Thank you. It's been a very interesting summer school for me so far, so thank you very much everyone for putting this together and the opportunity to speak. This is all joint work with Tom Bachman that you heard from a few days ago, and we'll start with the application to accounting linear subspaces. Let's give ourselves notation for k a field and f1 through fj homogeneous polynomials that are going to cut out what's called a complete intersection on projective space. So there's the homogeneous coordinates of projective space and we can look at this variety which is the common zero locus of f1 through fj. And if this is dimension n minus j, that's what it means for x to be a complete intersection. So we're going to be counting linear subspaces, let's say explicitly what a linear subspace is. So on our plane in x is a copy of p to the r cut out inside p to the n by linear equations. We're going to let these linear equations have coefficients in some field extension, side e, and then we get it will be on our plane in x if it sits inside x viewed as viewed as a scheme over e. So there's our linear subspaces of dimension r. So the space of all linear subspaces is a cross monion. So this is a cross monion parameterizing p, r's, n, p, n. Equivalently it's the space of r plus one dimensional subspaces of an n plus one dimensional vector space. And we've got some different choices for notation for this, but let's go with gr, r, n. And here if we have a subspace w, we can take its projectivization and we get a pr, we can even make it a different color. We have the subspace w sort of a point in this cross monion goes to its projectivization. And there we've got some notation for cross monion. So the cross monion. Give some excuse me. There's a question for you in the chat. Like you want this. Great. Thank you. So Hain says it's just a closed sub scheme. It's not. So, oh, and this one too. I guess in principle we could have x be a linear subspace and then maybe it would be equal. So xe is some interesting variety cut out by equations of different degrees. And inside them they might have points, lines, two-dimensional planes, three-dimensional planes. And I'm just saying that explicitly here that we're allowed to have our linear equations have coefficients in e in some extension. Does that make great? Thank you. So we've got a tautological bundle and it's a vector bundle so that over the point corresponding to the subspace w, your fiber is w itself. And we're allowed to do vector space operations on bundles. And the one that comes up for looking at these complete intersections, let's look at sin d of the dual of s. This is the vector bundle on the gross monion, which at a point w we have the degree d polynomials on the vector space w. So let's give ourselves notation for the degrees of the fi. So let di equal degree fi and fi determines a section of sin di s dual w. Let's call this section sigma i by sigma i at the point w is fi restricted to w. Fi is a fi is a polynomial on the entire vector space. So it restricts to a polynomial on each of the w and this gives an element of sin di of s w. So from the choice of our equations we get a section sigma as the sum sigma sigma one plus sigma d sigma j section of let's call the vector bundle v for convenience of the direct sum of the sin di s dual. Now we can express the space of all r planes in x as the zeros of this section. So let's let f r x, this is the space of r planes in x. It's the subscheme of the gross monion determined by sigma equal zero. And it's a result of Debarman-Navell that for generic fi this is smooth of the expected dimension for generic fi. So why is the vanishing of sigma the space of r planes in x? It's because we have a plane p of w is in x. If and only if the restriction of fi to w equals zero for all these for all these i's. So we know what our dimension is. We've got the space cut out as the zeros of a section of a vector bundle. So the the dimension of f r we'll call this delta is the dimension of the gross monion minus the rank of the vector bundle. And the rank the vector bundle is the number of polynomials of degree di in in our variables and it's all to be explicit about it is it's di plus r choose choose choose r. So let's do examples when we get a finite count.  To give an example where it's more than a hyper surface we could take lines on a complete ci for complete intersection of two degree n minus two polynomials follies in p n. We're going to say n odd because we're going to want all these examples to also be orientable in a second. In any event there are there are tons of infinite families of these for not just lines and three planes but but but all the way up for two planes too for that matter. So in any of these cases there's some finite number of r planes and a question is what is that finite number? So when delta equals zero how many r planes nx? And the answer at least for k equals c over the complex numbers. When we want to solve equations we have this nice algebraically closed field. We have a nice topology on it and and this is a classical topological Euler number. We can see that it's the Euler number of the vector bundle we called v this was the sum of the symmetric powers and one property of Euler numbers is that they can be computed with respect to any section as a sum over the zeros of the section and this is valid because the zeros of sigma are isolated and so we're taking the zeros of the section gr for gross monion and w is a zero means this is equal to zero and it's of some some local degree. We can view a section of a vector bundle as a function locally function from c to the dimension to c to the dimension. c has a nice orientation fixed on it and then we can take the topological degree of a map of small balls. By the debar manavelle result the zeros of sigma are also simple because the zero locus was smooth and everything is orientation preserving so what this gives us is a sum over one of these same zeros of sigma and as we commented above the zeros of sigma are exactly the r planes so this is the number of r planes in x. In particular this first equality here shows that the the answer doesn't depend on your polynomials it only depends on their degree their degree only depends on the di as opposed to the fi. So one very pretty example is that there are 27 lines on a cubic surface a generic cubic surface generic. Got off the internet a photo from the Göttingen University that's credited to Ozaozig and there's a clutch cubic surface and there are 27 27 lines on it. To go up some dimensions which means we won't look at it but there are also for example 321 489 three planes on a generic cubic seven dimensional hypersurface and for for any specific ones you want you could you could get this answer using cosmology of brass monions the splitting principle and useful tools. So let's let's change k from from c to r so when when k is equal to r we want to use an Euler number again and for this we need v to be orientable there's again a way to express this just in terms of the the constants we have around so the this is equivalent to this the sum of di over r plus one di plus r choose r plus and plus one being congruent to zero mod two and all the previous examples so examples delta equals zero orientable all of those above and we can again compute the the Euler number it's again can be computed with respect to a section and again since the zeros are isolated we have that this is a sum over the points of the grass monion of these zeros and then there's this local term local degree of a function so if we look at sigma in some small neighborhood u of a zero of w it's going to look like a function from from r to the dimension to the rank which is which is the same and then in coordinates you'd have let's say sigma upper i be the i coordinate when you view it as a function and we can take the the partials with respect to the coordinates xj on on rn let's let this be denoted by the Jacobian of sigma the determinant of of this matrix let's make this a little clearer and then the local degree is the sine plus one when it's positive minus one when it's a negative of this Jacobian and so what this gives is some plus ones and some minus ones this is a weighted count of the r planes and it's also a lower bound so uh while the the number of r planes can vary um from uh say uh a generic seven-dimensional cubic hyper surface to to another seven-dimensional generic uh uh cubic hyper surface there is some side count of of these um three planes uh which doesn't and um Finesha and Karlamov write a paper about the whole family of of three uh plane counting problems and uh in particular so so they do this on the degree d plus one hyper surface in general and there is 189 three planes on a seven-dimensional cubic hyper surface um weighted count um over r uh so um with uh the a1 Euler class introduced in in Marc Labien's talks we can obtain a count uh over any field um let's sorry to interrupt before you continue maybe there's a there's a question for you in the q and a um that's right so um this so uh the the q and a is pointing out that this needs to be an integer um and uh it is uh many times thanks um let's uh talk about a1 Euler um classes and numbers so let's let v over y be a vector bundle uh with a section on a smooth scheme y a section uh s uh and um uh barge and morrell uh defined an an Euler class uh in the oriented chow of y twisted by uh the the duality determinant um uh and this Euler class was there was a there's a one in oriented chow and um you can push forward the one by the section and pull back exactly as um as marc outlined um uh last week uh and uh let's let's list a whole bunch of Euler classes um uh uh so uh although we haven't introduced um oriented chow it's a a sum of uh of cycles with with coefficients um and and let's uh let's not worry about that uh too much at the moment and this was further developed by uh fizzle and ashock fizzle and marc levine um uh and um another description of the Euler class is it's a principal obstruction to having a non-vanishing section um and uh in a1 algebraic topology over a field morrell develops an Euler class um encoding that that principal obstruction um in joint work with jesse cas we made an Euler class designed for a number of problems that was the sum of the the degrees over the zeros of s of of local degrees of s this is an Euler number um uh in a beautiful paper on fundamental classes and uh degrees jin and kan uh give uh constructions of of Euler classes and in particular uh marc uh presented um uh using this uh last week and one of the things this does is we get Euler classes valued in cohomology theories uh that are represented by s l oriented um uh spectra um another thing that uh marc uh talked to us about was a pairing on the kazool complex um uh and uh in joint work with between levine and raxa they show that um this is the Euler class for the the tangent bundle um my coffins actually uh after a talk i gave uh eyeball the the pairing on the kazool and and and asserted it was the same and i've heard uh marc uh say a nice story about um a similar um uh responsive of of ser i'll just put everybody's named down if that's okay um the the last list in our in our point of view on Euler class list that that we have here um is to take the opportunity uh to talk about my women in topology group looking at the hawkshield homology um uh and putting the pairing um that the the folks who think of coherent duality in terms of hawkshield homology um give us uh and showing this is this uh a one Euler class and this is work of kandace bethea uh nini arcila maya morgan opi um uh inis akarevich so um one of the things done in the in the paper that this talk is about is to check um qualities um for for some of these uh so um uh the the these