3.00 Credits
Staff. Seminar on current and recent literature in probability and algorithm. Algebraic Number Theory. (M) Staff. Prerequisite(s): Math 602/603. Dedekind domains, local fields, basic ramification theory, product formula, Dirichlet unit theory, finiteness of class numbers, Hensel's Lemma, quadratic and cyclotomic fields, quadratic reciprocity, abelian extensions, zeta and L- functions, functional equations, introduction to local and global class field theory. Other topics may include: Diophantine equations, continued fractions, approximation of irrational numbers by rationals, Poisson summation, Hasse principle for binary quadratic forms, modular functions and forms, theta functions. Algebraic Number Theory. (M) Staff. Prerequisite(s): Math 620 or with the permission of the instructor. Continuation of Math 620. Complex Algebraic Geometry. (M) Staff. Prerequisite(s): Math 602/603 and Math 609. Algebraic geometry over the complex numbers, using ideas from topology, complex variable theory, and differential geometry. Topics include: Complex algebraic varieties, cohomology theories, line bundles, vanishing theorems, Riemann surfaces, Abel's theorem, linear systems, complex tori and abelian varieties, Jacobian varieties, currents, algebraic surfaces, adjunction formula, rational surfaces, residues.