Окей, спасибо большое. Я рад, что это последний спекарь. Подожди, это конференция. Так что, это фотография из Википедии. Так что, может быть, это первая фотография, которую вы найдете из Samsung, если вы гуглили. И эта фотография была с ИЧС. ИЧС был commonplace between me and Samsung В первый раз мы встретили, в 2006 году я был студентом в Принстон. Я пришел к ИЧС для студентов, пгс-студентов, для исследований, и встретил Samsung в первый раз. Мы ходили в форс, и говорили о том, что компонентаризация, структура H3 в Калаби-Яу, quantization of B-модель и так далее. И я был очень впечатлён, как Дипа Сотс, Samsung, что-то мне показал. И с того, как мы научились много раз, и главная тема моего current research, Gage theory, Centro integrable systems, это потому, что центральный тупик от школы, от которых мы пришли. Ну, я был тоже в Ленинграде, в фадеевской школе, Gage theory, Centro integrable systems, это продолжает мой исследователь. Итак, мы говорим сегодня о Several papers, я will summarize the key results from those, they made more recently in collaboration with the people, with the postdocs Rubin Ferasik, Alexander Tsumbalik and Chris Elliott and those are references. So, the topic of today's lecture would be a group version of a Hitchin system. And to start, we'll just recall what the Hitchin system is. So, maybe most of people are familiar but just a reminder. So, for a complex variety X and an effective divisor D of complex variety and complexative group G, G-Hicks bundle would be a pair P-Phi, where P is the principal G bundle and Phi called Hicks field or Hitchin field is a section of their agent valued bundle valued in the leal algebra, usually taken tensor with canonical line bundle on X with a singularity Cd. So, that's the usual thing. And then there is a theorem by Tachin, Mukai and others that there is an algebraically integrable system on the modular space of meromorphic Hicks bundles on a curve, on a Hitchin system. So, this touched physics in many contexts. So, a Hitchin system on a complex curve X that plays a prominent role since, you know, after the geometric Langlands program from Baylinson-Dreamfield and linked to n equals 4 supersymmetric gauge theory by Kapustin and Tvitten. And then there is a construction of the compactification of the 6d2,0 self-dual theory on X, viewed as 4dn equals 2 theory of Gallota and Diber-Kvitten system associated to that. After quantization, this Hitchin system or the integrable system of Hicks bundles, it relates to N'Krasov-Schittashvili limit of of the 6d2,0 self-dual theory compactified to the 4dn equals 2 theory, compactified on the curve on which Hitchin system is supported. And after further hyper-color rotation and quantization, or as in our slang we refer like in the case of two epsilon's, it relates to the total theory in correlation functions determined by the W-algebra. So, there is a hero here with like two ways of making the system quantum in a sense or deformation and quantization. There are two parameters which control like the classical story going to one way quantum or then going to the field theory quantum in a sense. So, then to move on and see how you can make that story like group like instead of the algebra like, let's recall an abstract Higgs bundle. So, there have been given a definition of abstract Higgs bundle, which is helpful for this work and it goes to Danagin Geitzgeri. So, to say it, reformulate and think about an ordinary Hitchin system on a kerfax with singularity as an example of an abstract Higgs bundles which will be valued in the canonical London line bundle Kx on D. Now, an abstract Higgs bundles would be pair p, c where p is the principal g bundle on x and c is the sub bundle of the agent bundle. And each fiber of c consists simply of centralizes in g of regular elements of the group g. So, then there would be an equivalence between an abstract g Higgs bundle and an abstract spectral data where spectral data consist of an abstract so-called abstract camera cover x tilde and this usually transformed on x. So, this is Danagin Geitzgeri construction and this construction then can be specialized to a valued Higgs bundle. Higgs bundle valued not in the canonical line bundle but instead on something else. So, concretely we can replace the space of values the usual canonical line bundle Kx by a family y of groups fiber over x. And then the Higgs field phi becomes a section of this thing, of the tensor product of the family y of groups and c which was mentioned on the previous slide. And then one can get let's see if I can close this one. What does this product mean if y is not effectable? No, we think about that as an abelian group a bundle of abelian groups fibers over x a bundle. So, then one can associate to this abstract spectral data a model space of Higgs sub g of y slash y over x. So, a canonical example of this fibrations studied mostly by works of Danagin was the case when y itself an algebraic variety which is fibered over base variety x and generic fiber is an elliptic curve. So, then you can consider model space of g bundles on y and this model space of g bundles on y is isomorphic to the model space of g Higgs bundles on x with values in the elliptic fibrations y over x. So, this construction of Danagin. So, in particular if y itself is two-dimensional algebraically integrable system fibered over x with elliptic fibers then the result in space bun g over y or g Higgs bundles of y over x is an algebraic integrable system. So, this is called also in slang like algebraic integrable system elliptical elliptical in vertical directions elliptical in momentum directions. So, now we can have vertical here or here in the classification of the previous page like we can consider the three cases for the structure of the vertical group of the vertical fiber namely if you take one-dimensional abelian group then it could be either non-degeneric elliptic curve or you can degenerate it by nodal degeneration to a multi-political group C star a nodal degeneration or you can first degenerate it to an additive group or just see a complex line additive group or that's the cut degeneration of elliptic curve, right? So, then I found the following quotation from the lectures of Rob Danagi in 2003 book. So, he says that Hitchin system is a modular space of bundles on arbitrary curve x bundles with arbitrary structure group with values in line bundle which is a group variety of rx with fiber g additive and then the modular space of g bundles on elliptic fibrations involves Hitchin bundles with structure group g and with values in elliptic fibrations so that's what was well studied by Danagi and other people and then he asked this question is there an interesting geometric interpretation in the remaining trigonometric case where there is no answer so it was open at that moment but apparently like many aspects of the answer to this question were known before just not connected for some reason together So, this is the question mark in the middle case where the fiber is multiplicative group while when the fiber is additive group it's the usual Hitchin system when the fiber is elliptic group then it's the modular space and then the modular space where the fiber is elliptic fibrations of rx So, the purpose of this talk would be essentially to clarify the geometrical aspects of this question mark So, we will describe and answer on some of Danagi question what is the multiplicative Hitchin models and how it connects to other topics in physics and mathematics So, we'll focus concretely here on horizontal horizontal-rational case when the base x is c or one point complication of c So concretely by x we'll take p1-infinity or well, maybe I'm mixing notations I'll be mixing notations in slides sometimes I denote by xc-point-infinity or sometimes by xp1 Usually, it will be clear from the context So, let's say that x is p1 and a pair with a section of canonical bundle with a degree 2 pole at infinity in the usual coordinates of the form dx and then we'll fix the divisor So, divisor which will be valued in account of the dominant co- weights of the co-weight lattice So, it means that to each point supporting the divisor we'll denote a co-weight by omega i check an element of the co-weight lattice lambda So, then a multiplicative g-hicks bundle on x which is framed at infinity with singularities in a co-weight value divisor would be pair p, comma g where p is the principle g-bundle on x with framing at infinity and g Now, unlike unlike the usual Hitching field, it's a section of a joint group valued bundle So, the difference with the Hitching definition is simply like little letter A is replaced by capital A So, which means that it's valued in groups rather than the algebras and the definition also singularities changed correspondingly So, namely, near each singularity where we have a specified co-weight Their singularity of the group value field is described by following You take, like the diagonal part or the carton part to be their image under this co-weight embedding the image of local coordinate near xi under this co-weight action multiplied from the left and from the right by analytical functions, group valued functions in that patch And we also fixed the framing bundle p and the value of the Hitching field at infinity So, that would be the module space of framed g-Hitching bundles So, that's the definition to continue, we need to get it There are questions about the definition Good Okay, so maybe some mathematicians will like another connection to the specification of the weights or singularities, namely they are canonically linked So, indeed if you take a formal neighborhood of which puncture xi then restriction of multiplicity of Hitching field g of x defines simply an element of the log group you expand in the local coordinate zx-xi so g double around parenthesis of z And this element is well defined after the joint action And also the singularity class by regular elements So, consequently the singularity class of an element of the log group would be a coset or like double orbit in the affine-grassemanian So, that's g of around parenthesis z quotient from the left and from the right of g double of g regular series in z So, orbits in affine-grassemanian are in canonical bijection of dominant covates of g And so fixing a degree of puncture is the same as fixing dominant covates at each xi So, so this spaces the modular space of multiplicative g-hicks bundles have been or their version of their particular versions in some particular cases have been considered before sometimes under the name of modular g pairs and some of earlier works include Batachin Artunaforov Medvedev Cherkis Kapustin Bredin Chernakov Dolgoshev Levin Alshanevsky Zotov Hurtubis Markman very extensive paper of the elliptic case and then Franklin Go and Boutier worked on with similar definitions for the Languines program Now, we'll take extra more conditions. Namely, we take Kalabiya condition on the base on X So, while the structure of multiplicative g-hicks bundle makes sense for any curve X, the modular space that we'll study, the modular space of multiplicative g-hicks bundles will carry canonical symplectic structure only in the very special situation. Namely, when we can equip the curve for the base X by a non-degenerate section of the canonical line bundle This is possible if X is a flat curve