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SUMMARY:Alan Sokal (University College London)
DTSTART:20230228T140000Z
DTEND:20230228T150000Z
DTSTAMP:20260422T201527Z
UID:CAvid/99
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/99/">M
 otion of zeros of polynomial solutions of the one-dimensional heat equatio
 n: A first-order Calogero-Moser system</a>\nby Alan Sokal (University Coll
 ege London) as part of CAvid: Complex Analysis video seminar\n\nLecture he
 ld in N/A.\n\nAbstract\nI study the motion of zeros of polynomial solution
 s $\\phi(x\, t)=\\prod_{i=1}^n[x-x_{i}(t)]$\nof the one-dimensional heat e
 quation \n$\\displaystyle\\frac{\\partial \\phi}{\\partial t}=\\kappa\\fra
 c{\\partial^2\\phi}{\\partial x^2}$\; they satisfy the first-order\nCaloge
 ro–Moser system \n\\[\n\\frac{{\\rm d}x_i}{{\\rm d}t}=\\sum_{j\\ne i}\\f
 rac{-2\\kappa}{x_i-x_j}.\n\\]\nI am interested in the behavior at complex 
 time $t$ (usually with real initial conditions). My goals are to\n\n(a) De
 termine the complex times t at which collisions can or cannot occur\; and\
 n\n(b) Control the location of $x_1(t)\,\\ldots\, x_n(t)$ in the complex p
 lane. I have no nontrivial theorems\, but many interesting conjectures.\n
LOCATION:https://researchseminars.org/talk/CAvid/99/
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