Risk and Decision-Making
Research in stochastic optimization models with stochastic dominance constraints and risk functions, including new optimization models constraining risk.
The Department of Mathematics is committed to stochastic systems and optimization as well as algebraic cryptography as its areas of emphasis.
New methods in mathematics have extensive implications across a wide range of disciplines. Currently there are ongoing seminars in nonlinear systems, stochastic systems, and algebraic cryptography. The graduate student organization, the Stevens Society of Mathematicians, sponsors a series of informal Wednesday afternoon talks as well other activities. Seminars and talks are open to the public; Stevens students are particularly invited to attend.
“It is important to engage students in substantive research. They are interested in what they can do with their studies after they graduate, and seeing the implementation of theoretical research is very appealing.”
Dr. Darinka Dentcheva conducts research associated with stochastic optimization models with stochastic dominance constraints and risk functions. Along with Andrzej Ruszczyski, Rutgers University, she has introduced a new type of optimization models constraining risk, which involve stochastic orders and risk functions. These problems are not only practically relevant—with applications in efficient energy production, economic systems, and medical treatment—but represent a mathematical challenge because they are nonlinear and non-smooth with respect to the decisions and nonlinear in probability. Dr. Dentcheva and Dr. Ruszczyski have jointly organized six Rutgers-Stevens Workshops on Optimization of Stochastic Systems.
“Everything in the field of cryptographic mathematics is wide open, presenting challenging and exciting opportunities for researchers such as myself and offering an exceptional chance for students to participate in this groundbreaking field.”
The Algebraic Cryptography Center investigates new techniques from computational algebra and their applications to practical problems in cryptography and cryptanalysis. The center investigates unique applications of mathematical algorithms that may be used to facilitate security in quantum computing systems – an integral blending of both computer science and mathematics in pursuit of a greater goal. Post-quantum cryptography is one of the research themes being investigated by mathematics faculty.