So, we'll take X to be C, C star or elliptic curve So, in the case of C or C star, this section develops a pole at infinity but not zero. What is the definition of non-degenerate section? So, that it doesn't develop zero So, in this case, one can equip the modular space of this multiplicative g-hicks bundle with a symplectic form like the other cases of hygenus. So, this is difference with the story of Hitchin systems. Hitchin systems are interesting to study for curves of arbitrary genus but here, we'll get a nice algebraic integrable system for nice symplectic structures on the modular space of multiplicative g-hicks bundles only when X is of genus 0 or 1, not hygenus So, in the case when X is an elliptic curve it was studied in the work of Hurtubis and Markman So, now let's go back a few tens of years and recall what's rational Poisson-Li group is and what's rational R-matrix which goes through many works on integrable systems, and stuff, right? So, let K of X denote the field of rational functions on X and G be the infinite-dimensional d-group valued in this field of rational functions and G sub 1 would denote sub-group of elements which are framed at infinity so that the value at infinity is 1 So, then this loop group carries a structure of Poisson, namely Poisson-Li group where this client Poisson structure defined by the rational R-matrix with this famous kernel 1 over X1 minus X2 where omega is the quadratic Casimir and this is back to the famous classical works from 80s about integrable systems So, quantization of this classical R-matrix leads to quantum rational R-matrix and definition of Yang-Yan etc. Yes This is your white vibration from the beginning which you haven't shown in three cases This constitutes like three probably in equivalent integrable systems But now you are talking about rational brackets Right So, there are horizontal and vertical cases We have... Now you are talking only about horizontal Yes, I'm talking about when it's rational horizontally So, usually also in some slang or jargon People say about integrable systems which are trigonometric rational elliptic in horizontal or like X-direction or trigonometric rational elliptic in the vertical or momentum direction So, our convention is that for this talk that we'll take it to be trigonometric in the vertical direction and the principalities of what is said here applies to all cases on X But, for concreteness in this lecture I'll take X to be P1 Okay So, this is a reminder about the scaling bracket which maybe more than half audience here doesn't need, but might want to look at it So, what's the scaling bracket? So, if you have an algebraic function on from G from this finite-dimensional group G we can consider the evaluation functions evaluation functions associated to a point X on a curve X which is just composition of the evaluation map and the value of this group sorry, composition of the evaluation map and that one So, and then the R matrix defines possible bracket on the evaluation functions by the formulas of the evaluation right gradients So, if the left gradient is defined by action from the left and the right gradient by action from the right of the vector fields then the Poisson bracket of two evaluation functions at points X1 and X2 is given by in the product of the left gradients at these points minus inner product of the right gradients In particular, if phi is a joint-invariant evaluation function then the left gradients right gradients coincide so consequently the Poisson bracket would be zero So, from a joint-invariant function one can construct a computing Hamiltonian and then the projection to the torus divided by the while group by the characters or a joint-invariant function would be isotropic for the Poisson structure So, one of the things I can concretely demonstrate today is the following statement So, the sub-variety namely the modular space of multiplicative Higgs bundles is a sub-variety in this infinite-dimensional Poisson group and namely it is a symplectic leaf and it is a symplectic leaf with respect to this kinetic Poisson structure defined concretely and consequently this modular space of multiplicative Higgs bundles it carries canonical halomorphic symplectic structure coming from this rational armature type and later in the talk we'll relate that symplectic structure to other definitions or other perspective on this modular space Yes In the previous slide the torus, the construction, how do you come is this TX inverse modular YW Yes, so what's the question? I didn't understand how the torus comes Yes You consider a joint-invariant function and then you have a projection to the conjugacy classes of elements in the group which is the torus mod the wild group Okay, so let's try to prove these statements we'll demonstrate the key steps here So, first of all let's see how can we identify the tangent space at the point on the modular space of multiplicative Higgs bundles So, to take a tangent space what can we do to a group element we can multiply it or deform it from the left and from the right and let's say that this deformation denoted by XI left and XI right and I will use the convenient notations for physicists thinking about all of that taken in some faithful matrix notations and here G is a group element XI is the algebra element but this multiplication means in a faithful matrix representation so if you like just think about them as matrices with a formula like that and then there is of course equivalence relation between you can conjugate and transform XI left to XI right with the same result so the equivalence relation on these pairs is that XI left to XI right is equivalent to XI left to XI right plus this deformation where you have a joint action on XI where a joint action is GXI G-1 So, geometrical way to say that is that away from the divisor the pair which defines the deformation is a section of the quotient bundle defined by this equivalence relation and then there are the usual gauge transformations infinitesimally parameterized by the sections of GP shifted by 1 so consequently the deformation complex of the multiplicative G X bundles is the following complex where this denotes their gauge deformations and A is a quotient defined here by equivalence class of left and right pairs so now let's consider a tangent space at some point at some particular configuration of the Higgs field and compute the dimension of the tangent space so at least to see some to feel what it looks like so let's say by the equivalence on this space left and right deformation pairs we can move everything to the left component right and then let's take the following assumption assume that G of X is generic near each singularity XI so let's assume that G of X is regular semi-simple when X goes to XI and in this case this map, a giant of G of X is diagonalizable near XI and then let X dependent carton subalgebra H sub X be a centralizer of that element and we'll assume that there is a limit of that centralizer as X approaches to singularity so in this case let's split in the usual way the algebra to the carton and it's a Borel positive and negative and let E alpha sub X would be generators of the root spaces so then we can see that the tangent space in the equivalence frame XI left XI left 0 is generated by the sections of this form where we have a sum over those root subspaces of the early algebra which are evaluated by the co-weight defining singularity with a positive number and then the deformations are parameterized by the terms of X minus XI to the contraction between the root and co-weight and arbitrary coefficients so this is concrete like coordinate choice to parameterize locally deformations and then assuming that we are in frame where every co-weight is dominant the total dimension of the deformation space would be just the sum over these local dimensions so that would be the sum over all the singularities and the sum over all positive roots and in a product between or a relation by co-weight and the root over which we sum and so we come to the formula that the total dimension of this modular space of multiplicity of his bundles is the evaluation of the total co-weight the half sum over the positive roots so that's the dimension other questions at this point ok so so now we can handle the dimension and we can feel what the tangent space is so we are like in a situation to study the symplectic form so let's come let's see what the symplectic form of objective Higgs bundle is and how come that it agrees with the Sklannian rational armatrix so we want to show that it's a symplectic with respect to the Poisson structure so a tangent space to a symplectic leaf locally at a point or in a Poisson variety and would be the image of the Poisson map from the co-tension bundle and the Jacobi identity would guarantee us that the distribution of the subvarieties of those images in the tangent subspace is integrable so the usual convention is shaded to a local function called Hamiltonian by physicist in the neighborhood of a pointed Poisson variety Hamiltonian vector field that's the action by the Poisson map on the differential of the phi so then the condition that the symplectic structure on S on a subvariety agrees with the Poisson structure would be the relation between the symplectic form evaluated on the vector fields associated to the Hamiltonian phi and psi and Poisson structure evaluated on the differential of this Hamiltonian so we want to show we want to give formula for the symplectic structure on the module space of multiplicative Higgs bundles and verify that for that formula this relation holds so but before that would be step 2 and the step 1 we also need to show that the image of pi, the image of the Poisson structure is the tangent space to the multiplicative Higgs bundles so I'll start by writing concretely the formula for the symplectic form on the module space of Higgs bundles question? so remember that we've parameterized the deformation of the multiplicative Higgs bundles but by pairs we have left-right modular equivalence relation and here is a formula for the symplectic form on the module space of Higgs bundles I'm just presenting you a formula and then we'll show that this formula agrees with the rational R matrix so the symplectic form is indeed induced on the sub-variety of the module space of Higgs bundles from the Sklianian Poisson structure on the infinidimensional group so what's the formula? you take here a sum over all neighborhoods of singularities and close these singularities by little disks and integrate over those disks this combination where 0 denotes excuse me, here somewhere okay so so we have disks ui and by 0 we denote a patch of x where all disks are subtracted like everything else and decompose xi into their local versions near each disk i and in everything else is denoted by 0 by subscript 0 so then the symplectic form has this formula so first let's notice that what's written here is well defined namely we need to show that under the change of the equivalence frame in the second argument when primes are shifted to some agent transformation their result doesn't change okay so let's shift then the deformation will be computed by this and then by integration by the contour integration we can see and moving by stocks the sum over d ui to the boundary and then integrating over the u0 we'll get