So, I am going to talk about a recent exciting result of Julia Shuzoi about a classical problem known as the edge disjoint path problem in networks. So, let me just start by defining the problem. You are given a graph along with the collection of sourcing pairs let us say S1, T1, S2, T2 through SK, TK and your goal is to route a maximum number of these sourcing pairs in the graph in an edge disjoint manner. So, when I say routing a pair what it means is if you route a pair SITI you assign a path in the graph to the pair SITI. So, you connect SITI to TI along this path. The phrase edge disjoint here means that if I look at the routing of any two pairs SITI and SJTJ then they do not share any edges. So, let us look at an example here in this graph. I am routing the pair S1, T1 along the red path S2, T2 along the green path and S3, T3 along the blue path. Once I have routed these pairs if you look at the pair S4, T4 there is no way to assign a path to this pair without violating the edge disjoint property. Any path that connects S4 to T4 at this point would intersect with one of the previously assigned path. So, this is an extremely well studied problem. There is a long and rich history of results on this problem. For now let me just review some classical results about the problem and I will say more as we go along. So, for one thing I should just point out about the expressive power of this problem. Even the EDP problem on star graphs which are trees of height 1. So, you have a single vertex connected to another vertices by directed edges. Even EDP on star graphs is equivalent to the general matching problem. We know how to solve matching in polynomial time, but that is a non-trivial thing. So, EDP captures this very easily. When the graph is directed even on two pairs just S1, T1, S2, T2 the problem is NP-hard to solve. If the graph is undirected the problem is poly-time solvable for any constant number of pairs, but this requires heavy machinery of the graph miners work developed by Robertson and Seymour. So, this is a highly non-trivial algorithm. And of course, once even in the undirected graphs once the number of pairs is unbounded the problem is NP-hard to solve. And I should point out that even on undirected trees if the edges of the trees have capacity then the problem is NP-hard. But in this talk we will not worry about capacities. We will talk of always assume all edges of the graph have unit capacity. So, since the problem is intractable there has been much work on designing approximation algorithm for this problem. And in this regard almost all the work on approximation algorithm starts with one common starting point which is linear programming relaxation, a very natural linear programming relaxation for this problem which is known as the multi-commodity flow relaxation. So, what does the relaxation do? First thing it does is that instead of routing a pair SI-TI along a single path it allows you to simply supply a unit of flow from SI to TI. So, this means you can use multiple paths each path carrying some different fractions of the flow. The second thing you do not even have to write route a pair SI-TI for a full unit amount of flow. You could say I am routing it for an epsilon amount of flow. So, now we can just define a variable XI which indicates for each pair SI-TI how much flow for the pair is routed by using a flow system. And then we have a variable f of p for every SI-TI path p which tells how much flow is carried on the path p. Your goal is to maximize summation XI which is the total amount of flow you route. And the main constraint here is to make sure that if you look at any edge E in the graph and you look at total flow on paths that go through the edge E this flow should not exceed 1 that is the implementation of the edge disjoint condition. So, as a warm-up let us just look at a very simple rounding algorithm for this relaxation. It is an iterative process. You start with the fractional solution for this multi-commodity flow relaxation. Among all the pairs which you have not yet considered for routing pick the pair SI-TI which has the shortest flow path on which LP routes some flow. So, this is shortest in the length of the path. Route the pair SI-TI along this path p and now any other flow path which intersect the path p you discard them. You keep repeating this process until no fractional flow is left. It is clear what you get at the end is an edge disjoint routing because each time you route along a path p you discard every flow path which intersects with it. What is not clear is how good is this algorithm. So, let us fix some notation and we will just analyze this algorithm. It is a very simple analysis. So, throughout the talk I am going to assume n denotes the number of vertices and m denotes number of edges and let us say opt is the optimal fractional solution. So, let us first consider the case when I end up picking a pair to route and I route the pair along the path whose length is less than square root m. In this case when I route the pair how much flow could I throw away? Well at most root m, I have only root m edges on the path and I might be throwing a unit amount of flow crossing every one of those edges. So, as long as I am routing path on path of length less than root m, I am within a root m factor of the optimal solution. At some point if the shortest available flow path has length more than root m, then notice that the total amount of flow that remains in the solution can be no more than root m. Why? The total routing capacity of this graph is m and every unit of flow being routed would consume root m amount of this capacity. You have no more than root m amount of flow. So, at this point even if you route just one more pair, you would be within factor root m of the optimal solution. So, if you combine these two observations, you get here is a rounding, which is within root m of the optimal solution, okay? So one may think that you could do better than this by being more sophisticated. After all as Madhu is pointing out, I'm not, I don't seem to be using the power of LP too strongly. Turns out there is a simple graph. An instance which was shown by, identified by Garg Vazirani and Yannaka case almost 20 years ago. Which