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# Lie Theory - Science topic

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Dear colleagues,

Could you please recommend conferences and Schools in 2020-2021 having Geometry (Symplectic, Lie theory) and topology (differential, low dimensional) as their main topics?

Hi everyone!

I am to write the history of some medical devices and two of them are very hard to find. I am talking about the polygragh and angiograph.

Can you send me some links where I can find valuable information to be used in official website, please?

On the contrary, whether the history is not available anywhere, it would be okay to have some case studies in which relevant cases are explained.

Thank you very much in advance!

Let's say I take the Lie group SO(2,3). It's maximal compact subgroup is SO(2)xSO(3). What I would like to know is what happens to this maximal compact subgroup if I deform to the quantum group SOq(2,3) [By this I mean a deformation of the universal enveloping algebra of SO(2,3) into the quantum group]. Is it simply SOq(2)xSOq(3) or is something more complicated going on?

Rationalism, beginning with Descartes, underlined the ‘concealing’ character of feeling; empiricism has instead emphasized the revelatory one. Based on this observation, it also presents the opportunity to penetrate more deeply the meaning of some clichés on these two forms of philosophical thought. It is usually said that rationalism based knowledge on reason, and that instead empiricism founded learning on experience. First of all, what does it mean here "know"? The "knowledge" is just knowing that was problematized by modern philosophy. It needs a "base" or "foundation" - and the "reason" and '"experience" are intended to be just such a foundation that is - precisely - the knowledge of external reality

Knowledge can not be reduced to the simple certainty of our ideas, but captures the authentic structure of the external reality, the reality in itself. The "knowledge" is therefore what goes beyond our representations; Also: it is the set of our representations as it is able to grasp the reality outside.

What does it mean to say that rationalism base of knowledge is the "right"? You can answer this question using the distinction between function revealing and concealing function of human sensitivity.

Rationalism is conscious of the concealing character of sensitivity: to know what is beyond our sensitive representations - this is the specific viewpoint of rationalism - we can not and we will never have to rely on our sensible representations. To know what is beyond the experience we can and we should never rely on the experience

The construction of "knowledge" will then be based on principles not drawn from experience. As such, the principles are called "a priori" or "innate". It is the path opened by Descartes, where the knowledge of external reality of bodies is based on the idea of innate God and proof that this idea corresponds to a real content; and such demonstration is in turn based on a principle - "nothing does not produce anything" - which is not drawn from experience, that is valid in itself, independently of it.

Contrary to what may seem, the knowledge "a priori" knowledge is not that you turn your back to reality and it is closed in on itself to develop its own content. In contrast, for the rationalism knowledge "a priori" (or "innate") is the "bridge" that bypasses the experience and leads in contact with the external reality.

The rationalist metaphysics is precisely this bridge, the overcoming of our sensible representations, which, precisely because it is able to cross them, is not derived from them. In pre-modern philosophy, the "metaphysics" is a move "beyond" of "physical things." Physical things are bodies ‘becoming’. Metaphysics goes beyond them, in the sense that, first, it asks whether there are other bodies in addition to those ‘becoming’, and then demonstrates the existence of the immutable beyond entity, ‘becoming’.

If the problem of modern philosophy is "how to go beyond our representations," and because, in them, the appearance is sensitive to rationalism concealing element (that is responsible for the difference between representations and external reality), it follows that the overcoming of the situation in which our performances are so certain, but not yet true - will only happen as they do not take as sources of truth our sensible representations.

The history of rationalism is the story of attempts to build the metaphysical parable that is able to conduct from our representations to the outside world. While in the pre-modern philosophy metaphysics determines the truth that we believe is originally owned by the thought, in the history of rationalism metaphysics has the task of leading to that unification of certainty and truth, which is the point of departure of the traditional way of philosophizing . The starting point thus becomes the point of arrival: metaphysics becomes, in rationalism, the instrument by which the problem of the value of knowledge is resolved. The solution of the problem is the metaphysical foundation of the solution of the problem of knowledge.

At this point, reconnecting us to the foregoing (reason, Popper, falsification, scientific theory, etc.), we conclude citing the ‘critical rationalism’ that is an expression coined by Popper and indicating the belief that reason, in the field of empirical knowledge, can not have a function strictly demonstrative, but only a critical task.

Reason does not legitimate, in fact, the truth of a theory, but it should be used to criticize the theory itself. Based on the principle of falsifiability, which states that a theory is scientific only if amenable to control possibly able to falsify it (by deduction of facts of experience from basic assertions), Popper assigns to reason the task of identifying the possible errors that lie in the theory under consideration. If the basic statements do not conflict with experience, that is, if the attempts of falsification coordinated by reason have no outcome, the theory is considered "supported", but never "verified", being verified only provisionally, given that other basic claims, in the future, may falsify the theory.

Can someone tell me something about Finsler structures on Lie groups? The idea is to pick a convex norm on Lie algebra. Does this define a convex ellipsoid and extend this convex body with left-translations through all over the Lie group? It should work but I never tried myself. The other interesting question is, what if the norm is not convex? These ideas came to me while reading a paper about homogeneous (in a rather wide sense) spaces.

I'm doing my bachelor in psychology, and my main area is lying; the social and intentional lie. My topic is on, how lying makes us feel and when we lie in different social contexts. My question is: Why is it a bigger problem to figure out if you have been lied to, than perhaps the lie itself?

M. I. Kuznetsov refers to a 1-graded Lie algebra in "Simple modular Lie algebras with a solvable maximal subalgebra, Math. USSR Sb30 (1976), 68–76". Does he mean Z-graded?

There are lots of textbooks discussing symmetry analysis on differential equations such as Applications of Lie group to differential equations. All of the methods (at least all of them I have seen) focus on high order differential equations. But is there anything that focuses on dynamic systems? Or is there any proposition stating equivalence of high order differential equations and dynamic systems?

I have an infinite set of functions F = {f1, f2, ...} mapping Rn into itself. I know that this set has a group structure with respect to composition, i.e. for every fi and fj in F there exist fk in F, such that fi * fj = fk (* stands for the composition). There is unique fe which corresponds to the group unity and for every fi there is inverse: fi * fj = fj * fi = fe.

I guess that this set of functions defines a Lie group, however I don't know the number of its parameters and the indeces have no topological meaning. Is there any way to find the number of parameters and to introduce them so that the family of functions F would be smooth with respect to those parameters? My first guess was to introduce a metric on F, but I don't know how to do that. Any help would be highly appreciated.