local degrees and and the push forward and for appropriate e and the kazool um uh for for general vector bundles um uh as a warning um there's a very interesting um paper of asha kandacelle about comparing these two and they are equal up to a unit but in a in a context where there are actually quite a lot of units um uh uh so um it's it's an interesting it's an interesting class it's an interesting number and there are a lot of different points of view on it um and uh for moving forward uh with with the the story um let's let's summarize this by saying when y over k is smooth the dimension of y is the rank of the bundle and v is a generalization of orientable called relatively orientable then we have an Euler number call it e of v uh living in the growth and defeat group of of k um i'm going to spell out what the growth and defeat group of k is very explicitly because it's um concrete and our accounts record concrete um arithmetic information valued in this group um uh so uh let's let a um be a ring and g w of a is going to be the group of um formal uh differences of um isomorphism classes of non-degenerate symmetric bilinear forms and this group of formal differences called a group completion and for a field this has a very nice presentation so presentation for a equals k a field then uh any um bilinear form uh can be diagonal symmetric bilinear form can be diagonalized so the generators are uh one-dimensional forms for a and k star over k star squared as in uh mark's talk is on the one-dimensional vector space k k cross k to k and we take as a bilinear form we take x y to to ax y and it just has a few um relations we have the a b equals a b and a plus b equal a plus b when that's not one plus a b um a plus b and um this implies that there are a bunch of ways to write a special form called the hyperbolic form that um a plus minus a um is this uh hyperbolic form um h uh one one plus minus one um uh i'll give a whole bunch of um explicit examples uh so uh the growth and date fit group of c um is that there's there up to squares uh all all elements are the same in in c star uh so if we just take the underlying dimension of the vector space um the growth and date fit group of c is z by the rank and over r um when we diagonalize we have some number of ones and minus ones the difference between those is the signature and um that induces an isomorphism up to a parity condition um the uh for for fields like um a finite field with q elements or c t um we have that um the first two invariance of quadratic forms coming from the the miller conjecture uh invariance give uh give the whole growth and date growth and date fit group the first two are the rank and the discriminant that's a determinant of uh of uh of when you write the bilinear form uh as a as a matrix um so this goes to z to k star over um k star squared which let's say q is odd i give z cross z mod two and then we have invariance coming from the the miller conjecture um which was a great achievement of um of a one homotopy theory the the title of this talk was about integrality results and that means that uh we want to use where the vector bundle is defined um if it's defined over over z or some sort of ring of integers we want to um uh compute or say things about the computation of what the Euler Euler number is so let's also say that the growth and date bit group of the integers although there are many very interesting highly non-trivial um uh non-degenerate uh symmetric bilinear forms over z once you group complete you you only get z cross z it's a number of ones and number of minus ones for instance for example sitting inside g w of q um or d g w of r maybe maybe more straightforwardly um uh we have a miller exact sequence giving us the growth and date bit group of z one over n and it'll sit inside the growth and date bit group of q and then there's some boundary maps to the bit group is the growth and date bit group uh divided by the the hyperbolic form um for q not dividing n um uh the um the last thing we'll need to state to state results um are the explicitly giving transfers um uh we can uh assume the only thing we'll need to write down um theorems is transfers for an extension of fields k l that we can assume to be finite separable because the department of l result will say that our zero look is smooth and so corresponds to separable extensions and then we will have a transfer map from uh l over k from the growth and date bit group of l to the growth and date bit group of k um uh and it'll take a bilinear form beta v cross v to l and it'll take its class to the composition of um beta with the the sum of the galois conjugates the the trace from uh uh from from galois theory um uh so um let's let's talk more about the um uh about growth and date bit um but i also i want to pause for any questions so far um if you if you think of others uh please don't hesitate uh to interrupt so the the gw of fields pieces together to make an unramified uh sheaf by a procedure in morrell's a one algebraic topology so it gives um unramified sheaf my gw say on smooth schemes over k um and uh the uh sections over x they're inside the the sections on um k of x on the on the field the functions of x and you can extend over uh uh any um close subset of co-dimension at least two it's given by intersection of kernels of certain boundary maps for co-dimension one points um and it has an alternative description it's the sheafification in the niznevich or as a risky topology of um uh sending x um to uh gw of x where now this means the symmetric non-degenerate uh bilinear forms on on vector bundles um uh on our on our ax and this is a great sheaf um uh uh but from the perspective of um of descent sheafifying isomorphism classes is an odd thing to do when we if we if we want to glue together objects we not only want to know their isomorphic on overlaps we might want to keep track of uh of the data of that isomorphism have it satisfy um conditions so uh one thing that that that comes up is that you can have a sheaf of spaces version make it uh curly uh curly gw um so let bilinear of x be the space of vector bundles uh with a symmetric non-degenerate uh bilinear form and then we can sheafify um the group completion of this so let's let one half be invertible let's let these be schemes um uh over uh z one half and have this be uh um a sheaf valued in spaces and we'll let it be the sheafification x goes to uh group completion of um the uh this uh these bilinear forms um and there's a map uh to the sheaf of spaces associated um to uh her mission k theory we've got a homotopy invariant uh version on the right um and uh our our sheaf version of uh growth and deke um uh the sheaves uh on the left um we can take uh or their classes um in the in in her mission k theory um or related theories and get good functoriality properties um associated with them uh uh to to give us um integrality integrality results let's get back to um counting our planes and less questions yes um so uh it's necessary to invert two when when considering uh duality so uh bilinear forms there are a lot of different that there when when two is not invertible bilinear forms and quadratic forms are different turns out there are a lot of different variants um uh uh for um uh for four notions of um uh of a duality uh on on vector bundles when when two is two is not invertible um uh so um it uh it makes a her mission k theory defined with with current machinery and there are a lot of interesting things to say about inverting two uh so so thank you for the the question returning to to counting our planes on complete intersections let's list some things we know um uh in in joint work uh with jesse cas we computed the account of lines on a on a cubic surface which is the the computation of the Euler number for sim three of s dual on the gross monion and it is 15 1 plus 12 uh times minus 1 and uh it's this is also a song over the lines of uh an index involving the field of definition of the line and some some information about how the tangent um how the tangent plane spins along the line um uh this is for k a field and um mark levine developed a theory of uh bit valued characteristic classes and uh computes that uh uh the Euler number of uh sim of uh 2d minus 1 of s dual counting lines um on uh um um pd plus 1 is uh 2d minus 1 factorial factorial tell you what that means plus a multiple of h and the multiple of h is is designed uh to make so ec for a Euler number of complex points minus um 2d minus 1 factorial factorial over 2 times the cyberbolic form um so here uh 2d minus 1 uh factorial factorial is 2d minus 1 times 2d minus 3 uh times 1 and uh it's okay as a field um uh with with characteristic uh primed it to and times 2d minus 1 um and uh ec is the normal topological Euler number of the the complex points of c um uh Steven McKean uh um gave a uh enrichment of bazoo's theorem along with geometric interpretations of local indices and that gives the calculation of um vector bundles sort of counting points on p n that's just p n um the multiple of h and uh Sabrina Powley also along with uh uh interesting geometric interpretations um uh re does the cubic surface and does the quintic threefold with um a theory of dynamic um intersections uh you can hear her talk about this at motive and motives and um and whatnot um coming soon uh so we have uh enriched counts of airplanes um let's uh formalize this notation ec so let's let um uh it's on july 29th uh thank you um so uh let's let ec be this Euler number of the complex points and er um be the Euler number of the real points and um uh a theorem I'd like to to talk about from this paper is um the the the enriched count is the sum of ones and minus ones that you would get from the from the real and and complex point counts so let's let um r be a ring with uh one half um uh in r let and you can also do just a field of characteristic two um we'll consider the vector bundle we started with um the sum of uh the di symmetric power of the dual tautological or um um uh the gross monion and let's let it be relatively um oriented with dimension of the uh the rank of the is the dimension of the gross monion um and uh so this has uh we can we can rewrite this in terms of parity conditions and and sum conditions so i.e. we want the sum of di over r plus one uh di plus r choose r plus n plus one congruent to zero um mod two and the dimension equaling the rank uh dimension of gross monion r plus one times n minus r is the the rank di plus r choose r um uh and so uh then the these vector bundles that we were interested in um the the Euler number is ec plus er over two times one plus ec minus er over two uh uh times times negative one um and for example we can get an enriched count of three planes on a generic seven dimensional cubic hyper surface so there are 160 thousand eight hundred and thirty nine one plus 160 thousand six hundred and fifty minus one three planes in a seven dimensional um cubic um hyper surface and uh as uh to put this back in terms of um accounting r planes if we take the sum over the r planes we'll call the r plane p in our complete intersection x of the this trace we know it's for a separable field extension by de barre manavelle of the Jacobian we express um our function sigma in terms of local coordinates and take some derivatives then this is uh the the same the same number up here um and while uh the number on the right hand side uh is uh some ones and some minus ones these these are not in general sums of ones and minus ones they just have to sum to them uh uh and as suggested by the title uh this is proven uh with an integrality result the count of the lines on x reduced to a bundle on a grass manian that was defined over z it's the section that is defined over the interesting equations of x and that's why the