integration of the regular part of the regular integrand here and that's 0 so omega would be invariant under equivalence in the second argument then we can also show that the previous formula is anti-symmetric so by suitable choice of equivalence frame set xi0 or prime to 0 and in this frame well maybe I'll just skip it because it's quite straightforward but anyways by doing this manipulations to save time we'll see that omega is anti-symmetric so then maybe a little bit more interesting calculation is to demonstrate actually agreement that the symplectic form that we've defined concretely before it comes from this client Poisson structure so we need to show that omega evaluated on those vector fields is equal to the Poisson bracket between the Hamiltonians which generate those vector fields so we'll choose for the equivalence frames for the vector fields in this form so xi of Hamiltonian psi x1 would be presented in this form and the other one would be presented in this form by setting to 0 their second component and then we'll evaluate the symplectic form of defined by concrete formula and this is a counter integral which involves like propagator 1 or w-x1 x1 extra insertion points and we integrate over w over all those boundaries of disks and then by taking the residues it's straightforward to see that the result is indeed the combination defined by this client armatrix so that's Poisson bracket between evolution functions psi and phi this component is consistent with a different patch dUi is the contour around each local patch and the sum of words is the same as the contour over the regular okay, so that concludes the proof but now let's just summarize the statement, what we had we had infinite dimensional Poisson league group with the client armatrix that g of k of x and I outlined the steps of the proof of the key statement that the symplectic leaves in the infinite dimensional Poisson league groups are exactly the module space of multiplicative Higgs bundles so the symplectic leaves are classified by picking a divisor on p1 valued in the co-weight lattice so you pick points attached to each point and element of the co-weight lattice dominant cone and that would be your symplectic leaf so, yes this requires an additional choice of performance about the you embed co-weight into tangent to the group at unity as far as I remember right? so co-weight for me is a map from the multiplicative group from c star to the maximum torus of g a map from c star or from u1 to the torus of g you embed the co-weight lattice into the tangent to the group no, we don't need to embed it no so in terms of like concrete parameters so what is the space of parameters for the symplectic leaves the space of parameters consists of the following first complex parameters namely the positions of the points of the singularities and discrete parameters and the choice of the co-weight at each singularity so the choice of the cartanza group inside the group no, no, no everything else is equivalent okay so that's one punchline to carry out of this from this talk that we know what are the symplectic leaves and those symplectic leaves are modulus space of multiplicative keys bundles and that's maybe important or illuminating to people who like geometric representation theory and studying representation theory by Kirillov in terms of the symplectic leaves so this quantization of this Poisson lig group or this rational Poisson lig group yields to Youngian then to this symplectic leaves one can attach the modulate of Youngian and understand representation theory of Youngian in terms of symplectic leaves okay, so we are good on that now let's give another connection to periodic monopoles what it came from yes point regarding here is it known or is it possible suppose if I consider some deformation of the explanatory bracket deformation of the explanatory bracket, okay I want to extend the hypocycles and get a minor right position so there is deformations or modifications of the symplectic correspondence that's a great question, I don't know I don't know I didn't look at it maybe, interesting question how much people suggest a comment found even more generalization I see, I see, I think okay, I think it's a nice question to explore, I didn't do any work about deformation okay, so we've had various motivation from physics and sort of physical argument why the same story could be captured by the module space of monopoles now let's give a concrete and precise statements like switching of context is a little bit so different in the sense that all the work on the previous slides we'll take the context of algebraic geometry we'll start from varieties but now we'll go to the context of nonlinear partial differential equations which describe the space of monopoles of course there is relation by two but we'll see what concretely we'll need so we'll take the following definition let x would be identified well, the x from the previous pages complex line C we'll identify it with R2 with flat Yve collision metric and we'll take M to be flat 3-dimensional equation manifold a product of X and S1 and we'll lift the divisor D the collection of points on X with values in covariates to divisor D tilde on M by attaching to each point some value in a circle in the vertical direction of the circle so the circle coordinate will be called T and the horizontal coordinate would be X as usual as before and G sub C would be denote a compact group associated to the complex reductive group G so then P sub C would be principal GC bundle on the 3-dimensional real-dimensional space equipped with the smooth connection A and the smooth Lie algebra value scalar field now it's Lie algebra value again V valued Higgs field, which was before so that's a mathematical definition for for the field content to say what Bogomolna equations are and then a monopole on M with Dirac singularities would be a configuration of A, phi which satisfy this Bogomolna equation or that's a reduction of self-dual equations to 3-dimension and the singularities are again specified by saying what is the co-weight near each singularity and here it's very transparent so since by definition co-weight is embedding a map from U1 to the maximum torus then we say that a monopole satisfies this singularity condition just when the configuration of the monopole near each singularity is the image of the unit of the standard unit Dirac monopole under this map so it sends the co-weight since unit Dirac monopole to a torus or the conjugacy class of the torus near each singularity so that's the traditional O ok, so in one direction the map from the monopoles to multiplicative Higgs bundles is very straightforward namely if you have a monopole next time S1 we can simply restrict the fields A, phi to a horizontal slice any point on S excuse me which doesn't contain singularities and then 0,1 part of the horizontal connection will determine structure of homomorphic G bundle on X so that homomorphic G bundle is a part of the definition of the multiplicative Higgs bundle and then we need the Higgs field so what will be the Higgs field? well monopole equations they imply in particular like one of the if you break the self-dual equations into the complex equations real equations then the complex equation could be written in this form and that implies that in the trivialization let's say in which del bar A is del bar the homonymy, the vertical homonymy of this complexified connection over the circle is homomorphic on X minus the divisor and so we'll have a homonymy morphism written by Kapustin and Cherkis from the modular space of monopoles to this modular space of multiplicative Higgs bundles so then we can define that the space of the polystable multiplicative Higgs bundles would be the image of the homonymy map in the modular space of multiplicative Higgs bundles and there would be version of Donaldson Ulinberg-Yauer or Kobayashi Hitchin correspondence which provide algebraic distribution of the stability condition on the modular space of Higgs bundles and the idea of this correspondence is to build the reverse map to the one which sends monopoles to Higgs so this reverse map would find S1 prime invariant harmonic Hermitian matrix on the extended four-dimensional space X times 1 prime where the zero circle is used to convert bogamon equations to self-dual Yang-Mann equations invariant around the circle and the Harmonian Hermitian matrix will equip in the solutions to the structure of instant solutions of the self-dual Yang-Mann equations so after the work of Donaldson and Consequent works a convenient way to build such harmonic matrix by running gradient descent on the Yang-Mills functional and it's quite straightforward to show well it's to show that the functional excuse me non-trivial part of this analysis is to show that when this flow continues it actually reaches the harmonic metric in the limit of the infinite time and for the compact complex surfaces the proof was given by Donaldson and in Simpson the heat flow was extended to non-compact surfaces with a certain assumption namely particular that assumption was an assumption of finite volume which doesn't apply to the present situation then further using essentially Simpson method Charbon and Hurtebes in 2008 they extended the proof to the case of monopoles still on a compact space total space X where X is compactified to a finite volume but they allowed singularities so they could handle the analysis which required in the proof of this flow to harmonic matrix near singularities and then again 10 years later Mochizuki in 2017 so just 2 years ago finally relaxed the finite assumption of Simpson and consequently from his analysis there is a proof that Donaldson-Olebek Yao Kobayashi-Hitching correspondence exist from multiplicative polystable bundle on P1 to singular monopoles on R2 times S1 so this is this line of works added more necessary analysis to the original ideas of Donaldson's for the heat flow over the Young Mills equations so now the space of singular monopoles on this 3-dimensional flat space R2 times S1 it comes with a natural hypercolostructure induced from the canonical hypercolostructure of the space of fields and the monopole equation treated as hypercolormap so hypercolostructure can be thought as twister family usually denoted with parameter by zeta of 2,0 symplectic form so we'll denote them to omega sub zeta,R so given the Donaldson-Olebek Yao Kobayashi-Hitching map we can pull back the hypercolostructure omega to the module space of polystable bundle and then define the omega zeta the symplectic form the module space of Higgs bundles is a pullback so what we want to show the few steps in the next slides is that the halomorphic symplectic structure on the module space of Higgs bundles induced by this vertical hypercolostructure on the module space of monopoles sometimes called like symplectic structure I in the slang of Hitching systems is equal to that symplectic structure defined in the previous part of the talk by this cloning rationalR matrix so in this way we'll connect the monopoles to rationalR matrix very completely by direct computation so let's do that so let's say that A would be the gauge field of the monopole and decompose it in terms of x and x bar x is the complex coordinate on x and here we extended the 3-dimensional case to the 4-dimensional case by just adding