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DTSTART:20260329T030000
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DTSTAMP:20260310T222729Z
UID:6687bf08e3e40031366181@ist.ac.at
DTSTART:20260210T171500
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DESCRIPTION:Speaker: Jonas Jalowy\nhosted by Andrew Campbell\nAbstract: The
  guiding question of the talk is "How do zeros of polynomials evolve under
  the action of differential operators?"For instance\, taking a Weyl random
  polynomial and applying the heat flow operator\, the (complex) limiting z
 ero distribution evolves from the circular law into the elliptic law until
  it collapses to the Wigner semicircle law--a transition that is well know
 n in Random Matrix Theory.In this talk\, I will focus on the case of polyn
 omials undergoing the (holomorphic) heat flow operator and begin with an o
 verview on results of such type as well as a description of the roots from
  various points of view such as (optimal) transport\, differential equatio
 ns and free probability. Then\, we will turn to a specific deterministic s
 etting of polynomial powers P^n\, where a novel limiting distribution can 
 be described along the time evolution: For small time\, the initial zeros 
 spread out in approximately semicircular distributions\, then intricate cu
 rves start to form and merge\, until for large time\, the zero distributio
 n approaches a semicircle law through the initial center of mass.This talk
  is based on joint works with Brian Hall\, Ching-Wei Ho\, Antonia Hfert\, 
 Zakhar Kabluchko\, and Alexander Marynych.
LOCATION:Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101
 )\, ISTA
ORGANIZER:boosthui@ist.ac.at
SUMMARY:Jonas Jalowy: Evolution of zeros of polynomials under the heat flow
URL:https://talks-calendar.ista.ac.at/events/6280
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