um the left hand side here has all sorts of interesting summands and um the the right hand side picks up the fact that the grass manian is defined over z um so uh uh theorem two this is all joint with tom bachman um uh so let's let um v over y be a relatively uh oriented vector bundle with v and y defined over um z join one over d factorial and d is greater than or equal to to to two um uh with y smooth and proper sm for smooth and proper over the same base um then the uh Euler number has to be in the subring uh uh generated by minus one and um the two three all the way up to d inside g w of k um and uh in the case of d equals two there this leaves two possibilities so then either um e v is the the quantity i think maybe i'll still be able to paste it this this quantity here um or uh it's what we get by um putting in a single two um but but keeping keeping the the signature the same um uh so um uh we can distinguish between these um possibilities uh by uh taking uh an an Euler number over some single prime where where two two is not a square and in order to to prove um the result about the symmetric powers um we use a characteristic class uh argument to get rid of this uh this second this second possibility um uh um the the characteristic class argument owes uh a lot to Mark Levine's fit value characteristic classes um uh this would be a good time to to pause for for questions are there any um so theorem two um is proven by using an an Euler class for uh good SL oriented theory um for example uh ko um and uh the uh the d greater than or equal to two restriction comes from uh it comes from wanting to use ko uh and there is um currently uh a collaboration on uh ko without inverting two um with uh Baptiste uh Calmez Emmanuel Dotto Yonatan Harpas um Fabian had the straight uh Marcus Land Christian Moy Dennis Nardan Thomas Nicolos Wolfgang Stumm and um Marcus Spitzveck I um I understand also has work around this let's let's put that let's let's put Marcus Spitzveck um here too um uh so my understanding is that um that uh it is expected that um they will show that uh if you take k theory let's call that uh kgl and taking a vector space to its dual gives a c2 action and you can take a homotopy fixed points um of uh c2 and it's expected that the um uh if you make a substitute for Hermitian k theory by taking the homotopy fixed points of kgl and completing it too that it can be shown that um uh this is the growth of the group of z uh completed it too um so this exists over at at z so it exists over z um it's uh SL oriented and there's a um you can read about it in a paper of Bachman and Mike Hopkins um and while it doesn't respect base change it does have some maps and so this is sufficient the um to show the same integrality statement for d equals one to show um the integrality result theorem two for d equals one um uh because the the Euler number with respect if we let this this gadget be um k o prime then the Euler number with respect to k o prime it's um it's here and there is enough functoriality so that we'll have to map to the if we pull back to z um joining one half um to k o prime it'll it'll map to the corresponding number um moreover there there's a map from k o to k o prime um giving that the uh Euler number when k o exists over one half maps here too um and the um uh since these two elements map to um uh the same element in there um they determine an element of this of the fiber product of g w of z one half g w of z completed at two over g w of z one half completed at two and this is g w of z um so uh the the we get this stronger um integrality result um uh with with with that work uh in the spirit of summer school i'd like to end with some open um problems uh the uh the zeroth open problem is can be expressed somewhat facetiously like this i mean there are a lot of um uh great results uh um in uh isenbud harris's uh 32 64 and all that or fulton's uh intersection theory um that uh give uh interesting enumerators results and um uh there are beautiful enumerator results having deep connections to uh uh many areas of of mathematics so the zeroth problem is can a one homotopy theory enrich enrich them uh so take a problem from isenbud harris 32 64 and all that fulton intersection theory let's give more of a preamble to this question so um there are beautiful results in a one enumerative in enumerative geometry can a one homotopy theory enrich them and enumerative geometry uh can a one homotopy theory enrich them i don't think i wrote down um to uh taken um uh somewhat haphazardly from uh isenbud harris and i don't have time to write them down but let me just just read to so that we're on the same page about um the uh what what question zero is is trying to suggest so uh let v1 through v2n be general tangent vector fields in pn and how many points of pn is there a cotangent vector annihilated by all of them and uh another one is given four curves c1 c2 c3 c4 and p3 up degrees d1 d2 d3 d4 how many lines meet general translates of all four i'll add these to the notes and and put them in um uh to be less um hand wavy about this um in the corollary above we didn't have the analog of um the uh of interesting descriptions in terms of the the complete intersection itself so geometric interpretation in terms of x um they're the very concrete uh examples of this uh um for this jacobian which is sort of living on the on the um on the moduli space so beyond uh cubic surface quintic three fold the zoo um to connect up with marco rubolo's talk the um the the hawkshield homology of that matrix factorization algebra that that showed up it has a pairing on it and that pairing is the a1 milner number of the singularity and element of the the growth indeed vid group but there's also inside this um k nought of varieties this cut and paste relation there's this motivic um milner fiber and a compactly supported a1 oiler characteristic that mark levine told us about so uh these this this should be all all equal um and uh the list should continue um the you you lose uh certain tools and you gain others for example and then yes he's um beautiful splitting principle uh the multiplicativity of oiler numbers in exact sequences is no longer nearly as useful because you really can't divide but the kazool uh interpretation of oiler numbers gives you some control in exact sequences but in general it's hard so um are there better are there are there better tools uh there there is really structure here and an arithmetic information um that that lies away from c and what is it um i'll stop there okay thank you kirsten for a wonderful talk so um let's hear some questions and maybe i can ask by um by asking you if there's some connection between your work and oriented schubert calculus so matias vent um uh absolutely um so uh matias vent has information on the oriented chow of um uh gras manians in in terms of uh some generalizations of of schubert calculus and that gives uh other interesting ways to um to compute um these oiler numbers it doesn't directly um use it but um that there is uh interesting things to be said about that great i have a question um from my face and so this last this last question the a1 milner number equals the um oiler characteristic of the notific milner fiber you said the left hand side comes from a pairing on hawkshaw's homology can you say a little bit more about that yeah um so um the i think maybe the um a better way to start with what the a1 milner number is is if um if you have a point p of f equals zero the a1 milner number um if this p is a singularity this um is can be defined to be this this local degree at p of the gradient of f but then this is also the hawkshaw homology of this matrix factorizations um uh uh for for f um and that's by explicitly marco told us that this was the jacobian ring and uh this this local degree um can be computed as the jacobian ring and this can be computed as the code jacobian ring and the pairing on hawkshaw homology is uh is the same so we get we get this equality here so this one wouldn't be part of the problem and then this one um uh i think is open what what natural guess what pairing is there on hawkshaw's homology ah great so um uh litman and uh uh um i'm blanking um so uh there's there's even a six functor formalism uh in in hawkshaw homology and it it's a way of expressing things about coherent duality in terms of of hawkshaw homology and um i am embarrassingly uh blanking on on the important names involved and in constructing that pairing um uh but it's also uh in in this context we wrote it down in the the women in topology group um to uh yeah great so and you're too young to be blanking on these things thanks i appreciate that okay and there's a nice question in the q and a just if you can see that yes so um uh the so for uh over a finite field the three planes that um give you a square um so over a finite field we had um we have we have this um this growth indeed big group and um so in particular we're going to have a parity condition coming from uh three planes associated to um square or non-square local um local contributions and uh if you if you sum all of those non-square over odd degree field extensions with the square ones over even degree field extensions you'll have to get an even number of those and over things like cubic surface this corresponds to the difference between um hyperbolic and elliptic lines um and if you come up with uh a sort of intrinsic to the complete intersection definition of what it means for this discriminant to be square or non-square or more generally what that Jacobian means then you get a concrete um uh totally independent of any um of any a1 homotopy theory restriction on on that complete intersection but even in terms of the Jacobian we get this this even parity condition so um um by motivic by a1 Milner number um uh we meant the left hand side and then by the motivic Milner fiber um uh I meant the um the construction uh that gives you this element of of canada varieties um with this motivic integration um uh so it's a yes uh um uh the construction um the construction is a little involved um uh the way I've seen it doesn't directly use I use nearby cycle sponges but I wouldn't be surprised if if that's um uh my not knowing how to how to show the two are are closely related okay great then I have another question because in this homotopy limit problem you're completing a two is that uh so so you don't don't expect that we need to complete with respect to the huff map eta um the uh as far as I know but I think Tom would be the the better person to um to answer this question okay then and then the q and a there's another question yes yeah this yes this is the um thank you so Cas um uh Jesse Leo Cas um and I did work on um on a1 Milner numbers thank you Stephen great any other questions I don't think so so thanks again Kirsten for a wonderful talk and see you all um again tomorrow we start 1 p.m. paris time


Hi, I'm Zena Sharman. I am the editor and author of the book, The Care We Dream of Libertory and Transformative Approaches to LGBTQ Plus Health. It is a book that asserts that it is both urgently necessary and wildly possible to create healthcare that contributes to the pleasure, thriving, liberation of LGBTQ Plus people. It brings together essays, interviews, poems, and stories by 16 LGBTQ Plus writers, activists, researchers, and healthcare providers from across North America, including some familiar faces and voices from the Bay Area. It's a book that offers possibilities grounded in historical examples, present-day experiments, and dreams of the future for more liberatory and transformative approaches to LGBTQ Plus health and healing. You can find The Care We Dream of at the San Francisco Public Library, and you can also pick it up at your local independent bookstore.


