Difference between revisions of "Colloquia"
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| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame) | | [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame) | ||
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Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. 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 the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems. | Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. 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 the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems. | ||
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+ | ===October 6: Jonathan Hauenstein (Notre Dame) === | ||
+ | Title: Real solutions of polynomial equations | ||
+ | |||
+ | Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model. | ||
== Spring 2018 == | == Spring 2018 == |
Revision as of 19:29, 20 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 | |||||
September 22, 9th floor | Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces | Rabinowitz & Kim | ||
September 29 | TBA | ||||
October 6 | Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations | 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 | ||
We, November 1 | Shaoming Guo (Indiana) | TBA | |||
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 arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. 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 the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.
October 6: Jonathan Hauenstein (Notre Dame)
Title: Real solutions of polynomial equations
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.
Spring 2018
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date | person (institution) | TBA | hosting faculty | |
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Spring Abstracts
<DATE>: <PERSON> (INSTITUTION)
Title: <TITLE>
Abstract: <ABSTRACT>