# Summer Graduate School

Parent Program: |
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Location: |
UC Berkeley |

## Show List of Lecturers

- Izzet Coskun (University of Illinois, Chicago)
- Eric Larson (Brown University)
- Hannah Larson (University of California, Berkeley)
- Isabel Vogt (Brown University)

## Show List of Teaching Assistants

- Carl Lian (Tufts University)

In the last few years, there have been extraordinary developments in many aspects of curve theory. Beginning with many examples in low genus, this summer school will introduce the participants to the background behind these developments in the following areas:

- moduli spaces of stable curves
- Brill–Noether theory
- the extrinsic geometry of the curves in projective space

We will also include an introduction to some open problems at the forefront of these active areas.

#### School Structure

There will be two one-hour lectures and two problem sessions each day.

#### Prerequisites

Basic knowledge of algebraic geometry up to the level of the Riemann–Roch and Riemann–Hurwitz theorems for curves. (These theorems appear, for example, in Hartshorne’s Algebraic Geometry as Theorem IV.1.3 and Corollary IV.2.4; or in Sections 2.3 and 2.1 in Griffiths–Harris Principles of Algebraic Geometry).

#### Application Procedure

For **eligibility** and **how to apply**, see the **Summer Graduate Schools homepage.**

**Keywords and Mathematics Subject Classification (MSC)**

**Tags/Keywords**

Moduli spaces of curves

canonical curves

linear series

Brillâ€“Noether theory

degeneration

Deformation Theory

**Primary Mathematics Subject Classification**

14H51 - Special divisors on curves (gonality, Brill-Noether theory)

14H60 - Vector bundles on curves and their moduli [See also 14D20, 14F06, 14J60]

**Secondary Mathematics Subject Classification**No Secondary AMS MSC