What's going on everyone Sam here with late in sports cards rip in at 22 23, but in the select basketball hobby six box break number 16 pick a team style We will read off the list of our names on our teams got Andrew H Hawks Brett W magic Ching-Hua H with the Timberwolves Chris F bowls Christopher P. Sixers Daniel D. Mavs Daniel E. Nuggets Eric R. Nick's Evan M with the Kings Evan G. Bucks H yeah with the Blazers Jeffrey H Thunderjazz Jeremy H with the Pistons Justin C. Rockets pelicans and wizards Ken I Heat Lursak why Spurs Lee Z with the Raptors Mark M. Cavs Robert J. Nets Rudy G Grizzlies Ryan T Clippers Steven G Hornets Thomas C warriors Tony T Lakers Travis M Celtics will Z with the Pacers and you Chen S with the Suns. Good luck everybody here we go And you guys 18 to go on chronicles breaking soon Chronicles football got two half cases of that and followed by four half cases a one full case of one And then two half cases select football That is what we're looking to fill up for the rest of the night on this gorgeous Friday night and pop the Florida APK the APK is correct. Evan Mobley is gonna be your try-caller a Malka Brogden court side We should do about a 1799 Shea Gilders Alexander purple throwback threads for the Clippers nice one there Jalen Brunson step car. I love that about select basketball the throwback threads. They're all game use though. Oh, really? Yep Say like LeBron on the heat last year Jabari Smith white nice one there to 149 for the Rockets Luca This is my favorite tapestry Sean 407 with a dollar sign as an S money, baby That is nice Carl Anthony Towns autograph memorabilia going to the Timberwolves nice one there congrats Minnesota Very nice That was awesome. Got silver Jalen Suggs and Jaden Hardy Wolves Palo Sparks Jersey card nice one there for the Magic that's on that Orlando silver down and Terry rookie drew holiday as well Luca KD silver Kelvin Johnson got his eye on Williamson as well Mine like Wesley try color Oh, yeah Oh God Jaden already nice one there try color for the maps Keegan Mary rookie silver Kyrie and Blake Wesley Yeah, I'm sorry.  Oh, let's go. Thank you a macro. Oh, yeah, we got yes piano on What's up, it's always wrong, but how much to get the watch Tray um now. It's true. It's Ray young to 299 Well, indeed I know literally we'll put a baseball game on and I'll look up in the first sitting. I'll look down I'll look back up again. I'll be like the bottom of the eighth. Yeah. What happened, dude Hey, happy 4th of July to you as well Zack. Zack. How you doing, buddy? Good to see you as always No, there's Devin Macelle orange to 65 for the spurs quiet Leonard Yeah, be I'll be on vacation for the 4th. I'm pretty excited about that. You gone out of here for about a week Be back on next Friday And then I've had a vacation since Christmas either My birthday You'd be out of commission Dennis Rodman 33 of 99 for the pistons the worm on an in-flight signatures nice one there Maximilian taken two in one. Thank you down to two to go There's Jalen Green and Clay Thompson. Oh, you're busy next Friday now. Macaron. Oh, man. Oh dang Jalen Green Pascal Siakum 32 of 99 nice spicy pee going to the rap. There's game used blue Damien Lillard 2 249 and a Chris Paul Mark Williams. There's Bradley Bealscope and Calden Johnson court side Silver Anthony Simons, Kate Cunningham as well and Fuego LeBron another zebra. Nice another zebra court side Jake Laravia on the rookie congrats on that Memphis That's awesome two Zebras in this case both Courtsides as well and a Kyrie Irving course I just Any zebra figure to throw in yeah Christian Brown Keegan Murray 15 of 75 on the blue jersey nice one Kings tie-dye Malachi Brannum going to the Spurs 22 of 25 that is Jersey numbered congrats San Antonio to tie-dye Malachi Brannum's in this Entirely of this case so pretty cool. Yeah, zebras are sweet neighbors are very sweet. They're silver Deontay Murray and a Jason Tim Can't believe macaroons all of a sudden busy next Friday Josh Giddy Palo Bancaro rookie She's Christian Wood There's Jimmy Butler tri-color Nicola, you know, you okay Kevin Porter Jr. to 249 Andrew Nemhard Whoa Bye-bye Keegan Murray rookie Donovan Mitchell, there's a Scotty Barnes tri-color and Andrew Wiggins All right Again guys, here's your link to chronicles 18 to go on that break and relatively soon. It's gonna be our first football break of the night Worst for us is he slacking again now. He's off. He's off today. He's off yesterday today and tomorrow Monitor moderator Sean also blocked Dylan Duran he go there's Johnny Davis a Tiger hero try color and Chris Paul the new Jinn Hardy quiet. There's a Jane and Ivy for a 249 silver rookie auto. That's clean with the throwback pistons Jersey Love that man. I swung there Detroit. There's a tie-tie Washington tri-color clay Thompson J Dubb Margarose and silver sexton and Cade Cunningham. You got force posted in the slack chat the birthday blast their heat Yeah Yeah, I agree Zach's one of my favorite jerseys of all time. There's a Carl Anthony Towns and a Terry East I think I'm gonna get a Cade jersey of that eventually Cater Ivy. I think that'd be pretty clean Because you can't get Grant Hill everybody's got Grant Hill already silver Wendell Moore Jr. Jason Tatum Josh Giddy Oh It's gonna be a light blue Blake Wesley to 299 for the spurs and and nem her pillow rookie There's Grant Williams nice one there silver rookie Jersey. I'm not rookie silver game you Jersey I should say for the Celtics blue scope Marjambot champ to 249 for the Bucks tie-tie Washington rookie scope Dear and Fox I swipa and court side Andrew Wiggins Matherin ex-Bennett and Cumbermatch Matherins Malcolm Brogdon try a color and Nicola Yolkich. He's gonna have to be number one next week if I'm gone Silver down and Terry and Kyrie Irving We're saying to trade wait trade who? Macaroon silver Irving out of bio and Andrew Wiggins Yeah, Grant Williams is pretty good. He's a good defender kind of sold in the playoffs a little bit, but Patrick Baldwin jr. That is gonna be purple rookie Jersey nice one there to 99 for the Warriors tie-tie Jalen Suggs second year Three of 25 one-off Jersey number congrats Orlando and a crisp ball on to the next one Halfway through the break now everybody it's gonna be a bronze Scotty Barnes nice one there on the bronze X Fractured of 49 These are sick Nice one there a J Griffin Jalen Brunson scope and Joel indeed court sign a tri-color is Malcolm Brogdon and Acme Kevin Durant red Jalen green on the die cut to 175 nice one Houston and Dyson Dennis James Harden blue Keldon Johnson to 299 shade on sharp rookie Ochaic poshie future Take Loravia and true holiday Not three don't want to there's Andre drumming 71 to 125 drum god nice one there for the Bulls Silva if we're gonna use on Chicago there's Anthony Simon's and Chris. I'll support this Jaden Hardy blue March on boat champ to 249 nice one there for the Bucks and Evan Mowley Lucanard 155 of 199 Jersey auto that should be game used for the Grizzlies Nice one there Duke legend three-point shooting legend Lucanard Sulta or silver is Blake Wesley not Celtics Silver for the Spurs Jabari Smith jr. To 99 red auto for the Rockets grass each town. I swan their space city picking that one up color match Silver Kauai Carl Anthony Towns Keegan Murray rookie Silver Jake Loravia and Jaumarant Silver Tyrese Maxi and Lamella ball and OBS Sick dude. Sorry guys. OBS disconnected. I'll give it one minute for people to get back in here Tony taken four in Bowman's best you as well Sorry again, everybody there's your link to Chronicles is what I'm social social in there They tested Pushing me pushing you over the edge Shade on sharp rookie I Would assume there's a blue Blake Wesley to 249 rookie for the Spurs dyke up Julius Randall March on boat champ Sensation Jill and Duran how you Duran the Aaron Fox and Luca of course I Bring in half some shirts back here does The bones Highland 85 of 249 for the Clippers that is a Clippers card Traded and It is Clippers on the card congrats on that L.I. Hopefully you'll catch and Walker Kessler Jill and Suggs Jaumarant Tri-color and Steph Curry courtside. Nice. It's very Smith rookie base Ochaic Bajie red die cut to 175 for the Jazz Utah Deontay Murray Scope Desmond Bain. There you go Grizzlies and Shet Holger and rookie on the back for the Thunder Thunder Jalen Williams. It's a white DeMar DeRozan to 149 Shagel just Alexander Ochaic Bajie rookie There's a shade on sharp a blue scope Dyson Daniels rookie to 249 and a Jalen Brown High Tide Washington Rigo Bear throwback threads nice one there for the Jazz congrats Utah cool card there for sure Either Michael taken two in Chronicles and Ray taking a spot in Bowman's best you Josh Giddy Silver and Nicola Yovitch Big baton scoop for rookie deer. That's actually that's that's fair chain and Ivy Rookie for the Pistons Silver Terry Eason rookie and Tyrese Halliburne. It's not a bad. I only got to bad bat enough I don't think that's a bad bet at all Jeremy Sohan, there's Nicola Yovitch Jaden Hardy 22 of 25 Ty Diodo for Dallas. I just won their Mavs. Congrats on that one gorgeous gorgeous gorgeous Jaden Hardy Some of Johnny Dips Anthony and Simon a Infuego Trey young silver silver Dyson Daniels and Ochaic Bajie Ochaic Bajie. All right last box here guys got two three boxes of select coming up after this as well Jack's winning the South. That's not a bad bet either. I would say Pretty solid that Jack's winning the South That very well my they're not the favorites, are they? Sensation Jalen turn. I don't know who would be favorited over them Scope is shade on sharp minus 150 Terry's Halliburne