## MATH 233A: Topics in Combinatorics

Geometry of polynomials and non-constructive proofs in combinatorics: The independence polynomial, the Lovasz Local Lemma and Shearer's Lemma. Real-rooted polynomials, stable polynomials, Ramanujan graphs and the Kadison-Singer problem. Strongly Rayleigh measures and negative dependence. Applications in algorithms.

Terms: Win
| Units: 3
| Repeatable for credit

Instructors:
Vondrak, J. (PI)

## MATH 236: Introduction to Stochastic Differential Equations

Brownian motion, stochastic integrals, and diffusions as solutions of stochastic differential equations. Functionals of diffusions and their connection with partial differential equations. Random walk approximation of diffusions. Prerequisite: 136 or equivalent and differential equations.

Terms: Win
| Units: 3

Instructors:
Papanicolaou, G. (PI)

## MATH 238: Mathematical Finance (STATS 250)

Stochastic models of financial markets. Forward and futures contracts. European options and equivalent martingale measures. Hedging strategies and management of risk. Term structure models and interest rate derivatives. Optimal stopping and American options. Corequisites:
MATH 236 and 227 or equivalent.

Terms: Win
| Units: 3

Instructors:
Papanicolaou, G. (PI)

## MATH 244: Riemann Surfaces

Riemann surfaces and holomorphic maps, algebraic curves, maps to projective spaces. Calculus on Riemann surfaces. Elliptic functions and integrals. Riemann-Hurwitz formula. Riemann-Roch theorem, Abel-Jacobi map. Uniformization theorem. Hyperbolic surfaces. (Suitable for advanced undergraduates.) Prerequisites:
MATH 106 or
MATH 116, and familiarity with surfaces equivalent to
MATH 143,
MATH 146, or
MATH 147.

Terms: Aut
| Units: 3
| Repeatable for credit

Instructors:
Mazzeo, R. (PI)

## 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:
Soundararajan, K. (PI)

## MATH 249B: Topics in Number Theory

Terms: Win
| Units: 3
| Repeatable for credit

Instructors:
Tsai, C. (PI)

## MATH 256B: Partial Differential Equations

Continuation of 256A.

Terms: Win
| Units: 3
| Repeatable for credit

Instructors:
Weinstein, M. (PI)

## MATH 257B: Symplectic Geometry and Topology

Continuation of 257A. May be repeated for credit.

Terms: Aut
| Units: 3
| Repeatable for credit

Instructors:
Ionel, E. (PI)

## MATH 257C: Symplectic Geometry and Topology

Continuation of 257B. May be repeated for credit.

Terms: Spr
| Units: 3

Instructors:
Latschev, J. (PI)

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