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SUMMARY:Michelangelo Marsala (Aromath\, Inria)
DTSTART:20220406T090000Z
DTEND:20220406T100000Z
DTSTAMP:20260422T225754Z
UID:Aromath/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Aromath/1/">
 Construction and Analysis of a $G^1$-smooth polynomial family of Approxima
 te Catmull-Clark Surfaces</a>\nby Michelangelo Marsala (Aromath\, Inria) a
 s part of Aromath seminar\n\n\nAbstract\nSubdivision surfaces are a widely
  used numerical method to reconstruct smooth surfaces starting from a poly
 hedral mesh of any topology. However\, in presence of the so-called extrao
 rdinary vertices\, i.e. vertices with valence $N\\neq4$\, the limit surfac
 e presents a loss of regularity like\, for instance\, the Catmull-Clark su
 rface. To recover smoothness around these particular points the multipatch
  approach can be used\, for instance\, imposing tangent plane continuity (
 $G^1$ smoothness) around the extraordinary patches. Starting from the work
  of Loop and Shaefer (2008) which presents an approximate bicubic Bézier 
 patching of the Catmull-Clark limit surface defined by local smoothing mas
 ks\, employing quadratic glueing data functions I modify the previous sche
 me to obtain $G^1$ continuity around the EVs. This construction leads to a
  family of surfaces that are given by means of explicit formulas for all i
 nvolved control points. Moreover\, I conduct a curvature analysis in order
  to assert the quality of the resulting surfaces\, both visually and numer
 ically. Furthermore\, dimension formula and basis construction for the obt
 ained space are presented.\n\nRemote participation via Zoom: https://cutt.
 ly/aromath\nMeeting ID: 828 5859 7791\nPasscode: 123\nJoin via web browser
 : https://cutt.ly/aromath-web\n
LOCATION:https://researchseminars.org/talk/Aromath/1/
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SUMMARY:Sebastian Debus (Univ. of Tromsoe\, Norway)
DTSTART:20220420T080000Z
DTEND:20220420T090000Z
DTSTAMP:20260422T225754Z
UID:Aromath/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Aromath/2/">
 (Even) Symmetric PSD and SOS forms</a>\nby Sebastian Debus (Univ. of Troms
 oe\, Norway) as part of Aromath seminar\n\n\nAbstract\nIn this talk we con
 sider the so-called non-normalized limits of symmetric and even symmetric 
 forms (homogeneous polynomials). To do so\, we identify (even) symmetric f
 orms of degree d for sufficiently many variables. The sets of positive sem
 idefinite (non negative) and sums of squares of fixed degree form nested d
 ecreasing sequences under this identification. We completely characterize 
 the question of non-negativity versus sums of squares in the non-normalize
 d limit case. We begin by examining the symmetric quartics and provide tes
 t sets for non negativity and the property of being a sum of squares for t
 he limit forms\, and give interesting examples. Then\, we consider even sy
 mmetric sextics and prove that the set of all psd limit forms is not semia
 lgebraic and provide test sets as well (based on the work of Choi-Lam-Rezn
 ick). Finally\, we study the tropicalizations of the duals to even symmetr
 ic psd and sos forms. Tropicalization reduces the study of even symmetric 
 limit cones to the study of polyhedral cones. \nThis is joint work togethe
 r with Jose Acevedo\, Greg Blekherman and Cordian Riener.\n
LOCATION:https://researchseminars.org/talk/Aromath/2/
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BEGIN:VEVENT
SUMMARY:Sofia Imperatore (U. Florence)
DTSTART:20220504T090000Z
DTEND:20220504T100000Z
DTSTAMP:20260422T225754Z
UID:Aromath/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Aromath/3/">
 Artificial geometry for spline models construction</a>\nby Sofia Imperator
 e (U. Florence) as part of Aromath seminar\n\n\nAbstract\nFor centuries ma
 thematics has been an activity carried out by\nhumans for humans. In recen
 t years\, a new perspective has arisen\,\nin which Mathematics is an activ
 ity that humans and machines\nperform for humans and machines. In the semi
 nar\, this duality\nwill be exploited with respect to deep learning archit
 ectures and\nfree-form geometric CAD model construction. In particular\, t
 he\ntalk will investigate different neural network architectures to\naddre
 ss the parameterization problem within the spline fitting\nframework.\n
LOCATION:https://researchseminars.org/talk/Aromath/3/
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BEGIN:VEVENT
SUMMARY:André Galligo (Aromath)
DTSTART:20220518T090000Z
DTEND:20220518T100000Z
DTSTAMP:20260422T225754Z
UID:Aromath/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Aromath/4/">
 Motion of random polynomial polynomial sets under differentiation</a>\nby 
 André Galligo (Aromath) as part of Aromath seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Aromath/4/
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