Quartz I Yeah, I was gonna say that makes sense that they're the favorites for sure. Show me so Han rookie Yolkitch Christian Coloco and Nicola Yolkitch court side rookie or Yovitch Yovitch court side Stop AJ. There's Anthony Davis 64 of 99 throwback threads for the Pelicans. Nice one there New Orleans Love these throwback thread cards. They're so clean Anthony, I'm taking four in Bowman's Best Lebron Scope and Carl-Anthony Tom Christian Brown rookie Try color Tyrese Maxie and Jalen Brunson Plus 450 in second. Good Lord King and Murray rookie Red Jaden Hardy nice one there to 199 and Caleb Houston redemption Kelton Johnson X Factor memorabilia signatures tie-dye that's going to the Spurs Nice one there San Antonio. Congrats on that Kildon Johnson silver Chet and Lamella ball Austin Reeves for your deal with the Lakers nice How much money did they give them they said they were prepared to pay as much as they needed which is nuts Jane Ivey select draft swatches Silver rookie nice one there Detroit Silva Julius Randall shade on sharp rookie as well Shade on sharp future There's a blue Scope RJ Barrett to 249 and Ja Marant Nice and Daniel silver Tyrese Maxie and KP Kristoff's Port of Zingis and Fuego is Ja Marant Silva Kevin Porter jr. Keegan Murray rookie Light blue is Donovan Mitchell for the Cavs 299 RJ Barrett and last back and break. Good luck See what we've got base Blue Dyke is Marcus smart for the Celtics to 249 now member of the Memphis Grizzlies Evan Mobley All right guys do a quick recap here pretty solid break overall again We had jade and ivy Anthony Davis Rudy go there at the Baldwin Grant Williams Keegan Murray Ask Alciacum Palo Bancaro Shea Gilgis Alexander Zebra Jake Laravia Keldon Johnson Bones Highland Jabari Smith Lucanard Andre Drummond jade and ivy Dennis Rodman Carl Anthony Towns and a jade and hearty tie-dye Rookie Auto to 25. I'll do it for the break guys. Thanks again for the fill up next. We've got our three bucks


Hello, thank you for joining me today. We're currently sitting upstairs on a double-decker bus in London We're not going anywhere. We're at the Wolfram Stowe Pump House Museum And this is one of the exhibits If you look out the window You can see they have a couple of Victoria line Tube trains of 1967 stock. So we go downstairs. We're gonna have a look And there's quite a lot here. There's some steam engines in the museum Downstairs of the bus This is a trailer carriage This is a trailer carriage. If we go in here, here we are Didn't think I'd ever do this again. Step onto a 1967 Victoria line train Since they withdrew them all and replaced them with the 2009 stock I just like it when they had the Even though the Victor lines entirely underground. It was still nice having seats that lined up with a window rather than the usual Longitudinal seat and you tend to get them underground trains, but here we are. It's very nice to see one. We've got Come outside There's a steam engine Bus behind us Go down here there's the 1967 stock train behind us and around this way We have a steam engine. Let's go have a look in the museum now and see the stationary steeping just So that's all the steam engines in the museum they do they are all still operational Hope you enjoyed the video. Thanks for joining me. I'll be more coming shortly


The first speaker is Dave Aftely from the University of New York, New York. Indefinite skill of all computing equals artificial life insurance. Thank you. Thanks for coming. I feel like I've been away from artificial life for a few years, and I'm happy to be back now. I remember at A Life 2, Jean Spafford gave a paper on our computer virus as a form of artificial life. And at the time, I thought that was silly. I was doing evolution and learning systems put together. I now feel after 25 years that, in fact, he was sort of just right. And the real issue is not our systems out in the real world, actual living systems, actual artificial living systems. They absolutely are. And the issue is why is it that the real artificial living systems in the world being used for evil and not for good? And we need to understand what the bad guys already understand. So I guess my one-word takeaway is we need more synthesis out of a conference on synthesis and simulation. We need to be building artificial living systems, not just in robots. Robots are great. And thank you for coming here. We've got great robots hanging, happening down the hall, not just in soapy water, but in bits. We need to be building, synthesizing, engineering living systems and digital systems as well. All right. Here is the talk in one slide. We are reaching in Naomi Leonard's terms. It's time for the honey bees to find a new home. Traditional computing based on deterministic serial processing has been revolutionary for 60 years. And it's just about tapped out. Clock speed increases have stalled. We're now going from a central processing unit to a multi-core, which is essentially going from a dictatorship to a troika or perhaps an oligarchy, but it's not moving to a sort of bottom-up, democratic kind of governance system that we could use to build computing in the large. There's another approach to computation. Instead of determining every step perfectly, instead of saying it must produce this or else not computation didn't even happen, the alternative is statistical parallelism where we have tons and tons of things happening at once. We do not try to control the action of every individual little step. We control them in the aggregate. We control them based on the law of large numbers. This is the same thing that is being done with electrons at the level of digital hardware. And that's why digital hardware is so alive because it's exploring the law of large numbers to get voltages to act the way we want. But then above that, somehow we think we have 100% reliability we can do anything we want. It's not true. We have to carry statistical parallelism up the stack. Once we do that, we can have computational systems that rather than displaying the incredible fragility of the computer systems that we have today, one bug and your system is owned. One fault and your system is crashed. Instead of that, we will offer systems not to provide guaranteed security, there are no guarantees of security, but will provide a basic level of sanity, not a level of curing cancer, but a level of washing your hands between patients. That's what we need from computation today. When we do build systems this large, when we start building systems at the level of parallelism that we're controlling the computations that we're performing statistically, rather than in detail, it's going to turn out that the architectural design principles that we need are artificial life. We are going to be having computations that will automatically reproduce themselves for redundancy and for performance improvement. They will reproduce competitively with other tasks using the same hardware. Us, the people in this room, the people studying artificial life can and should own that. The future of computer architecture is artificial life and it's time to get started. The honey bees are going to move. We need to send out the stouts now. That's my takeaway message. Now, it's a methodology session, so I'm going to talk methodology. I've already blown five minutes. I want to save at least eight or ten minutes for a demo because that's really what I want to do. But let's talk methodology for a minute. What I want to propose to you is that this idea of indefinite scalability is, on the one hand, it's a very sort of picky, oh, you didn't really mean that, yes, I really meant that thing. But on the other hand, it's a useful design razor. It's a useful principle for understanding the limitations in architectural designs. I want to talk about that. I'll talk about our little contribution as an example of an indefinitely scalable computer architecture based on artificial life principles called a movable space machine that I'm going to do a demo. This is a slide that is hopefully mostly preaching to the converted here, sort of talking about the two big styles of computation, where the artificial life side is on the right-hand side and sort of traditional architecture and computer science is on the left-hand side. People say the first computation to run is Hello World Program. The Hello World Program should be called the High World Program. The very first thing it does is die. A Hello World Program would live forever saying, hi, how are ya? That's what processes do and algorithms don't do. So the living system approach, the emerging bottom-up, evolution and so forth approach is the right-hand column, which is where we want to be. The reason I show this is because if we look in detail at many of our models, many of our artificial life software-based models, they ought to be indefinitely scalable, but they're not. They're not because of kind of stupid reasons that we should work on fixing. So here's the game. Imagine this is a thought experiment, just come along with me. Suppose you're given an indefinite supply of space and power and cooling and money for hardware. It's like DARPA, maybe even NIH, I mean big money. As much as you need. You've got space, power cooling and money. Your job is to invent a computer architecture, a tile of hardware that you can stack together and make a computer as big as you want and never have to stop and say, whoops, 640K. That's the goal. Be able to stack as much hardware as you want and never hit an internal engineering limit.  