In mathematics, tropical geometry is the study of polynomials and their geometric properties when addition is replaced with minimization and multiplication is replaced with ordinary addition:
William Gilbert Strang is an American mathematician known for his contributions to finite element theory, the calculus of variations, wavelet analysis and linear algebra. He has made many contributions to mathematics education, including publishing mathematics textbooks. Strang was the MathWorks Professor of Mathematics at the Massachusetts Institute of Technology. He taught Linear Algebra, Computational Science, and Engineering, Learning from Data, and his lectures are freely available through MIT OpenCourseWare.
Macaulay2 is a free computer algebra system created by Daniel Grayson and Michael Stillman for computation in commutative algebra and algebraic geometry.
Combinatorial commutative algebra is a relatively new, rapidly developing mathematical discipline. As the name implies, it lies at the intersection of two more established fields, commutative algebra and combinatorics, and frequently uses methods of one to address problems arising in the other. Less obviously, polyhedral geometry plays a significant role.
Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra.
Louis Joseph Billera is a Professor of Mathematics at Cornell University.
polymake is software for the algorithmic treatment of convex polyhedra.
The study of integer points in convex polyhedra is motivated by questions such as "how many nonnegative integer-valued solutions does a system of linear equations with nonnegative coefficients have" or "how many solutions does an integer linear program have". Counting integer points in polyhedra or other questions about them arise in representation theory, commutative algebra, algebraic geometry, statistics, and computer science.
In mathematics, the Newton polytope is an integral polytope associated with a multivariate polynomial. It can be used to analyze the polynomial's behavior when specific variables are considered negligible relative to the others. Specifically, given a vector of variables and a finite family of pairwise distinct vectors from each encoding the exponents within a monomial, consider the multivariate polynomial
Michael Lee Develin is an American mathematician known for his work in combinatorics and discrete geometry.
Richard M. Pollack was an American geometer who spent most of his career at the Courant Institute of Mathematical Sciences at New York University, where he was Professor Emeritus until his death.
Santosh Vempala is a prominent computer scientist. He is a Distinguished Professor of Computer Science at the Georgia Institute of Technology. His main work has been in the area of Theoretical Computer Science.
David Archibald Cox is a retired American mathematician, working in algebraic geometry.
Jesús Antonio De Loera is a Mexican-American mathematician at the University of California, Davis, specializing in discrete mathematics and discrete geometry.
Diane Margaret Maclagan is a professor of mathematics at the University of Warwick. She is a researcher in combinatorial and computational commutative algebra and algebraic geometry, with an emphasis on toric varieties, Hilbert schemes, and tropical geometry.
In mathematics, a polyhedral complex is a set of polyhedra in a real vector space that fit together in a specific way. Polyhedral complexes generalize simplicial complexes and arise in various areas of polyhedral geometry, such as tropical geometry, splines and hyperplane arrangements.
Melody Tung Chan is an American mathematician and violinist who works as Associate Professor of Mathematics at Brown University. She is a winner of the Alice T. Schafer Prize and of the AWM–Microsoft Research Prize in Algebra and Number Theory. Her research involves combinatorial commutative algebra, graph theory, and tropical geometry.
Michael Eugene Stillman is an American mathematician working in computational algebraic geometry and commutative algebra. He is a Professor of Mathematics at Cornell University. He is known for being one of the creators of the Macaulay2 computer algebra system.
Introduction to Tropical Geometry is a book on tropical geometry, by Diane Maclagan and Bernd Sturmfels. It was published by the American Mathematical Society in 2015 as volume 161 of Graduate Studies in Mathematics.
Cynthia Vinzant is an American mathematician specializing in real algebraic geometry; her research has also involved algebraic combinatorics, matroid theory, Hermitian matrices, and spectrahedra in convex optimization. She is an associate professor of mathematics at the University of Washington.
