Not available at this time.

Not available at this time.

Not for credit toward major. How cancer and AIDS begin and progress. The roles of individual cells, the immune system, mutations and viruses. How various physical and subtle factors influence one's chances of getting cancer. How to not get AIDS. The principles of vaccine development and why AIDS presents special difficulties. Established and new medical treatments for cancer and AIDS. What cancer and AIDS can teach us about health, healing, disease, living, and dying. (Gen.Ed. BS)

Maximum credit, 6.

Maximum credit, 6.

This course will study the mirror symmetry phenomenon of theoretical physics from a mathematical perspective. We will study the homological mirror symmetry conjecture of Kontsevich (1994) and the related Strominger?Yau?Zaslow conjecture (1996). We will develop the necessary mathematical background as needed, including derived categories of coherent sheaves on complex manifolds and Fukaya categories of symplectic manifolds. We will rigorously establish instructive special cases of the homological mirror symmetry conjecture.

Introduction to the modern methods in partial differential equations. Calculus of distributions: weak derivatives, mollifiers, convolutions and Fourier transform. Prototype linear equations of hyperbolic, parabolic and elliptic type, and their fundamental solutions. Initial value problems: Cauchy problem for wave and diffusion equations; well-posedness in the Hilbert-Sobolev setting.

Lie algebras are linear algebra devices of great usefulness in mathematics and physics as an efficient tool for the study of symmetries of objects. This course will cover the fundamentals of the subject, including nilpotent and solvable Lie algebras, as well as semisimple Lie algebras and their representations.

Representation theory studies the way groups, rings and other algebraic structures can act by linear symmetries. We will consider representations of finite groups, the general linear group, the symmetric group, and quiver algebras. If time permits, we cover the theory of Soergel bimodules and applications to knot homology. We will provide suggestions for further reading to explore the beyond the listed examples. Students will prepare a presentation on a topic related to class discussion. A list of topics will offered in class.

Elliptic curves, as the only smooth projective algebraic curves equipped with a group law, play a central role in modern arithmetic geometry. The goal of this course is to learn the tools and techniques required to study these groups over the rational numbers by first studying them over finite fields, p-adic fields and archimedean fields.