Difference between revisions of "Colloquia"

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(Mathematics Colloquium)
(September 22: Jaeyoung Byeon (KAIST))
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=== September 22: Jaeyoung Byeon (KAIST) ===
 
=== September 22: Jaeyoung Byeon (KAIST) ===
Title : Patterns formation for elliptic systems with large interaction forces
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Title: Patterns formation for elliptic systems with large interaction forces
 
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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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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.
  
 
== Spring 2018 ==
 
== Spring 2018 ==

Revision as of 11:06, 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 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.

Spring 2018

date speaker title host(s)
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>


Past Colloquia

Blank Colloquia

Spring 2017

Fall 2016

Spring 2016

Fall 2015

Spring 2015

Fall 2014

Spring 2014

Fall 2013

Spring 2013

Fall 2012