In Chapter 1, we have seen how the algebra of the polynomial rings k [x1,..., xn] and the
geometry of affine algebraic varieties are linked. In this chapter, we will study the method of …

The world is continuous, but the mind is discrete. David Mumford We seek to bridge some
critical gaps between various? elds of mathematics by studying the interplay between the …

Probability calculations under the IAC hypothesis - ScienceDirect Skip to main contentSkip to
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Ehrhartʼs famous theorem states that the number of integral points in a rational polytope is
a quasi-polynomial in the integral dilation factor. We study the case of rational dilation …

This article belongs to a series on geometric complexity theory (GCT), an approach to the P
vs. NP and related problems through algebraic geometry and representation theory. The …

McDuff has previously shown that one four‐dimensional symplectic ellipsoid can be
symplectically embedded into another if and only if a certain combinatorial criteria holds. We …

barvinok: User Guide Page 1 barvinok: User Guide Version: barvinok-0.39 Sven
Verdoolaege January 15, 2016 Contents Contents 1 1 isl interface 5 1.1 Library …

Motivated by the formula for the sum of the geometric series, we consider various classes of
sets S⊂ Zd of integer points for which an a priori “long” Laurent series or polynomial∑ m∈ …

Undergraduate Texts in Mathematics are generally aimed at third-and fourthyear
undergraduate mathematics students at North American universities. These texts strive to …

While much research has been done on the Ehrhart functions of integral and rational
polytopes, little is known in the irrational case. In our main theorem, we determine exactly …