Difference between revisions of "Colloquia/Fall18"
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Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev. | Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev. | ||
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+ | === September 22: Jaeyoung Byeon (KAIST) === | ||
+ | Title : Patterns formation for elliptic systems with large interaction forces | ||
+ | |||
+ | Abstract : Nonlinear elliptic systems coming from nonlinear Schroedinger systems have simple looking reaction terms whose corresponding energy can be expressed as quadratic forms in terms of density functions. The entries of the matrix for the quadratic form represent interaction forces between components for a system. If the signature of an entry is positive, the force between two components is attraction; on the other hand, if it is negative, it is repulsion. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study general patterns formation structure for systems with large number of components, I would like to illustrate a phenomenon for systems with two components, and for systems with three components introduce some recent results of several phenomena depending on the network structure of attraction and repulsion between components. | ||
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== Spring 2018 == | == Spring 2018 == |
Revision as of 08:28, 5 September 2017
Mathematics Colloquium
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.
Fall 2017
Date | Speaker | Title | Host(s) | |
---|---|---|---|---|
September 8 | Tess Anderson (Madison) | A Spherical Maximal Function along the Primes | Yang | |
September 15 | ||||
Wednesday, September 20, LAA lecture | Andrew Stuart (Caltech) | TBA | Jin | |
September 22 | Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces | Rabinowitz & Kim | |
September 29 | TBA | |||
October 6 | Jonathan Hauenstein (Notre Dame) | TBA | Boston | |
October 13 | Tomoko L. Kitagawa (Berkeley) | TBA | Max | |
October 20 | Pierre Germain (Courant, NYU) | TBA | Minh-Binh Tran | |
October 27 | Stefanie Petermichl (Toulouse) | TBA | Stovall, Seeger | |
November 3 | Alexander Yom Din (Caltech) | TBA | ||
November 10 | Reserved for possible job talks | TBA | ||
November 17 | Reserved for possible job talks | TBA | ||
November 24 | Thanksgiving break | TBA | ||
December 1 | Reserved for possible job talks | TBA | ||
December 8 | Reserved for possible job talks | TBA |
Fall Abstracts
September 8: Tess Anderson (Madison)
Title: A Spherical Maximal Function along the Primes
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.
September 22: Jaeyoung Byeon (KAIST)
Title : Patterns formation for elliptic systems with large interaction forces
Abstract : Nonlinear elliptic systems coming from nonlinear Schroedinger systems have simple looking reaction terms whose corresponding energy can be expressed as quadratic forms in terms of density functions. The entries of the matrix for the quadratic form represent interaction forces between components for a system. If the signature of an entry is positive, the force between two components is attraction; on the other hand, if it is negative, it is repulsion. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study general patterns formation structure for systems with large number of components, I would like to illustrate a phenomenon for systems with two components, and for systems with three components introduce some recent results of several phenomena depending on the network structure of attraction and repulsion between components.
Spring 2018
date | speaker | title | host(s) | |
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date | person (institution) | TBA | hosting faculty | |
date | person (institution) | TBA | hosting faculty | |
date | person (institution) | TBA | hosting faculty | |
date | person (institution) | TBA | hosting faculty | |
date | person (institution) | TBA | hosting faculty | |
date | person (institution) | TBA | hosting faculty | |
date | person (institution) | TBA | hosting faculty | |
date | person (institution) | TBA | hosting faculty | |
date | person (institution) | TBA | hosting faculty | |
date | person (institution) | TBA | hosting faculty | |
date | person (institution) | TBA | hosting faculty | |
date | person (institution) | TBA | hosting faculty | |
date | person (institution) | TBA | hosting faculty |
Spring Abstracts
<DATE>: <PERSON> (INSTITUTION)
Title: <TITLE>
Abstract: <ABSTRACT>