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SUMMARY:Man Cheung Tsui (University of Pennsylvania)
DTSTART:20210129T154500Z
DTEND:20210129T164500Z
DTSTAMP:20260422T225921Z
UID:KolchinSeminar/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/KolchinSemin
 ar/1/">Differential Essential Dimension</a>\nby Man Cheung Tsui (Universit
 y of Pennsylvania) as part of Kolchin Seminar in Differential Algebra\n\n\
 nAbstract\nRoughly speaking\, the essential dimension of an algebraic obje
 ct counts the number of parameters needed to describe the object. In this 
 talk\, we define an analogue of essential dimension in differential Galois
  theory. As application\, we show that the number of coefficients in a gen
 eral homogeneous linear differential equation over a field cannot be reduc
 ed via gauge transformations over the given field. We also give lower boun
 ds on the number of parameters needed to write down certain generic Picard
 -Vessiot extensions.\n
LOCATION:https://researchseminars.org/talk/KolchinSeminar/1/
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SUMMARY:Khalil Ghorbal (INRIA)
DTSTART:20210212T154500Z
DTEND:20210212T164500Z
DTSTAMP:20260422T225921Z
UID:KolchinSeminar/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/KolchinSemin
 ar/2/">Characterizing Positively Invariant Sets: Inductive and Topological
  Methods</a>\nby Khalil Ghorbal (INRIA) as part of Kolchin Seminar in Diff
 erential Algebra\n\n\nAbstract\nSet positive invariance is an important co
 ncept in the theory of dynamical systems and one which also has practical 
 applications in areas of computer science\, such as formal verification\, 
 as well as in control theory. Great progress has been made in understandin
 g positively invariant sets in continuous dynamical systems and powerful c
 omputational tools have been developed for reasoning about them\; however\
 , many of the insights from recent developments in this area have largely 
 remained folklore and are not elaborated in existing literature. This pres
 entation contributes an explicit development of modern methods for checkin
 g positively invariant sets of ordinary differential equations and describ
 es two possible characterizations of positive invariants: one based on the
  real induction principle\, and a novel alternative based on topological n
 otions. The two characterizations\, while in a certain sense equivalent\, 
 lead to two different decision procedures for checking whether a given sem
 i-algebraic set is positively invariant under the flow of a system of poly
 nomial ordinary differential equations.\n
LOCATION:https://researchseminars.org/talk/KolchinSeminar/2/
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BEGIN:VEVENT
SUMMARY:Vincenzo Mantova (University of Leeds)
DTSTART:20210219T154500Z
DTEND:20210219T164500Z
DTSTAMP:20260422T225921Z
UID:KolchinSeminar/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/KolchinSemin
 ar/3/">Intersecting the graph of exp with complex algebraic varieties</a>\
 nby Vincenzo Mantova (University of Leeds) as part of Kolchin Seminar in D
 ifferential Algebra\n\n\nAbstract\nA conjecture of Zilber\, motivated by t
 he model theory of complex exponentiation\, predicts the existence of many
  intersections between the graph of the exponential function (extended poi
 ntwise to several variables) and algebraic varieties\, as long as the vari
 eties satisfy some geometric conditions related to Schanuel's conjecture. 
 Some instances are known to be true\, most notably when the projections of
  the varieties onto the domain side of the graph have maximal dimension\, 
 i.e. equal to the number of variables (by work of Brownawell-Masser and D'
 Aquino-Fornasiero-Terzo).\n\nI will discuss the case of varieties whose pr
 ojection on the domain has dimension one\, that is\, it is a curve. Then s
 uch intersections always exist if the curve is not contained in a translat
 e of a rational hyperplane (and if it is\, a trivial geometric condition d
 etermines when there are no intersections). We can prove this by appealing
  to the classical theory of differentials on compact Riemann surfaces and 
 a suitable instance of the Ax-Lindemann-Weierstrass theorem. This is joint
  work with David Masser.\n
LOCATION:https://researchseminars.org/talk/KolchinSeminar/3/
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SUMMARY:Vincent Bagayoko (École Polytechnique)
DTSTART:20210226T154500Z
DTEND:20210226T164500Z
DTSTAMP:20260422T225921Z
UID:KolchinSeminar/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/KolchinSemin
 ar/4/">Three flavors of H-fields</a>\nby Vincent Bagayoko (École Polytech
 nique) as part of Kolchin Seminar in Differential Algebra\n\n\nAbstract\nT
 he model theory of H-fields\, introduced by van den Dries and Aschenbrenne
 r\, provides a general framework to study differential equations in ordere
 d fields. This theory admits in particular geometric\, formal\, and number
  theoretic models: Hardy fields\, which are fields of differentiable real-
 valued germs at infinity\, transseries\, which are formal series involving
  exponentials and logarithms\, and surreal numbers\, which are abstract or
 dered quantities that can mimic both germs and transseries. I will give an
  overview of the theory\, these different types of models and their connec
 tions.\n
LOCATION:https://researchseminars.org/talk/KolchinSeminar/4/
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