RAMMP Summer Colloquium
All talks

Wednesday, June 19, 2019, 01:45PM, Marshak 418N
David Aulicino (Brooklyn College), VertexToSelf Trajectories on the DodecahedronStarting at a vertex of a Platonic solid, is it possible to walk on the surface of it in a straight line so that we return to the vertex we started at without passing through another? Surprisingly, the answer depends on which Platonic solid we consider. We will review what the Platonic solids are and explain how to solve this problem for the tetrahedron. There will be lots of pictures, animations, and 3D models. Students are encouraged to bring scissors and tape!

Wednesday, June 12, 2019, 01:45PM, Marshak 418N
Benjamin Steinberg (CCNY and CUNY Graduate Center), Logic on wordsThe study of formal languages is a classical area in Logic and Theoretical Computer Science. The Chomsky hierarchy classifies languages by how complicated a model of computation is needed to describe the language. At the bottom of the Chomsky hierarchy sits the class of regular languages. Regular languages, while not powerful, are very versatile as they can be described via a number of different formalisms, including regular expressions and finite state automata, and most algorithmic questions about regular languages can be decided (often efficiently).
In this talk I will give a brief introduction to the concept of a regular language and explain how regular languages can be specified using the kind of logic you see in MATH 308, called first order logic, and a slightly stronger logic that lets you quantifying over subsets (called monadic second order logic). Logical specification turns out to be important if program verification. Büchi showed that regular languages are exactly those languages that can be defined by a sentence of monadic second order logic. However, to distinguish those languages definable in first order logic (the MATH 308 sort) and this fancier logic, one needs to use algebra. I’ll also indicate some of the surprisingly simple to state problems about logic on words that are still open and which one hopes to answer using algebraic techniques.

Thursday, June 06, 2019, 11:00AM, Marshak 418N
Gautam Chinta (CCNY and CUNY Graduate Center), Sums of squares and composition lawsWhich numbers can be written as a sum of two squares? Or of three or four squares? We will discuss these questions and explain how they tie into the fascinating subject of composition laws for binary quadratic forms.
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