the circle along which the fields are invariant so direction in this circle corresponds to the scalar field phi of the monopoles so y is s plus i t plus another direction so the complex part of Bogan-Wollin equations is 0 comma 2 flat curvature equation that's the commutator of the bar vanishes and then we can write the 2 comma 0 halomorphic form defined by the variations of the monopole fields by this formula where that would be which product of the variations of A and A prime which is the halomorphic 2 comma 0 form dx dy on x times y this is the same as writing the variations of 0 comma 1 or the bar parts of the connections because 1 comma 0 parts are projected out by waging with 2 comma 0 form so this is canonical formula for the symplectic structure then the modulus space of monopoles and our goal is to show that it coincides with the formula we've written down before for the symplectic structure of the modulus space of hex bundles which also shown before coincides with this clanning formula let's do this computation quickly so we have that the connections are self-duals so that means f 0 2 form f 0 comma 2 is 0 then for a local variation we can have a potentials so that the local variation delta of the connection is del bar of b so b are local potentials we cannot of course do it globally around like each chart i and so there would be corresponding bi local potential but by local gauge transformation we can ensure that if we pick a horizontal slice s equals 0 we can trivialize there so when restricted to those slices at s equals 0 we have just the canonical del bar variation now since this bi is this potentials generate local gauge transformations we can compute the variation of the group Higgs fields which was the monogamy of a bar dy bar over the vertical circle and those left and right vector fields are values of this potentials at 0 or 2 pi r we can present s1 as interval from 0 to 2 pi r between 0 and 2 pi r so now let's integrate this formula where the variations of the gauge connections are replaced by del bar of two potentials and for that it will be necessary to integrate twice by parts or apply twice stocks formula to connect that to formula B without del bars and one can do it carefully by decomposition of by cutting the 3-dimensional spacing to the cylinders the vertical cylinders built on top of each patch ui and then first you integrate to the boundary of the cylinder so then formula will involve B without del bar and another B with del bar and then using agreement on the boundary between the variations since this is variation of the gauge field one can move with the computation further I'm moving maybe fast but just to give the logic flow and then one can integrate another one by stock theorem reducing to the boundary and get in the final result that the omega form the symplectic form the module space of monopoles evaluated on the variations represented by the del bar of those potentials in terms exactly in the form that we had for the module space of Higgs bundles where xi is the value of B at zero or at the 2 pi r so so this concludes that concludes illustration of of the proof that there is a symplectomorphism between the module space of monopoles in the vertical hypercal structure in the module space of Higgs bundles so there are been very connected works of course I mentioned that the key is by Gerasimov-Harchov-Lebedev and Ablesin about Youngian and Contai single monopoles on R3 and by Karmitzer-Webster-Wiegs-Yakobi on Youngian slices and affine grass mania and by Braverman-Finkilbert-Nakajima on Coulomb branches and slices and affine grass mania so let me have a well I should finish soon let me say in a few words epsilon twist of the story you take the following you deform the module space of monopoles by considering them not on a straight like rectangular product between X and S1 but on a twisted product of epsilon so that X is moved by epsilon when you move it around the circle and then the result in module space is still hypercalametric and used from the flat Yiff-Klidian structure and we want to connect it to like in the previous slides so the appropriate version of the module space of Higgs bundles becomes the module space of epsilon difference connections namely the Higgs the usual group-valued Higgs field which could be treated could be treated as a epsilon difference connection so this is this is difference version and the picture becomes like a difference version of the usual case of the Hitchin system where the module space of flat connections on X viewed in the complex structure J so this is the complex structure J version of that case there is a there is a version for the Steinberg section which will be here like an allegro of Hitchin section or constant section for the case of Hitchin systems and and from that section one can construct the sub-variety of epsilon difference operas so this well I'm skipping because need to finish but just to give keywords again of operas it comes as a mirror of the canonical choisotropic brain quantizing the module space of Higgs bundles in the case in the usual case of Higgs bundles but in the case of their group-valued Higgs bundles we see that there is similar statement holds and so when you do quasi-digitalization of the epsilon difference operas you get bit ansatz like equations quantizing integrable system on the module space of multiplicity for group-valued Higgs bundles and the connected works goes to Frankyler Hitchin and Seva Stianov and later developments with Samson and Nikita connecting to the gauge theory to the supersymmetric gauge theory in 4 dimensions in omega backgrounds and furthermore second quantization or like if you do first the deformation of this operas and then quantize it then you get the difference W algebra or whose currents are also known as quantized QQ characters or in these notations in the current notation, epsilon, comma, H bar characters okay, maybe a few concluding remarks is that which I didn't explain but people know that the module space of this multiplicity Higgs bundles of G is of AD type is identified with Coulomb branches of N equals 2 AD quiver gauge theories but what was shown before sorry, my talk was about general case not necessarily AD then SPZ duality on the fibers of integrable system of this multiplicity of Higgs bundles it provides geometric view on the Q geometric length described by Frankyler Hitchin Frankyler Okonkov Well, we sort of explained that quantization of M-Higgs in the vertical complex structure provides Youngian's modules and various versions of Speedchase and Betanzatz H quantization of Steinbeer section leads to W algebras and then it relates to the vertex algebras at the corner and also Cocha of Konsevich and Sobelmann and maybe one more point is that you can do the quantization of this modular Higgs multiplicity of Higgs by the path integral of the form like PDQ the inverse of the symplectic form and that leads to semi-halomorphic Chain Simon theory on X times S1 times R the first section which I can see in Nikrasov's 96 PhD thesis and then the theory was developed independently by Costella and further concrete computations done in Costella, Witton, Yamazaki and this is very parallel to the relation between quantization of the flat connections on X and the usual Chain Simons on X times R1 like in the Witton work but making like a halomorphic version of the real coordinate Ok, so that's I conclude here with the Samsung Thank you Are there any questions or comments? So, is it the Bogomolny equation the modular space of solution is it SU2 modular space or U1 modular space you are considering? Compactly group Any compactly group So, but there is a result by Donelson that says that modular space of solution to this Bogomolny equation for SUT actually and also this rational function which is fixed at infinity or zero at infinity is fibred by the circle over this modular space of solution of this Bogomolny equation So, this Are you referring to R3? Sorry equations on R3 or on which place? Ok, so here we consider R2 times S1 a different setup Ok Yes Is there a good point in the last slide? Yes Is there an elliptic analog Yeah, is there an elliptic analog with bungee? Is there an elliptic analog with bungee? Well, yes I think it should be halomorphic chair assignments in three-dimensional complex space Like here this chair assignments Well, the short answer is yes but I'm not sure if it's written down somewhere but to me it seems there is a straightforward way to replace that circle which is here by elliptic group and instead of studying this semi-halomorphic chair assignments just consider the chair assignments theory on complex three-dimensional Yes I'm sure if I missed it was mentioned in the talk but still Do you have some analog of the spectral description of this space like the spectral curve and the line bundle on it Yes So the spectral description is the cameral curve We have concrete formulas in paper with Nikita from 2012 What is the final formulation? What is the final formulation? There we have each point of the syntax manifold kitchens can be described as a curve in some surface right? and the line bundle on it Right So here it would be slightly more involved maybe I will write a couple more formulas So let's say that you have x is our base curve So in the Hitchin case you would take t star to x Here we don't take t star to x We assume already that x is flat and we'll take x g the maximal torus of g but for j this should be In case of group j everyone can go to surface Yes one can go right right Excuse me Let me So let me just write it concretely Так как я беру here rank G and write. So the equations here, which define the curve here are given by writing a collection of the characters, where I run over fundamental representation of G. GFX — это группа, в которой есть философия, и вы выигрываете их к фиксированным функциям, скажем, TIFX. Ну, полиномиал или рациональные функции с фиксированными структурами — это устройство. Так что, вместо структуры оригинального группы, вместо структуры в спектрул-кюрфе, он вырезает камерал-кюрф в высокомерситете. Вы можете его заменить по спектруль-кюрфу в легкости, если группа есть GL, а потом можно вырезать детерминатор, который подбавляет всю информацию об этих характерах. Но это более генеральная конструкция, так что вы вырезаете эту кюрфу, так что это камерал-кюрф в 1-й классе, ронг-g, дименциал-спейс, и на этом камерал-кюрфе, опять-таки, есть линия-бандалов, которые находятся в структуре конструкции Донаги Гайсгори. Это было важным, что на поверхности, где спектруль-кюрф вырезает, это дименциально, и, поэтому, это фасон. И здесь я не могу понять, как структура в спектруль-кюрфе можно вырезать из-за этой камеры, потому что там была только часть генеральной конструкции, симплятия структура в модууме спектруль-кюрфов, на поверхности фасона. Но здесь, я имею в виду, это не необходимо для нашего аргумента. Мы конструктировали симплятию формы в модууме спектруль-кюрфов, в зависимости от камерал-кюрфа конструкции. Мы конструктировали их прямо из-за фасона. Мы конструктировали, чтобы показать, что модууме спектруль-кюрфов в модууме спектруль-кюрфов есть, на самом деле, симплятия структура в пауэсонной группе. Мы пришли из-за этого конструкции, без реферии к конструкции, которые вы увидели. Мы поднялись до конструкции, но мастер-фиггер продолжается.


