• Date: 1/16/26
  • Georgios Tsikalas, Vanderbilt University
  • Title: Holomorphic Interpolation: Old and New Results
  • Abstract: Suppose you are given points $z_1, \dots, z_n$ and  $w_1, \dots, w_n$ in the unit disk of the complex plane. Does there exist a holomorphic self-map $f$ of the disk such that $f(z_i)=w_i$ for all $i$? Pick's solution of this problem in 1915 impacted the development of function theory throughout the twentieth century. In 1967, Sarason gave an operator-theoretic reformulation of Pick's result and proved his seminal commutant lifting theorem, which was subsequently generalized into a powerful tool that encodes, unifies and extends a variety of classical interpolation theorems on the disk.
    
    In this talk, I will discuss Sarason's approach to the Pick problem and how it connects to a certain reproducing kernel Hilbert space. Further, I will explain how Sarason's theorem can be extended to more general spaces. 
    
    This is joint work with Scott McCullough (University of Florida).

• Date: 1/23/26
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• Date: 1/30/26
  • No meeting (tentative)
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• Date: 2/6/26
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• Date: 2/13/26
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• Date: 2/20/26
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• Date: 2/27/26
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• Date: 3/6/26
  • No meeting(tentative)
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• Date: 3/13/26
  • No Meeting, Spring Break

• Date: 3/20/26
  • Madeline Brandt, Vanderbilt University
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• Date: 3/27/26
  • (talk reserved for a participant of the Shanks workshop)
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• Date: 4/3/26
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• Date: 4/10/26
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• Date: 4/17/26
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• End of Spring Semester.

Past NCGOA and Subfactor seminars