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Title: Counting Blocks in Dimension 2, Part II Speaker: Nataša Jonoska Time: 4:00pm‐5:00pm Place: PHY 118
Title: Counting Blocks in Dimension 2 Speaker: Nataša Jonoska Time: 4:00pm‐5:00pm Place: PHY 118
We consider subsets of the set of all actions of \(Z\times Z\) onto a finite alphabet. These subsets (called shifts) are closed under the multiplication with the generators \((0,1)\) and \((1,0)\) and topologically closed (alphabet has discrete topology and the actions are equipped with the product topology).
We introduce the notion of “uniform transitivity” which is stronger than topologicaltransitivity, but, it implies topological entropy-minimal systems.
Title: Forbidding and Enforcing Systems, Part II Speaker: Daniela Genova Time: 4:00pm‐5:00pm Place: PHY 118
Title: Forbidding and Enforcing Systems Speaker: Daniela Genova Time: 4:00pm‐5:00pm Place: PHY 118
We present a new way of defining classes of formal languages through a set of forbidden subwords and a set of enforced words. Forbidding and enforcing systems were inspired by chemical properties of DNA and actions of restriction enzymes. These systems will be presented through description of several graph theoretical problems and some topological observations will be discussed.
Title: Algebraic Characterizations of Graph Regularity Conditions Speaker: Brian Curtin Time: 4:00pm‐5:00pm Place: PHY 118
A theorem of algebraic graph theory can be stated as follows: A finite simple connected graph is regular if and only if the all-ones matrix spans an ideal of the adjacency algebra. We show that several other graph regularity conditions have ideal theoretic characterizations in appropriate algebras.
Title: TBA Speaker: David Kephart Time: 4:00pm‐5:00pm Place: PHY 118
Complexity Measures and Least Fixed Point Logic Greg McColm 4:00pm-5:00pm PHY 118
We will look at a time complexity measure and a space complexity measure on Least Fixed Point logic. We will use the algebraic approach of Moschovakis (~1980) and Hodges that the audience seems to prefer.
Title: The Foundations of Least Fixed Point Logic Speaker: Greg McColm Time: 4:00pm‐5:00pm Place: PHY 118
This will be a basic introduction of least fixed point logic, from Tarski to Moschovakis. We will conclude with a look at two complexity measures.
Title: The Number of Recursion Variables Speaker: Greg McColm Time: 1:00pm‐2:00pm Place: PHY 109
The Number of Recursion Variables (also called “dimension” or “arity” is a space-complexity measure introduced two decades ago. We review its prehistory and its history, mostly in the logic of First Order Logic \(+\) Least Fixed Points, and then look at a conjecture I'm launching.
Title: Combinatorial and Inverse Relations, Part II Speaker: Mourad Ismail Time: 1:00pm‐2:00pm Place: PHY 109
Title: Combinatorial and Inverse Relations Speaker: Mourad Ismail Time: 1:00pm‐2:00pm Place: PHY 109
We show how generalized Taylor series lead to combinatorial identities and inverse relations. One example is a two parameter family of matrices \(A(a,b)\) with the property \(A(a,b)A(b,c)=A(a,c)\). Also \(A^{-1}(a,b)=A(b,a)\). No differential equations will be used.