## Tentative Course Schedule for the Graduate Program

This is all information for graduate courses in the **Autumn 2018** quarter.

Course | Title | Instructor | Time | Days | Room | |
---|---|---|---|---|---|---|

MATH 30900 | Model Theory 1 | Malliaris, Maryanthe | 2:00-3:20 | TR | Eck 207 | |

MATH 31200 | Analysis 1 | Souganidis, Panagiotis | 9:30-10:20 | MWF | Eck 206 | |

MATH 31700 | Topology/Geometry 1 | Weinberger, Shmuel | 9:30-10:50 | TR | Eck 202 | |

MATH 32500 | Algebra 1 | Ginzburg, Victor | 1:30-2:20 | MWF | Eck 202 | |

MATH 35600 | Topics In Dynamical Systems | Wilkinson, Amie | 2:00-3:20 | TR | Eck 206 | |

MATH 35712 01 | Literacy in Partial Differential Equations 2 | Souganidis, Panagiotis | 2:00-3:20 | TR | Eck 117 | |

MATH 36000 | Topology Proseminar | May, J. Peter | 2:00-3:20 | TR | Eck 203 | |

MATH 36501 | Perfectoid Spaces | Matthew, Akhil | 3:30-4:20 | MWF | Ry 358 | |

MATH 36801 | Complex Manifolds and Varieties I | Webster, Sidney | 2:00-3:20 | TR | Eck 312 | |

MATH 37000 | Proseminar in Probability and Statistical Physics | Lawler, Gregory | 1:30-2:50 | MW | Eck 308 | |

MATH 37106 | Topics in Geometric Measure Theory-1 | Csornyei, Marianna | 2:00-3:20 | TR | Eck 202 | |

MATH 38311 | (higher) Hida Theory | Calegari, Frank & Boxer, George | 1:30-2:50 | MW | Eck 206 | |

MATH 38511 | Brownian Motion and Stochastic Calculus | Lawler, Gregory | 9:30-10:50 | TR | TBA | |

MATH 38910 | Cobordism and Complexity | Weinberger, Shmuel | 2:00-3:20 | TR | Eck 308 | |

MATH 39702 | The 4-dimensional Poincare Conjecture | Calegari, Danny | 11:00-12:20 | TR | Eck 117 | |

MATH 39901 | Automorphic L-Functions | Ngô, Bảo Châu | 11:00-12:30 | TR | Eck 203 | |

MATH 42900 | Mathematical Modeling of Large Scale Brain Activity 1 | Cowan, Jack | 3:30-4:50 | TR | Eck 117 | |

MATH 47000 | Geometric Langlands Seminar | Beilinson, Alexander & Drinfeld, Vladimir | 4:30-8:00 | MR | Eck 206 | |

MATH 59900 | Reading/Research: Mathematics | (See faculty listing) | N/A | N/A | N/A |

### MATH 31200: Analysis I

Topics include: Measure theory and Lebesgue integration, harmonic functions on the disk and the upper half plane, Hardy spaces, conjugate harmonic functions, Introduction to probability theory, sums of independent variables, weak and strong law of large numbers, central limit theorem, Brownian motion, relation with harmonic functions, conditional expectation, martingales, ergodic theorem, and other aspects of measure theory in dynamics systems, geometric measure theory, Hausdorff measure.

### MATH 31700: Algebraic Topology

Fundamental group, covering space theory and Van Kampen's theorem (with a discussion of free and amalgamated products of groups), homology theory (singular, simplicial, cellular), cohomology theory, Mayer-Vietoris, cup products, Poincare Duality, Lefschetz fixed-point theorem, some homological algebra (including the Kunneth and universal coefficient theorems), higher homotopy groups, Whitehead's theorem, exact sequence of a fibration, obstruction theory, Hurewicz isomorphism theorem.

### MATH 32500: Representation Theory

Representation theory of finite groups, including symmetric groups and finite groups of Lie type; group rings; Schur functors; induced representations and Frobenius reciprocity; representation theory of Lie groups and Lie algebras, highest weight theory, Schur–Weyl duality; applications of representation theory in various parts of mathematics.

### MATH 35600: Topics in Dynamical Systems

An independent study in topics in dynamical systems.

### MATH 36000: Topology Proseminar

This informal "proseminar" is devoted to topics in algebraic topology and neighboring fields. Talks are given by graduate students, postdocs, and senior faculty. They range from basic background through current research.

### MATH 37609: Topics In PDE

We will study elliptic partial differential equations including regularity results such as De Giorgi/Nash theory, Krylov-Safonov theory, and nonlinear equations.

### MATH 38305: A Second Course In Number Theory

The goal of this course will be to introduce some new methods and techniques beyond those covered in MATH 32700, and also to give many worked examples on how to use these ideas in practice. Specific topics may include L-functions, applications of class field theory, and Diophantine equations.

### MATH 38704: Quantitative Unique Continuation For Elliptic Equations

In this course we will discuss classical unique continuation results for second order eigenvalue problems. Such results are of interest in themselves, but also in nonlinear pde problems, in mathematical physics and in nodal geometry. In this connection, we will also discuss the recent breakthrough works of Logunov and Malinikova on the Yau and Nadirashvili conjectures in nodal geometry.

### MATH 41005: Sheaf Theory And Homological Algebra

An introduction to Grothendieck's six functor formalism, aimed at second year students.

### MATH 42900: Mathematical Modeling of Large-Scale Brain Activity 1

An independent study in mathematical modeling.

### MATH 47000: Geometric Langlands Seminar

This seminar is devoted not only to the Geometric Langlands theory but also to related subjects (including topics in algebraic geometry, algebra and representation theory). We will try to learn some modern homological algebra (Kontsevich's A-infinity categories) and some "forgotten" parts of D-module theory (e.g. the microlocal approach).