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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?
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Dear Abdelmalek Mohammed thanks for the interesting link.
The following is interesting too
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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!
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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?
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Generally speaking few subgroups survives quantization. As an example the usual embedding o(n)->o(n+1) does not survive in quantization. A quantum group has few quantum subgroups (there are a couple of different notions of quantum subgroups though). In the strong sens of a Hopf subalgebra of the original Hopf algebra I have very strong doubts that U_q(so(2))xU_q(so(3) will sit inside U_q(so(2,3)). It has to be carefully checked with explicit formula of generators and relations.
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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.
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With rationalism, believing in innate ideas means to have ideas before we are born.-for example, through reincarnation. Plato best explains this through his theory of the forms,which is the place where everyone goes and attains knowledge before they are taken back to the “visible world”. Innate ideas can explain why some people are just naturally betterat some things than other people are- even if they have had the same experiences Believing that reason is the main source of knowledge is another clear distinction of rationalism. Rationalists believe that the 5 senses only give you opinions, not reasons. For example, in Descartes’ wax argument, he explains how a candle has one shape to begin with- but once the candle is lit, it begins to melt, lose its fragrance, and take on a completely different shape than it had started with. This argument proves that our senses can be deceiving and that they should not be trusted.
Deduction is a characteristic of rationalism, which is to prove something       with certainty rather than reason. For example, Descartes attempted to prove the existence of God through deductive reasoning in his third meditation. It went something like this: “ I have an idea of a perfect substance, but I am not a perfect substance, so there is no way I could not be the cause of this idea, so there must be some formal reality which is a perfect substance- like God. Because only perfection can create perfection, and though it can also create imperfection- nothing that is imperfect can create something that is perfect.
On the other bank lies empiricism  unlike rationalists, empiricists believe that sense perception is the main source of knowledge. John Locke explained this by dividing ideas into 2 parts: 1) simple, and 2) complex. Simple ideas are based only on perception, like color, size, shape, etc. Complex ideas are formed when simple ideas are combined.Another belief of empiricists is that ideas are only acquired through experience, and not through innate ideas. Empiricists reject the concept of innate knowledge because, in ex., if children had this knowledge, why do they not show it? Like why does a baby need to learn to walk or talk, why does he or she not have this knowledge at birth? Lock believed that only with experiences could one form simple ideas, which could then be combined into complex ideas.
Induction is the final characteristic of empiricists. It is the belief that very few things, if any, can be proven conclusively. For example, we know of things by using our sense perception. We know that the color of the chalkboard is green and that the color of the dry erase board is white, but we cannot without a doubt conclude that those perceptions agree with the objects themselves. There is no way to conclusively prove that the chalk  board stays green once we leave the room and stop perceiving it. There is no way to conclusively prove that the chalkboard even exists once we stop perceiving it. 
Through his Meditations and wax theory, Descartes clearly illustrates that he is a 0rationalist In his wax theory, Descartes explains how one cannot rely on ones sense perceptions using the example of a candle. When the candle is in its original state, it has a unique shape. Once the candle is burned down and melted, it clearly has a completely different shape as well as many other different characteristics.
In his Meditations, Descartes attempts to prove that both himself and God exist. When proving that he himself exists, he claims that because he is thinking, he exists. Because thinking requires thought, and in order to have thoughts you must exist. When proving God exists, Descartes concludes that you cannot think of God without thinking of existence, and because existence is a relationship and not a characteristic, God must exist.-
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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.
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The idea you suggest is classic. It has been used e.g. in the paper of P. Planche
Structures de Finsler invariantes sur les espaces symétriques (MR1366100). 
The Riemannian metric obtained from the John ellipsoid gives you an analytic metric in the case of a Lie group (or more generally a homogenous space). But on a generic Finsler manifold, this construction is not smooth and it is better to work with the Binet-Legendre metric; see  Matveev-Troyanov "The Binet-Legendre metric in Finsler geometry" (MR3033515). See also teh appendix in http://arxiv.org/abs/1408.6401
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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?
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Up-dates as regards telling lies:
Conflict in Roles: Lying to the In-Group Versus the Out-Group in Negotiations . Glac, Katherina; Warren, Danielle E; Chen, Chao C. Business & Society 53.3 (May 2014): 440-460
The relation between 8- to 17-year-olds’ judgments of other’s honesty and their own past honest behaviors. Evans, Angela D.; Lee, Kang. International Journal of Behavioral Development 38.3 (May 2014): 277-281.
“A life worth living." Langan, Robert. Psychotherapy 51.2 (Jun 2014): 322-323.
Trust at zero acquaintance: More a matter of respect than expectation of reward. Dunning, David; Anderson, Joanna E.; Schlösser, Thomas; Ehlebracht, Daniel; Fetchenhauer, Detlef. Journal of Personality and Social Psychology 107.1 (Jul 2014): 122-141.
Bullying in the digital age: A critical review and meta-analysis of cyberbullying research among youth. Kowalski, Robin M.; Giumetti, Gary W.; Schroeder, Amber N.; Lattanner, Micah R.. Psychological Bulletin 140.4 (Jul 2014): 1073-1137.
Collective Interviewing: Eliciting Cues to Deceit Using a Turn-Taking Approach Vernham, Zarah; Vrij, Aldert; Mann, Samantha; Leal, Sharon; Hillman, Jackie. Psychology, Public Policy, and Law (June 16, 2014).
Police interviewing and interrogation of juvenile suspects: A descriptive examination of actual cases. Cleary, Hayley M. D.. Law and Human Behavior 38.3 (Jun 2014): 271-282.
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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?
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Thank you for your responses. I agree with your suggestion that the '1' refers to the depth would be consistent with what he writes, Salvatore.
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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?
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1. Bluman, Kumei: Symmetries and DEs
Ovsyannikov: Group anal of DEs
Olver: Applications of Lie groups to DEs
Bluman Cole Similarity methods for DEs
2. If you have, say, a second order ODE for y, then you can turn it into an equivalent system of first order ODEs by introducing y and y' as new variables.
I hope this helps, János
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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.
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Dear Lee,
Take for a example a group of rigid transformations of a plane, i.e. translations and rotations. Imagine now that you have a set of this functions, say, a finite set of functions defined by the image of a regular grid of points.. Now I would like to determine the dimensionality of this set of functions and to parametrize the set I have, so that the parametrization would preserve the topology. For that I would like to introduce a metric on this functions and then use dimension reduction techiques, like isomap, to find the dimension of the corresponding manifold. This can be easily done for translations, but becomes less trivial for rotations. One idea is to define a metric based on a mapping of a bounded domain in the plane, e.g. rho(f1, f2) = ||f2*f1^-1|| + ||f1*f2^-1|| and ||f|| = max_{x in X} ||x-f(x)||, where X is a bounded domain in plane.
The problem with this definition is that I cannot be sure that there always exist such X that for every two different mappings the metric defined this way will not vanish.
Best,
Alex