamma and commensurator growth of Gamma. \\ | ||
| + | </ | ||
| + | |||
| + | **Thursday February 6, 4: | ||
| + | |||
| + | <WRAP box 90%> | ||
| + | // | ||
| + | Disorder is one of the central topics in modern science. | ||
| + | In this talk, we will discuss a mathematical treatment of a particular | ||
| + | disordered system modeling localization of quantum waves in random media. | ||
| + | The model in question was introduced by P. W. Anderson in his Nobel prize | ||
| + | winning work in physics which led to a rich mathematical theory of random | ||
| + | Schrodinger operators. | ||
| + | natural Hamiltonians on metric trees with random branching numbers are | ||
| + | suppressed by disorder. This phenomenon is called Anderson localization. \\ | ||
| + | </ | ||
| + | |||
| + | **Friday February 7, 4:30-5:30pm (NOTE SPECIAL DATE AND TIME)**\\ | ||
| + | applications \\ | ||
| + | |||
| + | <WRAP box 90%> | ||
| + | // | ||
| + | Markov semigroups lie at the interface of analysis, PDEs, | ||
| + | probability and geometry. Markov semigroup techniques, from both analytic | ||
| + | and probabilistic viewpoints, have important applications in the study of | ||
| + | functional inequalities coming from harmonic analysis, PDEs and geometry. | ||
| + | |||
| + | In this talk, we discuss regularization properties of heat semigroups and | ||
| + | their applications to the study of Sobolev type inequalities, | ||
| + | inequalities and $L^p$ boundedness of Riesz transforms in different | ||
| + | geometric settings. Fractal examples without differential structures are | ||
| + | emphasized. Besides, we also discuss sharp and dimension-free $L^p$ bounds | ||
| + | of singular integral operators via the martingale transform method. \\ | ||
| + | </ | ||
| + | |||
| + | **Monday February 10**\\ | ||
| + | |||
| + | <WRAP box 90%> | ||
| + | // | ||
| + | A classical theorem of Beckman and Quarles asserts that a function | ||
| + | $F$ from a Euclidean space of dimension at least two to itself and having the | ||
| + | property that $||F(x)-F(y)||=1$ whenever $||x-y||=1$ is necessarily an isometry. | ||
| + | Aleksandrov has been credited with the problem of determining those metric | ||
| + | spaces having this " | ||
| + | property. | ||
| + | |||
| + | Examples show that Riemannian manifolds need not have this property. | ||
| + | However, it is expected that self-functions of complete Riemannian | ||
| + | manifolds that preserve a sufficiently small distance are isometries. | ||
| + | I'll formulate a precise conjecture and will discuss supporting results | ||
| + | proved jointly with Meera Mainkar. \\ | ||
| + | </ | ||
| + | |||
| + | **Thursday March 19, 4: | ||
| + | |||
| + | <WRAP box 90%> | ||
| + | // | ||
| + | TBA \\ | ||
| + | </ | ||
| + | |||
| + | **Thursday April 23, 4: | ||
| + | |||
| + | <WRAP box 90%> | ||
| + | // | ||
| + | TBA \\ | ||
| + | </ | ||
| + | |||
| + | |||
| + | **PETER HILTON MEMORIAL LECTURE** \\ **Thursday April 30, 3: | ||
| + | |||
| + | <WRAP box 90%>// | ||
| + | </ | ||
| + | |||
| + | ----- | ||
| + | |||
| + | |||
| + | Archive: | ||
| + | |||
| + | /* * [[http:// | ||
| + | /* * [[http:// | ||
| + | * [[seminars: | ||
| + | * [[seminars: | ||
| + | * [[seminars: | ||
| + | * [[seminars: | ||
| + | * [[seminars: | ||
| + | |||
