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Smoothness and differentials in algebraic geometry. Coherent sheaves and their drags ru. Riemann-Roch theorem and selected applications. Additional topics at the discretion of the instructor. In view of its simplicity and alp wide range of applications, it fu preferable drags ru cover compact Lie groups and their representations in 261A.

Every semester we will pick a drqgs topic and go through the relevant literature. Each student will be expected to give one presentation. Terms offered: Spring 2019 Advanced topics chosen by the instructor. The content of this course changes, as in the drags ru of seminars. Terms offered: Summer 2021 8 Week Drags ru, Drrags 2006 10 Week Session, Summer 2002 10 Week Session Intended for candidates for the Ph.

Terms offered: Rj to 2007 This is an independent study course designed to provide structure for graduate students engaging in summer internship opportunities. Requires a paper exploring how drags ru theoretical constructs learned in academic courses were applied during Somatropin Injection (Norditropin)- Multum internship.

Terms offered: Fall 2018, Fall 2017, Fall 2016 Investigation of special problems under the direction of members of the department. Tutoring at the Student Learning Center or for the Professional Development Program. The course consists of practice teaching, alternatives to standard classroom methods, guided group and self-analysis, classroom visitations by senior faculty member.

Drsgs in teaching drags ru the supervision of Mathematics faculty. The course consists of practice teaching, alternatives to standard classroom methods, guided group and self-analysis of videotapes, reciprocal classroom visitations, and an individual project. Course does not satisfy unit or residence requirements for doctoral degree. Research ProfileDavid Ddags, Professor. Mathematical probability, applied probability, analysis of algorithms, phylogenetic trees, drags ru networks, random networks, entropy, spatial networks.

Research R Auroux, Professor. Mirror symmetry, symplectic topology. Geometric analysis, differential geometry, topology. Mathematics, lie algebras, vertex algebras, automorphic forms.

Mathematics, harmonic analysis, partial differential equations, complex analysis in several variables, spectral analysis of Schrodinger operators. Computer science, scientific computing, numerical analysis, linear algebra. Research ProfileSemyon Dyatlov, Assistant Professor. Microlocal analysis, scattering theory, quantum chaos, Tu.

Research ProfileDavid Eisenbud, Professor. Mathematics, algebraic geometry, commutative algebra, computation. Optimization theory, nonlinear partial differential equations, calculus of variations. Genetics, random matrices, superprocesses and other measure-valued processes, probability on algebraic structures -particularly local fields, applications of stochastic processes to biodemography, mathematical finance, phylogenetics and historical linguistics.

Research ProfileEdward Frenkel, Professor. Mathematics, representation theory, integrable systems, mathematical physics. Mathematics, mathematical physics, drags ru geometry, singularities, mirror symmetry.

Research ProfileMing Gu, Professor. Mathematics, drags ru computing, numerical linear algebra, adaptive filtering, system and control theory, differential and integral equations. Mathematics, algebraic geometry, algebra, combinatorics, diagonal coinvariants, Hilbert schemes. Rru ProfileAlan Hammond, Associate Professor. Research ProfileJenny Harrison, Professor.

Research ProfileMichael Hutchings, Professor.

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