Analysis of singularities in geometry, calculus of variations and applications.
日期：May 04, 2026 ｜ 時間：13:00 - 14:00
| 講者姓名 (Speaker Name) |
艾尼克 |
|---|---|
| 現職職稱 (Current Job Title) |
銘博士後研究員 |
| 經歷 (Experience) |
University of Toronto 2016-2017 University of British Colombia 2017-2020 University of Auckland 2020-2021 師範大學 2021-2026 |
演講摘要 (Speech Summary)
When a mathematical model is constructed via an optimization process, it is natural to expect certain regularity as nature tends to behave optimally and regularly.
However, most of the work in mathematics goes towards proving that the final object is indeed regular and yet, in many cases singularities are unavoidable.
We will discuss how we can estimate the worst case scenario of singularities from a simple local to global principle. Since nature has the tendency to behave in a stable manner, in our situation the understanding of stable solutions will be the key to controlling the singularities of all possible solutions.
We will see how this idea is used in the study of the geometry of minimal surfaces and other applications of this principle.
However, most of the work in mathematics goes towards proving that the final object is indeed regular and yet, in many cases singularities are unavoidable.
We will discuss how we can estimate the worst case scenario of singularities from a simple local to global principle. Since nature has the tendency to behave in a stable manner, in our situation the understanding of stable solutions will be the key to controlling the singularities of all possible solutions.
We will see how this idea is used in the study of the geometry of minimal surfaces and other applications of this principle.
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