## MATH 245B: Topics in Algebraic Geometry

May be repeated for credit.

Terms: Win
| Units: 3
| Repeatable for credit

Instructors:
Li, J. (PI)

## MATH 249A: Topics in number theory

Topics of contemporary interest in number theory. May be repeated for credit.

Terms: Aut
| Units: 3
| Repeatable for credit

Instructors:
Taylor, R. (PI)

## MATH 256A: Partial Differential Equations

The theory of linear and nonlinear partial differential equations, beginning with linear theory involving use of Fourier transform and Sobolev spaces. Topics: Schauder and L2 estimates for elliptic and parabolic equations; De Giorgi-Nash-Moser theory for elliptic equations; nonlinear equations such as the minimal surface equation, geometric flow problems, and nonlinear hyperbolic equations.

Terms: Aut
| Units: 3

Instructors:
Luk, J. (PI)

## MATH 256B: Partial Differential Equations

Continuation of 256A.

Terms: Win
| Units: 3
| Repeatable for credit

Instructors:
Ryzhik, L. (PI)

## MATH 257C: Symplectic Geometry and Topology

Continuation of 257B. May be repeated for credit.

Terms: Spr
| Units: 3

Instructors:
Varolgunes, U. (PI)

## MATH 263A: Algebraic Combinatorics and Symmetric Functions

Symmetric function theory unifies large parts of combinatorics. Theorems about permutations, partitions, and graphs now follow in a unified way. Topics: The usual bases (monomial, elementary, complete, and power sums). Schur functions. Representation theory of the symmetric group. Littlewood-Richardson rule, quasi-symmetric functions, combinatorial Hopf algebras, introduction to Macdonald polynomials. Throughout, emphasis is placed on applications (e.g. to card shuffling and random matrix theory). Prerequisite: 210A and 210B, or equivalent.

Terms: Aut
| Units: 3
| Repeatable for credit

Instructors:
Diaconis, P. (PI)

## MATH 263C: Topics in Representation Theory

May be repeated for credit.

Terms: Spr
| Units: 3
| Repeatable for credit

Instructors:
Bump, D. (PI)

## MATH 269: Topics in symplectic geometry

May be repeated for credit.

Terms: Aut
| Units: 3
| Repeatable for credit

Instructors:
Eliashberg, Y. (PI)

## MATH 272: Topics in Partial Differential Equations

Terms: Spr
| Units: 3
| Repeatable for credit

Instructors:
Berestycki, H. (PI)

## MATH 273: Topics in Mathematical Physics (STATS 359)

Covers a list of topics in mathematical physics. The specific topics may vary from year to year, depending on the instructor's discretion. Background in graduate level probability theory and analysis is desirable.

Terms: Aut
| Units: 3
| Repeatable for credit

Instructors:
Chatterjee, S. (PI)

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