History and Philosophy of Mathematics Seminar: Julia Tomasson (Columbia University)
Inventing the ‘Islamic Golden Age’: Orientalism and the History of Mathematics Abstract: TBA
Inventing the ‘Islamic Golden Age’: Orientalism and the History of Mathematics Abstract: TBA
We explore the application of spectral graph theory to the problem of characterizing linguistically-significant classes of tree structures. We focus on various classes of syntactically-defined tree graphs, and show that […]
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Young diagrams are all possible arrangements of n boxes into rows and columns, with the number of boxes in each subsequent row weakly decreasing. For a partition λ of n, […]
Suppose you are given a data set that can be viewed as a nonnegative integer-valued function defined on a finite set. A natural question to ask is whether the data […]
As $\lambda$ runs through all integer partitions, the set of Schur functions $\{s_{\lambda}\}_\lambda$ forms a basis in the ring of symmetric functions. Hence the rule $$s_{\lambda}s_{\mu}=\sum c_{\lambda,\mu}^{\gamma} s_{\gamma}$$ makes sense […]
I will explain how to apply presentations of algebras (together with some classical results from non-commutative algebra) to obtain some 5 polynomial invariants telling us when two pairs of 2x2 […]
In 1932, Tarski conjectured that a convex body of width 1 can be covered by planks, regions between two parallel hyperplanes, only if the total width of planks is at […]
Peg solitaire is a popular one person board game that has been played in many countries on various board shapes. Recently, peg solitaire has been studied extensively in two colors on […]
We describe a natural way to continuously extend arithmetic functions that admit a Ramanujan expansion and derive the conditions under which such an extension exists. In particular, we show that […]
By Hilbert’s theorem 90, if K is a cyclic number field with Galois group generated by g, then any element of norm 1 can be written as a/g(a). This gives […]
This talk is based on joint work with Jens Marklof, and with Roland Roeder. The three distance theorem states that, if x is any real number and N is any […]