Related papers: Virtual classes for the working mathematician
As more people work from home or during travel, new opportunities and challenges arise around mobile office work. On one hand, people may work at flexible hours, independent of traffic limitations, but on the other hand, they may need to…
Although interactive learning puts the user into the loop, the learner remains mostly a black box for the user. Understanding the reasons behind queries and predictions is important when assessing how the learner works and, in turn, trust.…
We consider virtual pullbacks in $K$-theory, and show that they are bivariant classes and satisfy certain functoriality. As applications to $K$-theoretic counting invariants, we include proofs of a virtual localization formula for schemes…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
In our days, the necessity of laboratory apparatus accustoming by building up specific software objects for studying the virtual evolution of physical phenomena is a major request. In this respect, the aim of the present paper is to present…
There is a need for remote learning and virtual learning applications such as virtual reality (VR) and tablet-based solutions which the current pandemic has demonstrated. Creating complex learning scenarios by developers is highly…
We describe a simple formalism for generating classes of quantum circuits that are classically efficiently simulatable and show that the efficient simulation of Clifford circuits (Gottesman-Knill theorem) and of matchgate circuits…
Group Theory has become an invaluable tool in the physics community. Despite numerous introductory books, the subject remains challenging for beginners. Mathematica has emerged as a popular tool for research and education, offering various…
Since the introduction of quantum mechanics, it has been taught mostly as a theoretical subject. It is also viewed as a theory that provides a best understanding of the nature, but which does not have much practical applications in our day…
This paper presents and analyses existing taxonomies of virtual and augmented reality and demonstrates knowledge gaps and mixed terminology which may cause confusion among educators, researchers, and developers. Several such occasions of…
Deep learning is ubiquitous, but its lack of transparency limits its impact on several potential application areas. We demonstrate a virtual reality tool for automating the process of assigning data inputs to different categories. A dataset…
These expository notes are based on a series of lectures given at the May 2018 Snowbird workshop, Crossing the Walls in Enumerative Geometry. We give an introductory treatment of the notion of a virtual fundamental class in algebraic…
We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.
These notes provide an introduction to standard topics on quantum computation and communication for those who already have a basic knowledge of quantum mechanics. The main target audience are professional physicists as well as advanced…
We outline an unified introduction to the evolution equations of classical and quantum systems intended for a high school students audience. The attempt consists in circumventing the lack of mathematical knowledge with the use of simplified…
Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.
We discuss the idea that computers might soon help mathematicians to prove theorems in areas where they have not previously been useful. Furthermore we argue that these same computer tools will also help us in the communication and teaching…
We suggest a construction of virtual fundamental classes of certain types of moduli spaces.
Interactive proof assistants make it possible for ordinary mathematicians to write definitions and theorems in a formal proof language, like a programming language, so that a computer can parse them and check them against the rules of a…
The virtual learning in University Education is the learning which is presented by set of integrated information and pedagogical technologies, in a process of interaction between subjects and objects as the virtual educational resources.…