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math.GM2026
On the polynomial values represented by quadratic forms
Bogdan Grechuk, Jamal Agbanwa
Many Diophantine equations can be reduced to the question of whether, for a given non-degenerate quadratic form and a univariate polynomial with integer coefficients, $P(x)…
math.OC2026
The Risk Quadrangle in Optimization: An Overview with Recent Results and Extensions
Bogdan Grechuk, Anton Malandii, Terry Rockafellar +1
This paper revisits and extends the 2013 development by Rockafellar and Uryasev of the Risk Quadrangle (RQ) as a unified scheme for integrating risk management, optimization, and s…
math.GM2026
On the shortest open cubic equations
Bogdan Grechuk, Ashleigh Ratcliffe
We use cubic reciprocity to prove that the equation has no integer solutions. Prior to this work, it was the shortest cubic equation for which the existence of i…