Welcome, Chris Lovejoy, Global Security and Resilience Practice Leader, Kendral, or for Kendral, to Dell's Navigating the Road to Cyber Resilience. Welcome. Thank you. It's wonderful to be here. Yeah, I really appreciate you being here. I know just looking at your LinkedIn, you've been all over the place. And I think that's bringing that global view to this event is really helpful. I think, again, security and cyber resilience is not a local thing. It's a worldwide thing and really needs to take into account all of those. So what does it mean to be the practice leader for security and resilience at Kendral? So I look after two things at Kendral. So first and foremost, as a practice leader, my responsibility is to run the business of security and resiliency for our customers. So that's what we build and sell vis-a-vis security services. And so today we've got about 8,000 or so folks within the team that are focused on this particular area around 50 different countries. So my other role is being on a plane a lot. And then the second role is leading the kind of how we manage security around our strategic outsourcing accounts. So think about that as more of a almost an internal look at the policies we've put in place to protect our customers and then ensuring that we're in compliance with those contracts. That's super interesting because I think, again, people may not know who Kendral is. I mean, Kendral is a fairly new company but has been around for a while. Do you want to kind of give a little color to that? Yeah. And thank you so much for asking. We are a really well-kept secret. So that almost exactly two years ago, Kendral split off from IBM. We are the services organization that was doing a lot of the strategic outsourcing IT services for IBM split off into an independent company. We are completely and wholly independent. We're a public company today of about 85,000 people altogether. And we focus on cloud security, mainframe and just infrastructure management around your more traditional infrastructure, applications, data and AI, digital workplace services, network transformation, and then my practice, security and resiliency. Yeah. No, I think that's the thing I've known about you because I've worked with you and partnered with you at previous employers. And I know that just to that example, even though you were part of IBM, now you're partnered with Dell. And I think that you take the best, always taken the best of breed technologies and brought them to with policies, procedures and processes and the people to deploy that at your customers. I know you're traveling around as you said, you know, on airplanes a lot and you're talking to customers and user customer organizations all the time. What are the most significant challenges and trends that you're seeing as it relates to cybersecurity, resilience and data protection across those customers? So I'm going to put those challenges into three basic buckets. So the first challenge is a compliance challenge. Many organizations today, and this is particularly in Europe where I just got back from our struggling with how do they address the new resiliency requirements that are coming out from the EU in the form of Dora and this too? You know, what's happening in the UK, you know, as well as some of the new obligations, you know, vis-à-vis the SEC guidance of public disclosure of material incidents. And this has got everybody really focused on the concept of overall business resilience. What does that mean? How do I ensure that I understand what is the minimum viable business? How do I understand whether or not I can anticipate risk? I can protect myself against those risks. I can detect and respond to those risks. And most importantly, and this is the big area that they're focused on in, you know, in particular is how do I recover in from those particular risks? So compliance around resilience and the board reporting, big focus. Second, big focus is more of a response to some of the current crises that we see in the news. Organizations are being hammered by ransomware. We just did a study with IDC and the results were pretty depressing about, you know, the number of, you know, cut up the companies that are getting hit by ransomware, the number of companies that are actually paying ransomware, the fact that even if they're paying the ransomware, they're not not. Depends on the ransomware fees. There may not be getting the data back. So this is a big issue, ransomware prevention, as well as the recovery from ransomware. And then the third big trend is more on the need for vendor consolidation, infrastructure simplification. And, you know, I think this is kind of a result of both the economic pressures that our customers are facing, as well as the fact that they are recognizing that one of the reasons why they're not able to recover very quickly or protect themselves, quite honestly, is they got too many vendors, too many bespoke solutions, too many subject matter experts that are necessary to manage those solutions, too much complexity in between the seams, so they're not able to actually recover their workloads. Anyway, all in all, this kind of complexity issue is driving customers to really look at how do they simplify their infrastructure, the control infrastructure and implement capabilities that really help them get to an overall resilient posture. Yeah, no, I think it totally makes sense that things like Dora, which is not the cute cartoon character with the backpack that you would see, it's, you know, what is it, digital operational resilience act, which more or less says, hey, financial organizations, you need to be able to either back out of the cloud you're in and set up shop either on premise or in another cloud in a certain amount of time to ensure operations and you have to be able to prove that, which is really just crazy. I think these types of things are coming and they're going to come to the US eventually, I guarantee that it, you know, like sustainability as well, but eventually, hopefully sooner rather than later. And I think it's really key, but how are you really looking at this and trying to, you know, help your customers stay ahead of these emerging trends and threats that are out there? Like you said, ransomware, we hear it all the time. And I'm sure that the IDC, I can imagine the stats are just, you know, abysmal about how many people are getting hit and what they're paying. I had heard some stat, it was like 1.8 million had been paid on average, which is just crazy that people are paying that versus being resilient. So how are you, what do you help clients be prepared? What are you doing to do that? Yeah, so a number of different things that we're doing, I mean, you know, let's just talk about, you know, first and foremost, how we're, how we get to the point where we're advising our clients.  And I think the reason for that practicality is we are one of the biggest providers of business continuity, disaster recovery services on the planet. We see everything.  Was it a network outage? Was it a data center outage? Was it a, you know, somebody just made a mistake and they took the system? Like what happened? And what we're finding is that most of the cases, there is a hardware software failure, that you know, it just happens, and we have no idea why it's happens. And quite frankly, sometimes we never find out why it happened, but it just happened. You've got so that's about 40 to 50%. Then you've got about 20% that are cyber related issues. And then you've got another set of, you know, issues that are related to networks, etc. Anyway, all in all, when you roll it up and you look at it, it informs us as to what happens, why things go wrong within an organization. So we've got this massive body of evidence that points to if there was a security incident, this is why it happened. If there was a data center outage, this is why it happened. And this informs the strategy that we take to our clients. And so what we do today to help our clients is typically we start with a cyber resiliency maturity assessment. So it's looking at the business and understanding where are you? What is what is your minimum viable business and what's getting in your way of actually being able to either protect it or bring it back. Once we've done that, then we recommend the approach that we take. And then we often work with client customers, not customers, I'm sorry, with partners like yourself, to bring the solutions, the right solutions to the customers so that they can achieve their overall resilience goal. Yeah, no, I think that's the key is working with the customers to get them prepared. Like you said, understand where where they are and meet them where they are, where they have that starting point. And I mean, obviously, you have a lot of customers. It's you're a very large company, like you said, well kept secret, but very large company, and it's out there working with a lot of different customers. Really, when things do go bump in the night and there are incidences, how do you help those companies that you're working with? Oh, I mean, my goodness, we do, we have managed recovery services. So oftentimes, cyber incident recovery services. So what we'll do is we'll actually run the systems, we will do the monitoring, we will do the actual, you know, the backups, the storage will do the vaulting of the systems vaulting of the data will run them the anomaly detection capabilities to ensure that what we're, you know, collecting is good. And if something goes wrong, we'll restore it for them. Now, if a client is not on contract, you know, for those kinds of services, we actually have a retainer service. It's a combination of an incident response and a recovery retainer. So if they have a cyber incident will fly people into the forensics, but what we'll also do is restore the systems into a clean room, as well as in parallel plan for the restoration of the entire business service. And if the customer needs an army of people to come in and restore those systems for them, I don't care if it's mid range, mainframe, it's cloud workloads, whatever, we can fly people in and help them. Well, that's great. I think that that full range of services is key to providing that. And, you know, let's kind of shift gears a little bit because I think that everybody's talking about gen AI. There's gen AI news every week. There's new models coming out. You had Google releasing theirs. Last week, you have a whole number of different things coming out. What's your, you know, point of view from a perspective of gen AI, both from a bad actor perspective, and from the good guys perspective and really trying to be the good actors and use that to our advantage. Yeah, it's a great question. So I think let me just take it from start with the good and then head to the bad. So I do absolutely think that there is a valuable role for gen