Pure Maths Colloquium: On some questions in Diophantine approximation
7 April 2014 16:00 in CM221
The theory of Diophantine approximation stems from a simple question "How well can a real number be approximated with rationals?". Development of this theory provided us with the first evidence that transcendental numbers do exist, long before Cantor invented his cardinality theory. Results that followed showed that the larger a number's Diophantine exponent is, the farther it is from algebraicity. In our talk we shall define the exponents just mentioned, consider a couple of their multidimensional generalizations, formulate some classical theorems, as well as some of recently obtained results. If time allows, we shall talk about transference principle which connects "dual" problems in multidimensional Diophantine approximation.
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