That's the game. And the only requirement, the only hard requirement is that each of these hardware tiles has to be fixed size, constant mass. Your tile is not allowed to grow with the size of the system, okay? That's it. That's the thought experiment. Imagine making a computer like that. When I ask people this, they think of a number of things and say, oh, this is obvious. And so just to drive home that it's not completely obvious, it's supercomputers. Supercomputers, not even close. In general, the supercomputer, in fact, has been scaled about as far as it can. That's what makes it super. And if you wanted to make one 20% bigger, you'd have to start over engineering. The internet, internet indefinitely scalable, infinitely large. Why not? What's wrong with the internet? Anybody know? Bandwidth? Well, at least if we build more hardware, we get more bandwidth. What are we saying? Addressing. We have IPv4 addresses, 400 billion addresses, whoever needs more, of course, we're always running out of them. Everybody says, oh, well, IPv6 has so many addresses, we could never run out. And that's exactly the point. It doesn't matter. For the game of indefinite scalability, any finite limit on address space is unacceptable. Touring machines, cellular automata, and that's the one that bugs me.  But most cellular automata models are not indefinitely scalable. The most number one reason is they presume a synchronous clock. They presume you can step the entire system all at once. That's not indefinitely scalable. So we start to think about this and we say, wow, ACK is really strict about this strict indefinite scalability. Yeah, that's the idea. Well, why? I mean, the universe might be finite. Why do we need something that could go beyond that? And here's the reason. I made a slogan. Every scaling limit implies a limit at every scale. Okay? If you look at a model and you find its scalability limits, each of those limits you can then turn around and find a corresponding design problem in the finite model, in the model as you're looking at it. Every scaling limit implies a limit at every scale. And here's a few examples. We assume perfect reliability. When we assume perfect reliability, there's no reason to add fault tolerance. There's no reason to add robustness. Well, robustness requires redundancy. Redundancy is inefficient. With perfect reliability, why do it? Presuming perfect reliability means we have catastrophic response if failures do occur. Synchronous clocking means we can't actually have any input output. The entire system is this one island of and because we're assuming synchronous clocking, we cannot talk outside that system because it's not synchronized to us. That's actually a problem we have with computers today. What we settle for 10 to the 9 chance of error, one 10. Totally unique node names, free communications, that's another one that happens a lot in artificial life models. Every scaling limit implies a limit at every scale. So it's a useful thing to understand the design limitations of any model. The takeaway message for artificial life is we can simulate whatever we want. Strictly speaking, if you want to do Conway's life, that's great. We can learn lots of things. The problem is when you offer up a model and say, this is just a simulation. This is just for science or pedagogy. Well, then someone else could turn around and say, well, I want to do synthesis. I want to build a machine. I think it would be cool. And they're going to want to look at your model and try to use it. And then these things are going to come and chew on our bus. We need to look for A-Life models that are indefinitely scalable to get the benefit of all of the things bottom up, emergence, robustness that we've been saying artificial life provides. The model that we've got is called the movable feast. I'm not going to go through this in detail. The slide's a little bit old. There's our little hardware tile. That's eight of them or whatever. That's the version one hardware that has some problems. This is what you learn by actually building hardware. We're hoping to build second generation hardware soon. We need a little more money. The way we can understand this is an object-oriented artificial chemistry. It's an asynchronous cellular automata with huge, huge neighborhoods from the point of view of cellular automata but teeny tiny memory from the point of view of conventional programmers like that.  From the point of view of cellular automata, it's a huge neighborhood. From the point of view of a programmer, it's incredibly tight. All right. So that's an example, but why don't we try to do a demo instead? Let's see what happens. All right. Well, we might or might not be able to see anything here. This is a... I'll tell you what we'll turn. Here's a field of tiles, simulated tiles. Where's my... I lost my control key. I don't know what it is. All right. Let's take an element. I'll put an element called drag in here. We'll put a field of them in there and we'll let it run. What's happening is they're diffusing around. Man, they're diffusing incredibly slowly. What drag does is it looks around at one neighbor and if it sees an empty spot, maybe it creates a resource there. If it sees an occupied spot, maybe it erases it. And the net effect over time is the drag dynamically regulates the empty spaces in the system that it sees. And here's a version that's been running for a little while. It's now full of about one-third occupied sites, two-thirds empty spaces. When we have a system like this, parallel systems, Naomi talked about this as well, how do you break deadlocks? In traditional system design, deadlocks are a huge problem for parallel systems. With a robust first approach, we break deadlocks by breaking deadlocks. We randomly erase stuff. We don't ask, is this part of an important computation? Oh, you are immune. We erase stuff with no regard for what it's doing, and the computation has to be robust to that. If we're requiring robustness at all levels, that gives us the freedom to have a little slop at all levels as well. So once we have a world like this that gets composed mostly, like 6% drag. Let's move on with this keyboard. The keyboard is not doing the keyboard. Without the keyboard, that's just the mouse. Nice. Well, I can do that. Let's pick another element. Pick a sorter element. We'll drop one of them in here. Did I get rid of the guy? Oh, but now I can't do it. We'll just move on to the next one. We've got another one here. What we've done here is we've used the drag and res, the churning mass of stuff. We've incorporated elements in here that are designed to be sorters. They look to their right. So the red atoms are the sorters. The blue atoms are data. If we get close enough, there we are. Actually, we'll see it. So each of these little SR guys is a sorter. Each of those blue guys is data. It looks to its right, takes one, says are you bigger or smaller than my threshold, and throws it above it or below it and to the other side.  You put data in on one side. It starts out random. By the time it gets to the other side, it's pretty well sorted. And that's what this does. You can also see some DRs. Those are the dregs. You can no longer see any res, the resources, because the sorters have consumed all of them to turn them into sorters. This is not an accurate sort. It often makes small errors. It doesn't get things quite right. But it's incredibly robust. We can blow holes. There we go. We can blow holes in the thing. And, well, what happens? The system rebuilds itself. There we go. Okay. All right. Now, I want to show one more thing. It's a period of a cellular automata, if you think about it, from a physical point of view. It's a driven media. You can make a rule that starts out with one lit cell and ends up with a world full of lit cells. That doesn't require any more food, any more power than doing any other rule. It's a driven media, which makes it unbiological in one point of view. But it also makes it very handy. And that means that we have a design problem, which is what happens if we get a fork bomb, an element that just reproduces as rapidly as it can? What happened to our sorter? Our sorter just got wiped out. With a fork bomb loosing the universe, there's basically nothing that you can fight it with, except possibly another fork bomb. We've got red fork bombs and blue fork bombs. It's a lot like the voter model with the neighborhoods and so forth. And the dynamics of this are complicated and long-term transients like that. My point is this. As we design these systems, as we try to build intentional computations with them, we have to engineer with this stuff. We have to recognize that this stuff is there. And here's the thing. Each of those guys, when it has an event, it's reproducing itself 12 times. It grows incredibly rapidly. But if we can have something else that can outrace it, that can run a little bit faster. And we've got an element like that. It's called AF, our anti-fork bomb. And what that does is just what you would think. When it sees a fork bomb in the world, it responds by being a fork bomb. But as soon as the world is clear to them, it dies back. So you can't see it right now. But right now the universe is full of 6% anti-fork bombs. So now if we try to come in and throw one of these guys, the system responds to it and then cleans up again. We can now build the same sorting network that we did before. Drop in six, actually, we only have to drop in one anti-fork bomb and it populates itself. And we can now defend the system that way. This is what I need you guys to help me with. We need to be understanding the dynamics of making intentional computations in indefinitely scalable systems. Thanks so much for listening.