AI in our businesses. I think I just want to be a little bit careful about this. We're still, I think we're on the road to maximizing use of ML, both structured and unstructured, sorry, supervised and unsupervised learning based machine learning, reinforcement learning, deep learning, et cetera. We're well on the road to using those technologies effectively. Generative AI, I think as a mechanism for augmenting human humans is well on its way. So what I mean by that is generative AI can be used to do things like if I'm doing incident, incident response call, gen AI is really good at creating the narrative of what happened in the call, doing the summarization, writing the email trail, creating that evidence. That's great. It can help you do some dumpster diving in your logs that you have to be very careful about how you craft the question. There's some things that it's very good at. Would I run generative AI today unleashed for something like threat detection and then automated response? I'm a little less comfortable with that. And the reason I'm a little bit less comfortable with that is because historically in this field, data is not necessarily available in a format that can be completely trusted. And so what I would say is, I would use, if you're going to be using generative AI for threat detection and automated response, it has to be done with guardrails in place, very strong guardrails in place. You can ensure that if there is any suspect in the integrity of the data that is being used to train the corpus, feed the corpus or feed the algorithm, you've got to have somebody involved. So that's on the good side. Yes, it can be used with guardrails. On the bad side, attackers, we are seeing attackers use generative AI in one really scary way, which is in social engineering. We're beginning to see some language, natural language models being used to create what we're calling multi vector attacks. So voice, email, text, kind of attacks coming in. At the same time, it may be targeted one individual, their colleagues are beginning to get the same kind of echoed attack coming in, which is reinforcing the social engineering. So we're seeing that kind of in faith right now. That's very hard to protect against because it just seems so legitimate. And then the next area that we're beginning to see a little bit is the use of generative AI and creating malware. You can kind of tell that they're creating malware because the code is so clean. Usually when you're doing forensics, you can tell which actor created it because you can see from the comments. In this particular case where it comes out real clean, you're like, I see where that's going. But in any case, you know, those are the two areas where I'd say we're seeing the mal actors use generative AI. I would say the third area that I'm particularly worried about, this is my looking around the corners and I'm beginning to just is making me really nervous is the use of generative AI when it comes to creating drones that can use biomimicry. That scares me. Drone security is already something that's keeping me up at night. Drones with biomimicry that can act like birds and cannot be found and cannot be taken down. That's really scary. So if you think about where I'm looking, you know, a couple years from now, it's that area. Wow. Yeah, that that that's going to keep me up tonight. So that was definitely that definitely was not where I thought you were going to go with the third point, which is I think fascinating because I think again, it's one of these things. We talk about gen AI and I like how you broke it down by the way that AI has been around for quite some time, ML, DL and so on. Then that gen AI is really just, you know, looking at the unsupervised side of that that spectrum. I think, you know, it's really key to understand that these things are going to continue to evolve. But with that, I mean, what would you be recommending? Where should customers really where should those end users really get started when they're trying to put kind of a comprehensive cyber security and resilience plan in place?  And so what I would say is, you know, the market is kind of defining generative AI, not just as sort of the unsupervised side, but it's also what I see is they're they're also conflating automation into that picture. And so what Nirvana is, is sense and response, right? So I see nowhere coming in and I see that my system has not been patched. And I see that that system that hasn't been patched is a really, you know, very critical asset, so I'm going to automatically patch it. Okay, like I get that that's, I wish I'm not there yet, you know, I'm just not there. So what I'd say is, first and foremost, I always advise people to understand what is the role of machine learning AI more generally within the business. How are you defining generative AI? What are the business goals and then marry the right technology to that right business problem? And I think generative AI, it's a tool. It is a tool that gets you to an outcome. So again, you start with the strategy, the problem, and then you find the solution to the problem. Generative AI might be a great solution within the confines of the problem that you're trying to solve. It's kind of basic. Yep. No, that makes sense. And from a kindral perspective, if somebody was looking to get one of those, you know, I think you called it a cyber resilience audit type things, they go to the website and sign up there. How do they, how do they reach out? Yes, we will happily you can go to the Kindral website. There's a request for more information. There is a security and resiliency site where you actually have contacts where you can call in and get more information. But that's a great place to start. You can always reach out to me on LinkedIn and I will respond as well.  Well, hopefully we'll see it. Excellent. Well, Chris, I want to thank you. This has been a pleasure.  So definitely definitely going to be thinking about this for a while. So I really want to thank you for coming on board here. Thank you. Yeah, everybody thinks I'm crazy, but it keeps the hand. It's coming. It's coming. Oh yeah, absolutely. I'm sure I'm sure. Well, well, thank you again. All right, thank you. Okay, we're rolling along live in the studio and on demand from our Palo Alto studios. You're watching navigating the road to cyber resilience, a summit bringing together practitioners, cyber experts, analysts, technologists to explore cyber security and resilience. Keep it right here.


Once everybody Jason here for Jasper's case breaks.com 10 immaculate spots we give it away here the last 10 to unlock the break with this 2021 canine prison multi-pack cell a one-pack break number 233 So okay guys first we do the break right on my cousin names and teams are shooting the hits out then at the end Randomize the original customer names top ten get in roll it Four to two six times one two three four five Six Nick Smith down to Brian Frank. There you go six times one two three four five six Again down to the Knicks. So there you go stick to what you got to give of course guys, you know quick little pack filler No, but it's Kevin Durant though Nice not too bad. It was centering and look at that MVP's right there and the Yanis under the combo color match green. That's pretty nice Solid solid So that's next Terry and then no wonky that's Brian Frank.  That was close All right, here we go guys. Good luck Roll it four to one five times top ten are in one two three four bone five times Top ten are in just missing. I was nicked on a nick. I appreciate you guys, but good luck Brian Frank you're in Carl Carl Nick Carl Brian Nick Carl Carl and Brian Frank. There you go Boom top ten are in congratulations guys. So those will be the last ten spots there Paste you guys in here now and coming on that is immaculate itself. Appreciate it


What's up everybody, Jason here for jaspyskazebrakes.com guys, happy new release day, new release here with 2223 Panini Select Basketball This is a six box half Kazebrae PGT number one And again guys, all carts ship So here we go So there is the list of customer names, now if you have a little character sign at the end of your name That means you won that from like a little quick little pack filler team random So you paid a small fraction of the price to get one of those teams All right again guys obviously it's a fresh full case of 12 so We're gonna use the same boxes for the Other six boxes for PGT number two so very little one two three. We're gonna go to the left side four five six for the right side See we got here and it is a six so one two three four five six So these six boxes here will be used for picketing number two Which we could run it back if you guys saw it all pretty quick if not you guys are running back with Joe No worries But we'll go with these six boxes here And we'll probably rip two boxes at a time. Hi guys. Here we go. So we got a silver Michael Porter, Jr Got a chat rookie And our first relic is a Dame dollar Dame.  Is he gonna stay in Portland?  Where's he go? Where's he going? Maybe his future teammate right here Bama DiBio 12 out of 199 for the heat With a Yanis unstoppable so Chen a little Christian would That white and blue and I think those are not numbered in basketball though Bar smith got a Dame dollar Dame. I think of these are like little red wine blues chat courtside And we got our first numbered card. That's a KPJ for the Houston Rockets to 199 Nicola Yolkic Benedict Mather and silver and then we got a Sean Kemp in Flight for the Seattle Supersonics, which of course goes through the Oklahoma City Thunder, which is Jackson David Rodney and Caleb Houston a little bit of a teaser there for the magic But that is a RPA Orlando magic is going to shodmatic a little Scotty Barnes The Toronto Raptors to 249 you got a so Chen Tricolor got a James Harden scopes Let's keep it going guys David Rodney to 189 little RPA Memphis Grizzlies Grizzlies is a young young PG little tricolor Bryson McGowan's to 99 249 Jalen Brunson a little chat select futures Joellen B Paulo Boncaro Payne Watson 249 Kyrie Irving relic a little throwback there when he was a Cavalier We have a David Rodney little lime green to 75 like Wesley Luke Adonich Brunson Alright, nothing super crazy yet in the first two boxes. Let's see how the next to go. All right. Here we go next one Chathongan Kyrie Irving. Then we got Baji Chathongan Getty X Factor Little giddy up patch autograph there number to one at United Desmond Bain so that giddy is gonna go to the Thunder and Jackson Jeremy so Chen a little Russell Westbrook patch Lakers When a Ken Bon and have a little Usman Dieng. He's also a first-round pick. He was actually picked right before j-dub was Number to 175 We got cheated on the auto in this box or another relic usually what? Three autos with three man ability cards. I feel like we got cheated on one I'll double check right now the stack just to be safe, but Unless the Kyrie. Oh, you know what maybe the Kyrie was actually a relic No No, we cheated one actually double check. I didn't miss anything. Maybe I put it over here by accident Hopefully we just get an extra hit in the other ones No, the tricolors are not numbered. I'm sleeving them up though But in basketball the tricolors are not in football. They are though But in basketball, they're not Yeah, it looks like we just looks like we just didn't get an extra hit there, but No, the tricolors are not I've got a lawyer marketing out of 65 and a Jalen Durant Yeah, well, I mean honestly man.  