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DTSTAMP:20260206T030633Z
DESCRIPTION:CRM-Montreal-Quebec Analysis Seminar\n\nTitle: A Schwarz-Jack L
 emma and its Application\n\nAbstract: The Schwarz lemma is one of the corn
 erstones of geometric function theory. Jack’s lemma is another influential
  result in the field\, though it is somewhat less well known. In this work
 \, we introduce a new result\, the Schwarz–Jack lemma\, which is strongly 
 inspired by both of these classical lemmas. The main requirement of the le
 mma\, known as the Jack condition\, can be satisfied in several different 
 ways\, some of which we discuss. This result emerged from our study of the
  celebrated Crouzeix conjecture\, which asserts that the numerical range o
 f any $n \times n$ matrix is a 2-spectral set. While the conjecture has be
 en established for the case $n = 2$\, it remains open for $n \ge 3$. Exist
 ing proofs for $n = 2$ are highly technical and rely heavily on explicit f
 ormulas for conformal mappings from an ellipse onto the unit disk. The bro
 ader aim of our work is twofold: first\, to clarify the intrinsic properti
 es of the conformal mappings involved\, thereby reducing reliance on expli
 cit formulas\; and second\, to provide a conceptual framework that may all
 ow for further generalizations. The Schwarz–Jack lemma plays a central rol
 e in achieving these goals.\n\nJoint work with A. Moucha\, R. O’Loughlin\,
  O. Roth\, and T. Ransford.\n\nVenue: hybrid seminar at ULaval\, Pavillon 
 Alexandre-Vachon\, room 2820\n
DTSTART:20260213T193000Z
DTEND:20260213T203000Z
SUMMARY:Javad Mashreghi (Université Laval)
URL:/biology/channels/event/javad-mashreghi-universite
 -laval-371121
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