What does the $\land$ mean in this sum?
$$ H_{m,n}(z_1,z_2) = \sum\limits_{k=0}^{m\land n}(-1)^k{m \choose k}{n \choose k}z_1^{m-k}z_2^{n-k} $$
The formula is a definition of the complex Hermite polynomials. I saw it in the paper "Analytic Properties of Complex Hermite Polynomials" (PDF link via AMS.org) by E. H. Ismail.
It's not common notation, but $m \wedge n$ may be used to denote $\min\{m,n\}$: the smaller of the two integers. (Similarly, $m \vee n$ may be used to denote $\max\{m,n\}$.) This makes sense in context: we want $k \le m$ and $k \le n$ for the binomial coefficients $\binom mk$ and $\binom nk$ to make sense, and otherwise, we want $k$ to range as high as possible. If you are fine saying that $\binom nk = 0$ when $k>n$, then you can drop the upper bound on the summation and take a sum $\displaystyle \sum_{k=0}^\infty$.
This notation is derived from the join and meet operations on partially ordered sets. This is a more general idea. If $x$ and $y$ are two elements of a partially ordered set, then their meet $z = x \wedge y$ (if it exists) must satisfy
If $\le$ is the usual ordering on real numbers, then $x \wedge y$ reduces to $\min\{x,y\}$.