I mean hopefully it does get definitely some help, but just It's hard Julius Randall and then him being a celebrity and big-time, you know comedian. I mean Obviously can do as many things as he wants can get exposed to a Lot of drugs and this and that so it's even worse man Eight out of ten gold nice one there for the Knicks. There we go second half Anthony Edwards Bradley Beal Jabbar Smith Junior Relic Yeah, I mean honestly, I mean I think deep down.  I think it's just more like you need to surround yourself with people that really care for you You know Being in the spotlight like he is As long as he doesn't lose that he'll be fine, you know in that sense, but sometimes obviously The spotlight can consume you David Roddy Chandler all right you guys down the last Two boxes here So we haven't seen a zebra or anything like that yet. Nothing's super crazy. That's what depending on what happens in these next two boxes A second half to be very very massive I guess if you guys wanted to sell it up pretty quickly. I can probably still do it But it looks like maybe actually hold on didn't it put in a pack filler ready?  I've been seeing a lot of J. Will, you know, we're not J. Dub So I'm just saying that I think that thunder can just be a massive team because obviously I don't get to home And you have J. Dub, you know, the Aang has a rookie and then obviously you can throw in a giddy SGA All the other players they have but yeah thunder have worked out great for you, especially through a pack filler But I still think they could be a lot more for the thunder honestly some good stuff. Oh, yeah, I forgot about Sean Kim, too Yeah All I'm saying is that the thunder I think can still be a pretty big team to get in the second half There may be pricey, but their checklist is pretty deep John Morant Car in the new towns at 249 a nice Jeremy So-Chan For the spurs kai-shan.  I guess I haven't seen a lot of Jalen Williams at J. Dub though Anthony Davis relic or sorry die cut I should say 99 our last box here guys. Here we go Tim Hardaway jr. To 49 That's one for the Dallas Mavericks No, the checkouts okay sound, but what I would do is I would email our support button So if you go to our website You'll see right at the bottom left hand corner support You click it and you let us know that's the way to contact like the sorting and shipping team much faster But or you can email support at Jaspie's That's also a direct email. It's better to email us and contact us through support Just because it's better to do it that way Because you can leave a note in Shopify, but Not everybody sees those notes, but us so for like the sorting and shipping team to see that they Rather go through support But there's a little button on the website that you can click right there Or just email that's that email Straight up direct as well works But yes, you can easily pick these up just give us a couple business days of course to sort it out and then We can always notify you too when it's ready to pick up and then You can come pick it up in the store. It's no problem. Yeah, Chris Milton to 249 All right last half here guys, so again, I think this half had some nice stuff But I definitely think it's a lot better in the second half guys D'Angue Those are Jaylen Williams Yanis Just feel like there's got to be some bigger stuff and if you haven't hit a zebra yet So should be in the second half to D'Angue there that should be at a 49 very nice And Fuego and a Walker Kessler. That's nice. You taught jazz David Bazzarino Malcolm Brogdon And a nice LeBron James. How about that little color match, too? That's a white parallel to 149. That's sick Lakers Ken Bob little Johnny Davis Yeah, guys, like I said some nice stuff still popped out of here regardless, but I just feel like was select There's definitely got to be more No bigger rookie like RPA yet. We did get some nice rookie autographs. So like Jeremy so Chen You know stuff like that, but definitely feel like there's got to be more I'm more optimistic that way because I've seen so much select over the years I feel like with this draft class here. There's definitely got to be more We did match the pool one gold little Jaylen Durand right a couple nice relics giddy David Roddy Right Sean can been flight. There's a so Chen Brandon Clark Kessler was a nice one LeBron white Tim Arduy Jr. So like I said just because of that I feel like the second half could be pretty nice And of course you're gonna get everything shipped to you regardless from the base and stuff like that And I sleeved up a lot here as well for you guys with its reviews try colors numbered cars, etc So regardless though select those look really nice. I like it But like I said, I definitely thought they could be much better So I appreciate it guys Like I said next one is still in the store if you guys wanted to sell out straight up You can if not make my booted an impact wheeler soon guys. So appreciate it. Jasper's case breaks calm


Well, hello everyone. I wanted to give you guys a tour of my quarantine office setup. A lot of you guys have been asking for this, so I figured I would just show you around a little bit in the office, give you a little bit of a detailed look of what I need on a day-to-day basis to do my job. My actual job title is a process engineer, and what that means is I interpret drawings from design engineers and calculate out material for it to be fabricated. That's kind of the easiest way to describe it. So basically I look at prints and drawings all day as well as I do a lot of math. So that's kind of what I do, and it's all not all of its data entry, but a majority of it is data entry and entering it properly into our systems to make everything work. So this is my second bedroom, and this is now an office. I used to have it as a guest room, but I converted it into an office quite a while ago. As you enter, we're going to look down right now because Doyle is there sleeping, doing his due diligence as the co-worker. And let me give you like a little desk tour right now. Since we're dealing with COVID and all of that stuff, I have like a little heart thing. I actually got this on Amazon yesterday. This came in. It's like a little rope rainbow, and I thought that was really cute.  So yeah, I'm going to link as many things as I can find it down below for you guys over here. Actually, let's start with this wall. So clearly this is not required, but I have these prints on the wall. I got them from home goods, I believe like home goods or marshals. I can never remember which one, but I got them at the same time. They're beautiful. They've got like some sparkles on them. And I just love like the gilded frame. I think that's so so sweet and so pretty. Anyway, over here, I have a little envelope opening thing. I have right now just a little book in there, but I actually do keep like my paper bills in there. Anything that gets mailed to me that I have to like financially take care of, I will put in there as a reminder. And then when I deal with it, then it goes in the file cabinet, which I will show you in just a moment. I have two of these lamps, which are on both sides flanking, got those from IKEA. I also have this little funny looking thing. That is a tripod, like I can actually put my camera right here. It's like a little mount. I will link it is actually already linked below, but it works really well for my setup when I do planning videos and such. Over in the corner here are my planners that I got in PR that I have some things I need to do with or like deal with with them. I also have some stickers that I'm going to be doing a haul with. I have more stickers coming, so I'm just kind of stacking them there for the moment. Over here, I have this really cool washi cart and a bunch of simply gilded washi. You gotta have hand cream, especially now when we're all washing our hands, like crazy. And then over here, I've got some calendar setups. So this is from Aaron Condren. Those planners are from Aaron Condren as well, but this is from Aaron Condren. This was just kind of keeping track of my vlogging and things like that and like what I needed to film. So today is actually the 28th. I did a little bit of decorating, but not too much. So yeah, today's the 28th and then I'll be posting this, I don't know, at some point. I actually got this acrylic easel, like acrylic stand on Amazon the other day and I really like this a lot. I like that that just like sits there and I can see it because I've got a lot of things going on. So yeah, like this is today and I'm down here filming things, some filming things. So yeah, but that's that. Over here, just some stuff I need to deal with. This is some UPS returning labels that I still need to hold on to until Amazon credits my account.  It's not. It's actually a bookmark, but I use it to cut washi. I just leave it right here.  So we have that. I've got a little coaster because you need a coaster for all your good stuff. I also have some just random sticky notes. I was writing some sticky notes that I got to put away, but whatever. And then I have a new pad of sticky notes. So I just always have a fresh pad of sticky notes ready.  