##### Department of Mathematics,

University of California San Diego

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### Food For Thought Seminar

## Adriano Garsia

#### UCSD

## WANTED N! DERIVATIVES --> {\Huge\$}1000{\Huge\$}<-- REWARD

##### Abstract:

Let $S=\{ (a_1, b_1), (a_2,b_2),\dots, (a_n, b_n)\}$ be a set of lattice points in the first quadrant $\{(x,y): x \geq 0, y \geq 0\}$ and set \[ \Delta_S (x,y) = \det \lVert x_i^{a_j} y_i^{b_j} \rVert_{i,j=1}^n \] Let $\mathbf{M}_S$ denote the linear span of all the partial derivatives of $\Delta (x,y)$. Computer data reveals that these vector spaces of polynomials intersect in the most remarkable ways. Since the eary 90's we have accumulated a variety of conjectures most of which are still open. In this talk we will give a glimpse of this amazing mathematical Kaleidoscope.

### April 24, 2008

### 11:00 AM

### AP&M B412

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