Snestrunk. Welcome back to Snestrunk Place, Secretamanna, and I have everything I need from this store. There's not much there. Thank you, dad, for selling me stuff. What's Ned Flanders over here got to say? Guy is Navel. Yes, common knowledge. I do enjoy that this is one RPG, adventure-style RPG, where the villagers actually say things and give you clues and hints on what's happening like that woman upstairs that was talking about the ruins Grandma went senile and all that stuff. So it is worthwhile going in and talking to all these people. Hey, it's the cannon travel center guy Look at that. He's got his own his own pad. He's got the misses upstairs. Got a nice Wife there. Good, good for him. Good job. I guess he's into green hair. I guess it's more lime colored hair Anyway Yeah, I love the detail they put in here all the way to paths, flowers, those called mills. I don't know what exactly they're doing and maybe they're providing electricity or something Sure, we want to stay at the end here and rather than waste candy and whatever Good night. I don't know about you, but I always do a fist pump when I wake up We do not want to save our game Not necessary whoop technical difficulty there anyway Let's get going to Gaia's naval which is really a pretty long not long I guess You know it takes a few minutes to get there all while stopping to destroy all enemies in our path Regardless of how cute and cuddly they may look that means you were a bike Yeah, I'm through cutting grass for a while.  I don't know what they were smoking when they made those decisions, but it really works It makes it that much more fun to kill these things So I personally Enjoy it. I don't think I'm gonna stick with the spear for with the girl for a while Once I get another wet, there's another weapon coming up and not the next very very after equipping Now what you could do or what what was supposed to happen? Another possibility I shouldn't say supposed to put another possibility Is if you decide if you didn't go to Pandora?  Why are not why aren't I leveling up? if you talk to this guy Oh, oh wow, he like references the our next character that will meet That's pretty cool. But if you come here, but without the girl without meeting her in Pandora, you He just says a girl ran in here by herself and Disappeared so at this point you go into the haunted Whatever god 20 damn it. I better get out of here. She can't she's not leveled up enough She doesn't have a good enough equipment This will do nice for a leveling now. Ah, there we go. But yeah, and then you face these like tiger boxer God, excuse me tiger guys.  I think that happens anyway spoiler alert But anyway, I just wanted to show that off there are different a few different paths the game still linear obviously But there are different. There's different paths that lead to different things that do different things Pretty cool. Let's just keep going though. Let's get get to that door filling Find this underground palace. I Guess that's technically what we're supposed to do right underground palace Whatever Yeah, we will be shortly adding a third member to our party and yes, this game is three player If you have the Super Nintendo multi-tap you can use all three Characters at once very cool the sequel seconded. I'm sorry sakin did setsu three I get so much shit from people Sorry Jesus Christ No, I honestly don't care Really, I care about getting it right, but I don't care about people nagging me about it The yeah, you can It's the same sort of thing where it's three members to a party three player game a lot of fun I think the combat in that game is even better Let's see what we got here Slam this thing into the water. Oh, it's a trap.  There's also poison needles.  Let's get in here.    You can do whatever you want So yeah, she gets the hell out.  Well, good luck lady So yeah at that point she goes running into the haunted forest and when you go back there That's what the guy says you you can skip all that entirely You don't have to meet her at Pandora because I guess yeah, that just happens anyway kind of cool. Oh I love killing these guys They're falling there's fast asleep.  I think they're called slimes.   I think I came in from there But why was that enemy down there? We're downstairs here I get lost so easily it's absurd Wasn't very good at games like Metroid or Stuff like that early on that took takes me a while a few playthroughs to really understand what the hell I'm doing Well, this is no good. It's all full of Chili looks like Maybe that chili I think needs some cowboy Bob's bold sauce Damn, I wish I could remember that history science theater joke It's one of their best host segments for Mike and the bots are promoting a Barbecue sauce and it's bold. I can't remember what it's called. It's got some preposterously long And I can't remember it's cowboy Mike's something something something bold sauce Anyway, we make our way up here for all fairly linear No diverting paths or anything like that. We just need to know how to get rid of the the chili flowing through collecting treasures along the way trees you use with 28 gold pieces inside that'll buy you know might buy Super Mario All-Stars, maybe maybe a copy of like turtles in time, although that's been going up in price So let's smack this skull right here fracture its jaw and its eye socket poor guy I'm sorry, but I needed to do it to get rid of the lava Apparently it's disappeared. I'm coming up on the 10-minute mark here. So I'm gonna call this an episode Thanks for watching and have a great rest of your day


Hi, this is Michael Lewis. I'm the CEO at Microsoft AI and In our first installment of who are you and what are you doing here? I'd like to introduce Mike Hansen he's the newest member of our development team and I just want to Talk to him a little bit about why he's here and you know what his interest in in Microsoft is so He's he's the creator of the raspy project and so I'd like to ask you Mike, you know, what was your motivation for for getting into that? Sure So I actually got I got some hardware I was working at the Air Force Research Lab got some raspberry pies and the condition for me getting these was that I needed to teach Raspberry Piking out for kids and I Actually enjoyed teaching so I thought no big deal So I did that and we were I put home assistant on this pies and then wanted to do a little voice assistant as well Kind of an offline thing and I found a project called Jasper But it didn't work so well And so I thought well, maybe I could improve this a little bit So I got something that worked pretty well for me But unfortunately it turns out if you have 20 20 10th graders in a single room all trying to talk to Their voice assistants doesn't doesn't work out so well But I enjoyed the experience and I kind of kept kept at it. I put the code up as an open source add-on and Then just kind of worked on it in the background but then kind of when COVID Shut down the Air Force Base and I moved remote. I was able to work, you know much more on raspy With the approval of my boss and just found that I loved it and So over time I decided, you know what I want to make this my full-time job and That's kind of where I am today What now my understanding is that raspy is The goal is to make that entirely offline, right? So there's no server connections for that. Why is that? well, the idea was Basically so that if somebody wanted to cut out, you know, any kind of third-party Listening to their voice or anything and they could do that. So there's a privacy aspect But for me there was also like a Kind of a robustness aspect to it I had read about people who you know sometimes people who don't have full mobility or something who might use voice Assistance around their home to help them and I remember reading a blog post by a gentleman who said, you know when the internet goes out I I have a huge problem And so I thought, you know the technology I felt like was far enough along that we could do this fully offline Now this can't do everything, you know, it's It's still limited in its in its own commands that it can take but it's still like it's way better than it was back in Back in the days of even the Raspberry Pi one So so there's a privacy aspect and then also the robustness for big things Yeah, that's that's great What so you recently joined microp just a couple of weeks ago What you know, what was what was it about? What we're doing here at microp that that really interests you well, it's it kind of It would be like the the dream for me as as the creative raspy to become something like a mycroft right, you know to to be able to Reach a large community of people Like with with open-source software to be able to provide, you know a private service to people and to to work on You know the hardware so I'm excited to work on the mark to Something we struggled with in the raspy community was you know, everyone has such diverse hardware They're trying to get this level of performance on but if you don't have You know the nice microphone that's tied to the speakers and such it makes it for a degraded experience I think and so I'm excited to To join a company that actually embraces kind of the values that I had in starting raspy the privacy aspect And such and can kind of come into a large community. It's great What do you think you can bring from the raspy project into mycroft? Well, I'm hoping to bring a number of things. I've I've worked on Getting things to run offline is is the big one. So raspy speech to text can run offline You pre-program it with a with a grammar right now They can still have millions of voice commands, but it's it's it's restrictive. So I'd like to bring Some of that and expand it out and then I've also worked on text to speech So I've I've trained at this point dozens of voices in different languages And those those are able to run offline as well on the Raspberry Pi hardware So the offline aspect is a big one and then I'm also interested down the road You know, my my background is in cognitive science as well as computer science. I'm interested in how we can Kind of take voice assistance a bit further than you know, right now a lot of them are basically chatbots with You know voice components stuck on either end But I think we can develop things that has a real dialogue with the user and can do more That's I'm interested in that aspect awesome well, I for one I'm very excited to have you on the team and Thank you for jumping into you know the the startup experience, which is always very exciting But Yeah, this this all sounds great. I mean, it's you know for us. It's a it's a perfect alignment And you know really glad to have you on the team. So thanks Thanks for the chance to get to know you a little better too. Sure. They excited to see where we go. All right. Thanks