I don't know. I just kind of put them in there. It's easy. I'm right handed. So it makes sense when I'm at my, all my monitors that I have on the right side. I also have my phone and it's on a little stand right now. It's being charged. That's really easy to like, you know, do this or have it sit like that like for video calls or what have you. And then I also have a wireless keypad and mouse that all gets connected into this bad boy over here, which is my laptop. And then over on the side here, I have like a big pen holder, but you know, this doesn't really fit anywhere else on the desk. So I just put it over there. And then when I need pens, I just throw them in there because it works because I usually just use the same two or three over and over again. And if you guys are wondering, I got my desk at IKEA. I can't remember the name of it, but I had to, you know, everything was separate. So you got the file cabinets and then the top and the one leg all separately. So yeah. And then the chair I actually got on Amazon. I will link that below. And then I've got like everything on Amazon for the most part. And then I've got this, which I actually got the other day. I'll make it look pretty for you. You can kind of make it look funny here. But this is supposed to help with like, I don't know, your nerves or something. But anyway, I did read on the Amazon reviews that this can kind of stain your chair. So I put Aaron Contran Sherpa throw down so it didn't stain the white. Anyway, but it seems to be working just fine. And I really like it. And then underneath my chair, I actually have a foot roller because I have plantar fasciitis in my feet. And that helps. Moving over here, I have all my cords, just like a hot mess, but they are, it's a labeled hot mess, you guys. And then I have my paper shredder. I've got my printer, which I really don't need to use to be honest for the most part. But every once in a while, I do need to physically sign something and then scan it. So it's nice to have this. And this is a laser jet printer. And I absolutely love it. And I've had it for a few years now and I really, really like it. As for the file cabinet, it's a three tiered file cabinet also from IKEA had it for several years now. This tiered cart is from IKEA. Everything's from IKEA, you guys. And this is my planner cart that has all my stickers and all my washi and sticky notes and all my little doodads to decorate my planner, which is right over here. So, you know, I needed to put something in my planner or whatever. I can just wheel the cart over and plan. And then over here is nothing really interesting. I have these two bookcases. They're the Billy bookcase. And this is what the inside looks like. I really don't have much going on in either of them. This used to be storage for my Etsy shop, which is no longer in business because it was just too much. I didn't need to do that anymore. So I just said Sayonara and this is all the extras. And then on top here, I just have a little bit of tissue, another little organizer. This one is from HomeGoods. And then I've actually got some, like these are these two are like work notebooks. And then I have another work thing here. This is a medical binder. And then this is also a medical like binder slash tracker. So that's basically it for my at home work setup. I try not to eat up here, but it's really, I feel like it's super difficult right now just with everything going on. What I'd like to do is when I'm working from home, there's a dog right there, is I like to take him on a nice long walk, usually about like 10 10 30 somewhere in there that kind of just helps my brain. Like I, you know, in the morning I check my email, I get my emails out, do all of that good stuff.  He's getting really excited when I'm saying a word walk. Anyways, and then yeah, grab some water or whatever, take my coffee or tea or whatever I'm drinking for the morning. And oh, don't want to lay across. And then take that downstairs and then, you know, bring up, bring up some water or juice or whatever I want to drink and, you know, kind of reinvigorate a little bit. So yeah, but let me back up a little bit here. You know, back that train up here. Come on. So yeah, that is it for my working at home office setup. I hope you guys enjoyed the video and enjoyed just a little look at the office. I, you know, don't use too much pen to paper except for my little notes. I do have to write myself little notes once in a while, but that's about it. Everything is digitized. I send over all my completed work actually to my boss. He goes from there because he's actually in the office right now. I think he's he is the actually the only person in the office. Everyone else is working in production and they're taking all their precautions and things like that. And they actually all work more than six feet away from each other. So not sure when I'm actually going back into the office that has not been announced yet. But yeah, I'll try to get this video up for you guys. And then I will, like I said before, I will link as many products as I can find down below. And then if you have a home office set up, do you have any like tips or tricks or little things that really help you, you know, like the dog helps me because kind of breaks up the day and things like that. But yeah, right? Doyle, do you help me? Do you like all of his bones, by the way? They're just sitting there excited. He's just an excited guy. But yeah, he's got, he's got several bones just hanging out over here. Just just waiting for him. Anyway, okay, this is getting long-landed. Sorry about that guys. All right, I'm gonna go. Thank you guys so much for watching. If you like the video, make sure to give it a thumbs up. Feel free to subscribe and I will be back for more content very, very soon. Bye guys. You want to say bye? No, okay. Talk to you later guys. Bye. Well folks, it's time to kick it old school. So you can feel cool.


Hi, today we'll be learning about light dependent resistors. So have you ever wondered how automatic street lights work or perhaps how light seeking rescue robots work? They all use this, the light dependent resistor, to differentiate between varying degrees of brightness. Light dependent resistors are basically semiconductors. Impurities are added to the semiconductors to make it more efficient at conducting electricity when light hits it. Just like us humans can only see certain wavelengths of light. The same way light dependent resistors like these are sensitive to only certain wavelengths of light. If these certain wavelengths of light go ahead and hit the light dependent resistor, what happens is that the resistor becomes a lot more conductive with just a little bit of light energies. To understand how conductivity actually works, we must understand that if electrons can flow freely, it's a good conductor. If electrons cannot flow freely, it's a poor conductor. In materials such as this, when light actually hits a sensor, electrons can physically move from a valence band where they're not free to move, right, so bad conductor, to a conduction band. So they actually physically jump and when they're in the conduction band, they can actually move freely making it a good conductor of electricity. A good analogy for this is actually car parks. When a car is parked on the side of the road, it can't really move, but as soon as it signals and turns out into the main road, the car can speed up and move freely. The same way when there's no light hitting the sensor, the electrons are kind of stuck in this car park-like situation, but when light hits it, the cars are free to move out of the car park into the main road. These brightness sensors are considered analog sensors. So unlike the digital sensor counterparts, which just give zero to one, these sensors can give a value that can be read as zero to 1,023. Wiring up this sensor is actually super simple. It just has two pins and better yet, because the sensor acts like a resistor, the order of the pins as in the way you connect them doesn't matter. All you need to know is that the first pin will connect to a power source. Typically, this is a five volt power source in a microcontroller. The second pin actually has two connections. The first connection is actually to a resistor that will connect it to ground. The resistor helps normalize the values that your analog read pin measures. The second electrical connection is to an analog read compatible pin. Make sure it's an analog read compatible pin and not a digital read compatible pin. Now that we've actually wired up a sensor, let's write some code and actually test it out. But before we do that, if you want to see more tutorials like this, do consider subscribing. Now let's actually write some code. So here I've got two sets of code. This one is in Python for people who code Raspberry Pi. This one is in Arduino, so C++. You can use similar codes such as this on your Raspberry Pi as well because Raspberry Pis can compile and run C++ code. Let's start with the Python code here because it's very simple. First of all, I've imported a very simple library that allows us to use the GPIO pins of the Raspberry Pi. What I've created is an object here, an object LDR, which is the light sensor object attached to pin four. Next, we have a forever loop, which is while true. In this forever loop, that means it's going to run forever, we're going to print print reads show on screen the value of the LDR object, which is attached to pin four. So basically it's going to read the value at pin four and consists and just forever show that on the screen. On the Arduino side, I've done very something very similar. I've created an integer to hold the sensor pin. So the sensor is attached to pin A0. I've initially set the value of the sensor to zero. This is just, again, I'm just setting it initially. Once we start getting readings, this is going to change from zero. Then I've started a serial monitor, which is basically the same thing as printing it on the screen. And in our loop, basically we set sensor value to analog read the sensor pin. So we're going to basically read the pin A0 and we're going to print that. So the code's actually really straightforward. Let's actually flash it and test it out and see what results we get. Okay, so I've got everything wired up and the code flashed. We're going to use an Arduino for this demo, but you can also use the Raspberry Pi. That's the difference. And as you can see, we're already getting a live number from the brightness sensor. So let's go ahead and actually test our sensor out. As I bring my hand closer and cover up the sensor, the number goes down, down, down, down, down. And as I still let more light in, the number goes back up. Again, if you're using a different microcontroller such as the Raspberry Pi or Microbit, the range of values might differ. Instead of getting something like zero to 1,023, you might be getting a range of decimal values from 0 to 1 or maybe 0 to 100. That doesn't change how the brightness sensor behaves. It's just that the range might be shifted one way or the other. Anyway, that's a tutorial. If you have any questions, you can leave them down in the comments below where I'll be answering them. And if you want to watch future tutorials like this, do subscribe. Thanks.


money would not keep the home. It's a good variable. Poverty can damage the home. I'm going to talk about it this week. Poverty can make you very useless. But the first thing you need when building the home is to find out this young man, this young woman does do. Is he having the technical skills? Is she having the technical skills, the ability, the capability? Listen to me. Some of you have been married. The problem, the reason why there is a lot of problem in the home. Yesterday we said it is what? A sin problem. And one of the sin problem is your husband lacks the capacity.  He is just not having the wisdom. If you are not wise, you are what?