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In the last decade, there has been a growing interest in the study of rational points on homogeneous spaces of linear algebraic groups defined over fields having good arithmetical properties other tha...
A difference field is a field with a distinguished automorphism. Automorphisms of a finite field are powers of the Frobenius map. In this talk, I will discuss how to estimate the number of rational po...
Let $\{a(t):t \in \mathbb{R}\}$ be a diagonalizable subgroup of $SL(d,\mathbb{R})$ for which the expanded horosphere $U$ is abelian. By the Birkhoff ergodic theorem, for any point $x \in SL(d,\mathbb{...
Of all the creatures on Earth, humans manipulate their environments the most. But, how far can we push it before something drastic happens? Scientists are calling for a better understanding of past ex...
Scientists last autumn revealed that the gas phosphine was found in trace amounts in Venus’ upper atmosphere. That discovery promised the slim possibility that phosphine serves as a biological signatu...
With the first day of spring around the corner, temperatures are beginning to rise, ice is melting, and the world around us is starting to blossom. Scientists sometimes refer to this transition from w...
Research by Rice University Earth scientists suggests that virtually all of Earth’s life-giving carbon could have come from a collision about 4.4 billion years ago between Earth and an embryonic plane...
The first direct evidence that humans played a substantial role in the extinction of the huge, wondrous beasts inhabiting Australia some 50,000 years ago -- in this case a 500-pound bird -- has been d...
Lush greenery rich in Douglas fir and hemlock trees covers the Triangle Lake valley of the Oregon Coast Range. Today, however, geologists across the country are more focused on sediment samples dating...
The ring of projective invariants of eight ordered points on the line is a quotient of the polynomial ring on V , where V is a fourteen-dimensional representation of S8, by an ideal I8, so the modular...
Consider the projective coordinate ring of the GIT quotient (P1)n//SL(2), with the usual linearization, where n is even. In 1894, Kempe proved that this ring is generated in degree one. In [HMSV2]we s...
The ring of projective invariants of n ordered points on the projective line is one of the most basic and earliest studied examples in Geometric Invariant Theory. It is a remarkable fact and the point...
A central question in invariant theory is that of determining the relations among invariants. Geometric invariant theory quotients come with a natural ample line bundle, and hence often a natural proj...
We develop a rather elaborate computer program to investigate the jointly periodic points of one-dimensional cellular automata. The experimental results and mathematical context lead to questions, con...

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