The ecology of major human, plant and animal diseases from the Black Plague to the Irish Potato Blight to AIDS. How microbes, people and other organisms interact in a changing environment, leading to new threats and controls for disease. (Gen.Ed. BS)

Maximum credit, 6.

Algebraic geometry is the study of geometric spaces locally defined by polynomial equations. It is a central subject in mathematics with strong connections to differential geometry, number theory, and representation theory. This course will be a fast-paced introduction to the subject with a strong emphasis on examples. In the algebraic approach to the subject, local data is studied via the commutative algebra of quotients of polynomial rings in several variables.

The goal of this course is to study knots, surfaces, 3- and 4-dimensional spaces. Topics include: Morse theory, handlebodies and Kirby calculus, classification of surfaces, Heegaard splittings of 3-manifolds and Dehn surgeries, h-cobordism theory in higher dimensions, Wall and Freedman theorems, constructions of smooth, symplectic and complex manifolds, Gauge theory, exotic 4-manifolds.

Maximum credit, 6.

An introductory course in complex algebraic geometry. The basic techniques of Kahler geometry, Hodge theory, line and vector bundles which are needed for the study of the geometry and topology of complex projective algebraic varieties will be introduced and illustrated in basic examples.

This is an introductory course on symplectic topology along with its connections to differential, algebraic, complex and contact geometry and topology.

Inverse and implicit functions theorems, rank of a map. Regular and critical values. Sard's theorem. Differentiable manifolds, submanifolds, embeddings, immersions and diffeomorphisms. Tangent space and bundle, differential of a map. Partitions of unity, orientation, transversality embed-dings in Rn. Vector fields, local flows. Lie bracket, Frobenius theorem. Lie groups, matrix Lie groups, left invariant vector fields, tensor fields, differential form, integration, closed and exact forms. DeRham's cohomology, vector bundles, connections, curvature.

Not available at this time.

In this course, we will consider maximization and minimization problems in graphs and networks. We will cover a broad range of topics such as matchings in bipartite graphs and in general graphs, assignment problem, polyhedral combinatorics, total unimodularity, matroids, matroid intersection, min arborescence, max flow;min cut, max cut, traveling salesman problem, stable sets and perfect graphs. One of our main tools will be integer programming, and we will also sometimes rely on semidefinite programming.