**Title:** Enumerative Geometry and Physics

**Speaker:** Sheldon Katz

**Speaker Info:** UIUC

**Brief Description:**

**Special Note**:

**Abstract:**

Enumerative Geometry is concerned with counting geometric objects which satisfy prescribed geometric conditions. The field is quite ancient. For instance, more than 2200 years ago, Appolonius investigated circles which are tangent to each of three given circles in the plane; there are typically 8 such Appolonian circles.Over the centuries, the field of enumerative geometry has undergone many cycles during which it has flourished, fallen out of favor, and then become reinvigorated by new questions and ideas.

Since 1991, a torrent of new ideas from physics has informed and inspired enumerative geometry with no end in sight. Mathematicians have returned the favor by advancing string theory and quantum field theory using geometry, setting up a positive feedback loop benefiting many areas of mathematics and physics.

In this talk, I will provide an example-based tour of the field from the dual perspectives of algebraic geometry and string theory, beginning with antiquity and ending with some of the questions that practitioners are scratching their heads about today.

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