Niho’s last conjecture (Daniel Katz, Cal State Northridge)
A power permutation of a finite field F is a permutation of F whose functional form is x -> x^d for some exponent d. Power permutations are used in cryptography, […]
12 events found.
Algebra / Number Theory / Combinatorics Seminar
Events
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On Zoom
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Frame coherence and nearly orthogonal lattices (Lenny Fukshansky, CMC)
On ZoomA frame in a Euclidean space is a spanning set, which can be overdetermined. Large frames are used for redundant signal transmission, which allows for error correction. An important parameter […]
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Recent trends in using representations in voting theory – committees and cyclic orders (Karl-Dieter Crisman, Gordon College)
On ZoomOne of the most important axioms in analyzing voting systems is that of "neutrality", which stipulates that the system should treat all candidates symmetrically. Even though this doesn't always directly […]
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Gap theorems for linear forms and for rotations on higher dimensional tori (Alan Haynes, University of Houston)
On ZoomThis 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 positive integer, the points x, 2x, … , Nx modulo 1 partition the unit interval into component intervals having at most 3 distinct lengths. We […]
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Equidistribution of norm 1 elements in cyclic number fields (Kate Petersen, University of Minnesota Duluth)
On ZoomBy 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 rise to a natural height function on elements of norm 1. I’ll discuss equidistribution problems and show that these norm 1 elements are equidistributed (in […]
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Continuous extensions of Ramanujan-expandable arithmetic functions (Matthew Fox, Perimeter Institute for Theoretical Physics and Chai Karamchedu, Sandia National Labs)
On ZoomWe 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 […]
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Peg solitaire in multiple colors on graphs (Tara Davis, Hawaii Pacific University and Roberto Soto, Cal State Fullerton)
On ZoomPeg 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 mathematical graphs. We will present our rules for multiple color peg solitaire on graphs. We will present some student and faculty results classifying the solvability of the game […]
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Covering by polynomial planks (Alexey Glazyrin, University of Texas Rio Grande Valley)
On ZoomIn 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 […]
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Geometrization of Markov numbers (Oleg Karpenkov, University of Liverpool)
TBAIn this talk we link discrete Markov spectrum to geometry of continued fractions. As a result of that we get a natural generalization of classical Markov tree which leads to […]
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A conjugacy criterion for two pairs of 2 x 2 matrices over a commutative ring (Bogdan Petrenko, Eastern Illinois University)
On ZoomI 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 […]
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Bounds for nonzero Littlewood-Richardson coefficients (Müge Taskin, Boğaziçi University, Turkey)
On ZoomAs $\lambda$ 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 […]
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Beran’s tests of uniformity for discrete data (Michael Orrison, HMC)
On ZoomSuppose 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 can be viewed as a sample from the uniform distribution on the set, in which case you might want to apply some sort of test […]