EXPLORING PROSPECTIVE ELEMENTARY MATHEMATICS TEACHERS’ KNOWLEDGE: A FOCUS ON FUNCTIONAL THINKING [PDF]
, 2021 The importance of students being acquainted with algebraic ideas before secondary education has been revealed in the research literature. It is therefore essential that prospective elementary teachers (PTs) be prepared to instill an early algebra ...
Henriques, Ana +2 more
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On representation varieties of Artin groups, projective arrangements and the fundamental groups of smooth complex algebraic varieties [PDF]
, 1997 We prove that for any affine variety S defined over Q there exist Shephard and Artin groups G such that a Zariski open subset U of S is biregular isomorphic to a Zariski open subset of the character variety Hom(G, PO(3))//PO(3). The subset U contains all
Kapovich, Michael, Millson, John
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Equational reasoning: A systematic review of the Cuisenaire–Gattegno approach [PDF]
, 2022 The Cuisenaire–Gattegno (Cui) approach to early mathematics uses color coded rods of unit increment lengths embedded in a systematic curriculum designed to guide learners as young as age five from exploration of integers and ratio through to formal ...
Bruce D. McCandliss +3 more
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`Third' Quantization of Vacuum Einstein Gravity and Free Yang-Mills Theories [PDF]
, 2006 Based on the algebraico-categorical (:sheaf-theoretic and sheaf cohomological) conceptual and technical machinery of Abstract Differential Geometry, a new, genuinely background spacetime manifold independent, field quantization scenario for vacuum ...
A. Ashtekar +39 more
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Skeletons and tropicalizations [PDF]
, 2016 Let $K$ be a complete, algebraically closed non-archimedean field with ring of integers $K^\circ$ and let $X$ be a $K$-variety. We associate to the data of a strictly semistable $K^\circ$-model $\mathscr X$ of $X$ plus a suitable horizontal divisor $H$ a
Gubler, Walter +2 more
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On representation varieties of 3-manifold groups [PDF]
, 2015 We prove universality theorems ("Murphy's Laws") for representation schemes of fundamental groups of closed 3-dimensional manifolds. We show that germs of SL(2,C)-representation schemes of such groups are essentially the same as germs of schemes of over ...
Kapovich, Michael, Millson, John J.
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On the density of second order differential equations without algebraic solutions on P2 [PDF]
, 2011 We prove that a generic second order diferential equation in the projective plane has no algebraic solutions when the bidegree is big enough.
Falla Luza, M.
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About Hrushovski and Loeser's work on the homotopy type of Berkovich spaces [PDF]
, 2015 Those are the notes of the two talks I gave in april 2013 in St-John (US Virgin Islands) during the Simons Symposium on non-Archimedean and tropical geometry.
Ducros, Antoine
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The Tate conjecture for K3 surfaces over finite fields [PDF]
, 2012 Artin's conjecture states that supersingular K3 surfaces over finite fields have Picard number 22. In this paper, we prove Artin's conjecture over fields of characteristic p>3.
A. Beauville +32 more
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New symplectic V-manifolds of dimension four via the relative compactified Prymian [PDF]
, 2007 Three new examples of 4-dimensional irreducible symplectic V-manifolds are constructed. Two of them are relative compactified Prymians of a family of genus-3 curves with involution, and the third one is obtained from a Prymian by Mukai's flop.
Markushevich, D., Tikhomirov, A. S.
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