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SUMMARY:Michelangelo Marsala (Aromath\, Inria)
DTSTART:20220406T090000Z
DTEND:20220406T100000Z
DTSTAMP:20260404T111135Z
UID:Aromath/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Aroma
 th/1/">Construction and Analysis of a $G^1$-smooth polynomial family of Ap
 proximate Catmull-Clark Surfaces</a>\nby Michelangelo Marsala (Aromath\, I
 nria) as part of Aromath seminar\n\n\nAbstract\nSubdivision surfaces are a
  widely used numerical method to reconstruct smooth surfaces starting from
  a polyhedral mesh of any topology. However\, in presence of the so-called
  extraordinary vertices\, i.e. vertices with valence $N\\neq4$\, the limit
  surface presents a loss of regularity like\, for instance\, the Catmull-C
 lark surface. To recover smoothness around these particular points the mul
 tipatch approach can be used\, for instance\, imposing tangent plane conti
 nuity ($G^1$ smoothness) around the extraordinary patches. Starting from t
 he work of Loop and Shaefer (2008) which presents an approximate bicubic B
 ézier patching of the Catmull-Clark limit surface defined by local smooth
 ing masks\, employing quadratic glueing data functions I modify the previo
 us scheme to obtain $G^1$ continuity around the EVs. This construction lea
 ds to a family of surfaces that are given by means of explicit formulas fo
 r all involved control points. Moreover\, I conduct a curvature analysis i
 n order to assert the quality of the resulting surfaces\, both visually an
 d numerically. Furthermore\, dimension formula and basis construction for 
 the obtained 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://stable.researchseminars.org/talk/Aromath/1/
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SUMMARY:Sebastian Debus (Univ. of Tromsoe\, Norway)
DTSTART:20220420T080000Z
DTEND:20220420T090000Z
DTSTAMP:20260404T111135Z
UID:Aromath/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Aroma
 th/2/">(Even) Symmetric PSD and SOS forms</a>\nby Sebastian Debus (Univ. o
 f Tromsoe\, Norway) as part of Aromath seminar\n\n\nAbstract\nIn this talk
  we consider the so-called non-normalized limits of symmetric and even sym
 metric forms (homogeneous polynomials). To do so\, we identify (even) symm
 etric forms of degree d for sufficiently many variables. The sets of posit
 ive semidefinite (non negative) and sums of squares of fixed degree form n
 ested decreasing sequences under this identification. We completely charac
 terize the question of non-negativity versus sums of squares in the non-no
 rmalized limit case. We begin by examining the symmetric quartics and prov
 ide test sets for non negativity and the property of being a sum of square
 s for the limit forms\, and give interesting examples. Then\, we consider 
 even symmetric sextics and prove that the set of all psd limit forms is no
 t semialgebraic and provide test sets as well (based on the work of Choi-L
 am-Reznick). Finally\, we study the tropicalizations of the duals to even 
 symmetric psd and sos forms. Tropicalization reduces the study of even sym
 metric limit cones to the study of polyhedral cones. \nThis is joint work 
 together with Jose Acevedo\, Greg Blekherman and Cordian Riener.\n
LOCATION:https://stable.researchseminars.org/talk/Aromath/2/
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SUMMARY:Sofia Imperatore (U. Florence)
DTSTART:20220504T090000Z
DTEND:20220504T100000Z
DTSTAMP:20260404T111135Z
UID:Aromath/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Aroma
 th/3/">Artificial geometry for spline models construction</a>\nby Sofia Im
 peratore (U. Florence) as part of Aromath seminar\n\n\nAbstract\nFor centu
 ries mathematics has been an activity carried out by\nhumans for humans. I
 n recent years\, a new perspective has arisen\,\nin which Mathematics is a
 n activity that humans and machines\nperform for humans and machines. In t
 he seminar\, this duality\nwill be exploited with respect to deep learning
  architectures and\nfree-form geometric CAD model construction. In particu
 lar\, the\ntalk will investigate different neural network architectures to
 \naddress the parameterization problem within the spline fitting\nframewor
 k.\n
LOCATION:https://stable.researchseminars.org/talk/Aromath/3/
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SUMMARY:André Galligo (Aromath)
DTSTART:20220518T090000Z
DTEND:20220518T100000Z
DTSTAMP:20260404T111135Z
UID:Aromath/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Aroma
 th/4/">Motion of random polynomial polynomial sets under differentiation</
 a>\nby André Galligo (Aromath) as part of Aromath seminar\n\nAbstract: TB
 A\n
LOCATION:https://stable.researchseminars.org/talk/Aromath/4/
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