Event(s) on October 2022

• Wednesday, 5th October, 2022

  Title:	Applied Mathematics Problems and Opportunities in Energy Industry
  Speaker:	Joseph Ma, Global Signal Processing Center of Excellence, Halliburton, Singapore
  Time/Place:	16:00  -  17:00 Zoom, Meeting ID: 981 4682 7176
  Abstract:	With strong quantitative foundation, Mathematics students are open to career options, and will find themselves sought after, in technology positions across various industries. Once dominated by engineers, technicians and hands-on labours, the oil and gas industry are looking for more data scientist and geophysicists who are equipped with intensive quantitative training to face the ongoing and upcoming challenges. For instance, solving wave equations in complex geometry, formulating inverse problems with environmental constraints, design of fast algorithms for real time applications. In this talk, Joseph would share with students his journey from a mathematics student to becoming a R&D scientist at the oilfield servicing industry. Several industrial project examples will be presented in this talk to illustrate how Mathematics talents can find themselves valued at driving for solutions for these frontier industrial problems.

  
  

• Wednesday, 19th October, 2022

  Title:	Crouzeix's Conjecture
  Speaker:	Prof. Michael Overton, Courant Institute of Mathematical Sciences, New York University, USA
  Time/Place:	10:00  -  11:00 Zoom, (Meeting ID: 929 8218 5199)
  Abstract:	Crouzeix's conjecture is among the most intriguing developments in matrix theory in recent years. Made in 2004 by Michel Crouzeix, it postulates that, for any polynomial p and any matrix A, ||p(A)|| <= 2 max(|p(z)|: z in W(A)), where the norm is the 2-norm and W(A) is the field of values (numerical range) of A, that is the set of points attained by v*Av for some vector v of unit length. Crouzeix proved in 2007 that the inequality above holds if 2 is replaced by 11.08, and in 2016 this was greatly improved by Palencia, replacing 2 by 1+sqrt(2). Furthermore, it is known that the conjecture holds in a number of special cases, including n=2. We use nonsmooth optimization to investigate the conjecture numerically by locally minimizing the "Crouzeix ratio", defined as the quotient with numerator the right-hand side and denominator the left-hand side of the conjectured inequality. We also present local nonsmooth variational analysis of the Crouzeix ratio at conjectured global minimizers. All our results strongly support the truth of Crouzeix's conjecture. This is joint work with Anne Greenbaum and Adrian Lewis.

  
  

• Tuesday, 25th October, 2022

  Title:	A Level Set Method for the Dirichlet k-partition Problem
  Speaker:	Dr Kwun Lun CHU, Department of Mathematics, Hong Kong Baptist University, Hong Kong
  Time/Place:	10:00  -  11:00 Zoom, (Meeting ID: 966 5758 8227)
  Abstract:	In this talk, we would introduce a new level set method for the Dirichlet k-partition problem, which partitions an open domain into K different subdomains as to minimize the sum of the smallest eigenvalue of the Dirichlet Laplace operator. We first formulate the problem as a nested minimization problem of a functional of the level set function and the eigenfunction. As an approximation, we propose to simply replace the eigenfunction by the level set function so that the nested minimization can then be converted to a single minimization problem for easier computation. We apply the standard gradient descent method so that the problem leads to a Hamilton–Jacobi type equation. Various numerical examples will be given to demonstrate the effectiveness of our proposed method.

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