Thank you Zahra, Salamu alaykum. Welcome to Morning Baraka and in this segment we're going to be discussing health and nutrition and here with me is Sanaa. Welcome Sanaa. Thank you. And we're going to be talking about Middle Eastern food but hopefully bringing it in a healthy way of eating. So what have you got for us today in our first? So today I'm going to be making a grilled pepper and tomato salad. Okay I haven't heard of that before. It's not something you really think about when you're making salad but it's a traditional Moroccan salad that we have and it's very tasty and really quick and easy to make. Okay so tell us about the ingredients that you use. So we're going to be using some red peppers, yellow peppers, green peppers and some tomatoes. They've all been grilled so before obviously we start we will grill them. You can grill them in the oven. Traditionally they would put it on the fire stove and let it go all black and then you would put it in a bag and seal the bag and let it sweat and then when it sweats the skins will come off easily. Okay so let's see you prepare this. So let's prepare yeah. Well these are interesting ingredients and I know that peppers generally are very rich in vitamin C's and it also contains a lot of water. It's like 92 percent water which is really really healthy for us. I mean a lot of the times we don't realize how much we need to hydrate ourselves. How much we need to keep because our brain actually contains majority water. A lot of people don't understand this fact. We always say we have to have a lot of water and it's for a reason because there is a function that we have to maintain in our body and being hydrated constantly you know sometimes we forget. So having these ingredients that contain the extra water and in this general you know salad there's no lettuce which normally has water. So the green peppers or the red and you know which ones you're using that actually do contain quite a lot of water. Exactly yeah and I mean it depends on what you would like to use. You can use just one color or you can mix like we're doing today. I prefer to mix because I just think it makes the salad look a lot more bright and vibrant and it just looks a lot more you know attractive to the eye when you're looking at it. But it is something that we use a lot in Morocco and it's something that like I said it's very quick it's tasty and we're going to be mixing you know and a lot of other things in there like the parsley and the coriander and the olive oil which will also give it that additional taste. You've got even health benefits of green peppers which in you know it basically reduces sort of several chronic diseases and even not just taking into consideration the health benefits from you know normal studies that have done even in Islam when we Imam Ali alaihi salam says that its type of taqwa is to actually take care of your health yeah not just you know spiritually but physically and this type also can help you prevent any sort of diseases and so we need to take more interest in what we eat and I know even when I coach clients as even though I'm not a you know nutritionist I do take a lot of interest as to how clients diet works because even though I work with the mind we have a lot of foods nowadays that actually make a difference to your mood there are foods for your mood it can increase or decrease stress or anxiety it can help with your you know mental you know ability to give you more boost and all of these ingredients that we're going to use hopefully throughout the show it's going to give us that insight and awareness and what I also think is really important is that we want to stick to sometimes our own culture food which is we always think that if we're going to diet we're going to be healthy we cannot do that with our own food but we actually can exactly yeah it's really important that you know we highlight that when we use these ingredients this is from our you know the cultures in the background that we used to and we can actually use it to our benefit exactly we can adjust it so for example where you know sometimes they would fry this in oil yes so you can think you know what I want to be a bit more healthier today so instead of frying it put it in the oven and grill it so the taste obviously we do know when something is fried it does taste a lot better but it's not much of a big difference really because you're still getting the benefits and the taste absolutely so you know remind me again so how did you prepare this so with the peppers and the tomatoes I grilled them and once they went quite dark and I placed them in a in a bag and I allowed them to sweat for about ten minutes okay and once I did that I took them out and then I peeled the skin off the outside which was when the good tip with the bag is that it's a lot easier to take it off okay so it will be a bit messy so I would advise to do in the sink and I even see you using gloves at the moment which would you normally use at home well not all the time but because we want to promote you know health and and to keep hygiene exactly to keep hygiene in mind as well so it's quite important to do that so yes so now what I've done is I haven't used a little bit because I don't think we need it yes but I've just chopped a bit of each and now what I'm going to add is a mixture of the just a bunch it obviously again it depends on what you like and your taste buds of course if you prefer to put more in it's up to you so what herb is that so this is a mixture of both parsley and coriander I love parsley in my salad it actually makes such a difference it's lovely and the fragrance of it is so so nice absolutely it adds color taste and it is really another part of your healthy plan exactly because a lot of the times we might put it on certain foods are just as a garnish but we can take advantage of having more if you add it to the salad exactly yeah and again with this you can chop it as you know as fine as you want I prefer to do it a bit more fine and some people like to just put it in completely of the leaf and mix it in again it's down to your own individual choice of how you prefer and now another thing that I'm going to put in there is olive oil I put a tablespoon of olive oil okay olive oil it's really really good for the health and it can low because that cholesterol so I think it's really really advisable that we should use more olive oil in our cooking generally yes exactly I mean in Morocco traditionally we always use olive oil for most of our cooking so we hardly use sunflower even a normal food cook foods normal food so you know in our stews in our curries any of these things we would always use olive oil mainly vegetable and sunflower or if we're frying like potatoes or chips or these things we would use it but olive oil is pretty much used in most of all in our cooking so I mean it's really really good it normalizes blood clotting and it can prevent sort of high blood pressure we don't realize these ingredients are so important exactly you know subhanAllah these ingredients are natural and they are so good for us and even you know we always think that we have to live a healthy life just by thinking in a particular way but actually our body and our mind has to work hand in hand and it's really important that we understand you know a lot more about food and how we can actually use that to our benefit and even still enjoy what we normally used to exactly yeah that's amazing by the way yeah no we just need to season it and it's with a bit of basic seasoning really just salt and pepper and I would put in here about a teaspoon I love balsamic vinegar but because you've put the olive oil the salt and you've got the parsley I mean it is a choice to put lemon or balsamic vinegar that's an extra or do you think because you having this as a side does that make a difference it depends I mean it would probably be very tasty with the vinegar okay and some lemon juice but and this is how we traditionally make it so you can add it how do you have it alongside what particular food so we would have this as traditionally on a table we would have the main meal in the middle okay so whether that will be like a chicken tagine or a lamb tagine and around the the actual main meal will be little plates of these salads okay and so and each plate would have a spoon so each person around the table would have their own salad portion exactly so that's why we're not making a lot because it's not something that you don't make huge amount I was gonna say yeah yeah I wanted a big bowl and again obviously you can choose to have it you know on its own if you don't want to have it with a meal it's you know you don't need absolutely if you just want a quick snack it's really healthy and it's quite hydrating and it's really colorful and tasty I'm just looking at it I can't wait to taste it yes so it smells very nice amazing especially when you've roasted it like grilled it like you have it's just so beautiful if anyone can you know it's not it's really lovely and I'm gonna also add obviously again this is based to your own taste yeah of course I don't like too much black pepper so I'll put about half a teaspoon or even less about quarter and then that's everything I see we've also got some lovely bread here as well is that something that you normally have or is it like rice normally with a meal or do you have both no we actually traditionally have bread so all of our dishes even our curries our shoes our tajins they're all with bread fresh bread so even salads we have we have it with bread yes and traditionally they would eat it with the salad with their fingers because you know like as part of the center is they say it's good to eat with the definitely with your hands with your hands because exactly yes so and what I'm gonna do is I'm gonna now serve it just move this out of the way let me help you there a bit put that behind you okay now again I said it's very basic it's very simple anyone can make it home really quickly and most of us have these ingredients in the fridge well to be fair like I said it's not the traditional salad and I think it's really healthy to have a different way of having salad which includes different ingredients which actually have more health benefits than the usual salad and again this could be a little bit more filling because you can have the salad alongside bread yeah and as that even as a lunch meal I personally would have that as a quick lunch you know snack if I was really busy and didn't have time to prepare and make anything or even to take that away because I don't know you mentioned before you could have that hot or cold exactly yes so this one is a cold one but if you would like to make it hot similar things that we've just done right but we would put it on a pan and put a little bit of again olive oil in the pan right and but this time we would add some just a little bit of onions a bit of garlic and then put all the ingredients inside allow it to just kind of simmer and absorb all of the the flavors right the salt the pepper and also the parsley and it will become a little bit more mushy yeah soft so exactly yes so it's even easier to eat with bread so sometimes it could become almost like a little stew yeah and you can have it with bread or even with a spoon on its own yeah and so there's two ways this is the cold version and the warmth they're both very tasty so you can give it a go and do you find that having this sort of ingredients especially with children do you find that they can easily you know take that because it's very difficult to have children eat these types of vegetables and greens for example it's true you know what one of the things that you can do is now not all children like fresh peppers they will prefer it grilled or vice versa they would like it the other way so for example one of the things that I've noticed is that my daughter prefers it if it's grilled so she enjoys it like that if I was to give it to her fresh she'd be like I'm not really it's a different texture and different taste exactly it's easier to have it in that sort of form and just looking at it looks absolutely delicious yes and the crunchiness I guess you know again you said it's a just you know it's a personal sort of it is yeah exactly and like I said it's not for everyone but you can give it a try it's very easy it's not the normal salad that we would have lettuce and which is what I love because it's nice to have something different and again it's it is traditional it comes from you know what we would normally have you know in our cultures and backgrounds but at the same time we use it for our own health benefits to improve our way of living and being and we don't realize that you know what we have and what we intake in our body makes such a difference to our everyday dealings yeah so this is why it's really important that we learn so much about what we have generally so anyway I'm just gonna tuck in yes I can't wait trying to try this a bit of parsley as well mmm it's delicious yeah I love it I mean I love vegetables anyway so I'm oh my god it's probably nicer as well when you put it in the fridge and let it get a little bit cool I love it and the thing is and just on its own not even having any bread alongside it yeah and that's an amazing plate just to have with so you know like I said there's a takeaway meal that you just you know in a rush and if it was you know for the next day if you're going to work yeah it's just perfect if you have guests as well it's also something that's really easy and quick to make because you know when you have guests over you always think what can I serve with the main meal this could be something that you could do at home it's quick and easy and it's something new that you can you know show to the to your visiting well thank you so that was really interesting and hopefully you know audience have sort of gained a little bit more awareness of these ingredients and this recipe and I hope you use this in your home and enjoy thank you for watching and shall I will see you next time salamu alaikum