2022-2023 Colloquia

Abstract:  

This talk will be about joint work with Gershom Bazerman and Raymond Puzio on a mathematical model of package management systems, which are pervasive in modern software development. An example of such a system is when using packages in latex. We introduce structures known as Dependency Structures with Choice (DSC) that provide a mathematical account of such dependencies, inspired by the definition of general event structures in the study of concurrency. We equip DSCs with a particular notion of morphism and show that the category of DSCs is isomorphic to the category of antimatroids. We study the exactness properties of these equivalent categories, and show that they are finitely complete, have finite coproducts but not all coequalizers. Further, we construct a functor from a category of DSCs equipped with a certain subclass of morphisms to the opposite of the category of finite distributive lattices, making use of a simple finite characterization of the Bruns-Lakser completion, and finally, we introduce a formal account of versions of packages and introduce a mathematical account of package version-bound policies.

Abstract:  

This talk will discuss and prove Bell's Theorem, a strange result in physics.  The theorem, combined with experimental results, shows that the universe is non-local.  This means that an event in one location can have an instantaneous effect on another location, any distance away, from a few feet to light-years.  The topic is timely, as the 2022 Nobel Prize for physics was awarded for related experiments. 

Abstract:  

Somewhat recently, there has been a surge of activity in almost complex geometry (ACG) while little to no work has been done in almost symplectic geometry (ASG) even though ACG is equivalent to ASG.  Interestingly, complex geometry and symplectic geometry are not equivalent.  Indeed, there are complex manifolds with no symplectic structure and symplectic manifolds with no complex structure.  For this reason, there may be some value in establishing a `dictionary' between ACG and ASG.  Results in ACG could be translated into ASG, and since symplectic geometry is a special case of ASG, one hopes that some new tools could emerge which would be beneficial to symplectic geometry.  Of course, the reverse is also possible.  One can also imagine generalizing known results in symplectic geometry to ASG and then translating them to ACG where they could be useful to complex geometry.  In this talk, we give a gentle introduction to ASG.  If time permits, we will speculate on some tentative ideas that could be developed as part of an ASG research program.  (This is joint work with Fei Ye.)