shows that this LP has an integrity gap of square root m, okay? And this instance is actually just a grid like graph, okay? So here is the instance. So you have along the x-axis the sources and along the y-axis you have the sync vertices. And the green blobs actually correspond to that little gadget up there, which ensures that paths which enter the green blobs, they have to traverse through a common edge to get to the other side of the green blobs, okay? So once I put this gadget in this instance, let's see how good is an LP solution. You can always route half unit of flow for every SITI pair. How? Pick a pair SITI, start at SI, go up all the way to the level of the sync TI. And just turn towards the sync TI at that level. So just a straightforward right routing up and then left. Everyone does that. Any two paths will intersect just once. And when they intersect, their only constraint is they don't have flow of more than one passing through the common edge. That's ensured if you're routing only half units of flow. So you can route K over two units of flow. But now let's look at an integral routing. Take any pair SITI. Moment you route SI to TI, no matter in what fashion. You essentially create a wall. No other pair can reach there. No other source can reach it sync without crossing this wall. And that means causing a congestion of two on some edge. So you can actually just route integrally one pair. K can be set to, may roughly, root M. And this will show you an integrity gap of root M for this LP. And this gap holds for planar undirected graphs, okay? So it's happening on a very simple class of graph. And actually the news is bit worse if the graph happens to be directed. You can turn this integrity gap into a hardness of approximation result. Remember, I pointed out earlier that the two-pair problem on directed graphs is NP-hard to solve. So now those green blobs, I can just replace them by a gadget, which is the two-pair gadget. And if the two-pair gadget admits a solution, that means both pairs can be routed in an edge-to-joint fashion. You will be able to route all SITI pairs. And if there is no solution, then it serves as an obstruction, as before. And you will not be able to route more than one pair. So this intractability where it seems even hard to approximate the problem, motivates naturally the question, can we relax the problems slightly and get stronger approximation guarantees? Root M is not a very appealing approximation guarantee. And a natural relaxation is to consider EDP with congestion. So from here on, when I say EDP with congestion C, I mean the following version of the problem. I would let you violate the edge-to-joint condition in the following manner. Through every edge in the graph, I will allow up to C paths to use the edge. So the case we have been talking about so far is with congestion value C equal to 1, and what we want to understand is what happens when the congestion is allowed to exceed 1. In particular, the question that's focused on this talk is, is it possible that with constant congestion, EDP becomes well-approximable? Like approximately within a polylog factor. And if you notice the integrity gap example that I showed, it completely breaks down if the congestion of 2 is allowed, okay? It relied very strongly on no congestion condition. Congestion of 2, you can just route like the fractional solution. So once we start looking at EDP with congestion, there is a beautiful result of Ragman and Thompson from 1987, which gives a randomized rounding scheme for solving EDP with congestion. That goes as follows, take the fractional solution, look at a pair SITI, toss a coin, which let's say comes up heads with probability Xi. Xi is the amount of flow that is routed for the pair SITI in the fractional solution. If it comes up heads, you say I'm going to route this pair. So you're routing a pair SITI with probability proportional to Xi. And once you make the decision to route the pair, you look at the flow paths used in the LP solution for this pair. And you sample one of these flow paths, the probability proportional to the flow on them, and that's it. That's how you will do the routing. How good is this routing? It turns out if you allow a congestion of roughly log n over log log n, you can get a constant factor approximation to EDP. And then building on the same ideas, it was shown subsequently that for any constant congestion C, you can get n to the 1 over C approximation with congestion C for EDP. So things do improve once you allow congestion. But notice that as long as the congestion value C is a constant, the approximation factor is still a polynomial factor. So it's better, it's improved, it goes down, the ratios go down as C increases, but they remain polynomial for constant C. So, could we do better than this rounding framework? Okay, so can we do better? Well, it turns out if the graph is directed, this randomized rounding approach is pretty much the best you could do. In fact, there is a hardness result of the form n to the omega 1 over C for EDP with congestion C in directed graph. And also, if you wanted to get something like close to the constant factor approximation, you can't avoid having a congestion which is log n over log log n. So this, for directed graphs, qualitatively, at least, right? We are not matching the exponents exactly in the hardness and in the upper bounds, but qualitatively the question seems to be well understood. Things are not so clear for undirected graphs. You do have hardness results, even when congestion is allowed. But these hardness results are of the form log n to the 1 over C. So the upper bounds looks like n to the 1 over C and the hardness looks like log n to the 1 over C. So, from this point onwards, I'm going to focus only on undirected graph, and this is the state of the art for undirected graph. Or this was the state of the art as of two months ago. So what is the state of the art? For any constant congestion C, you can get log n to 1 over C hardness. And you get n to the 1 over C approximation. So there's a striking gap between upper and lower bounds. So this gap has essentially disappeared with the remarkable result of Julia Shuzai, which shows the following. With constant congestion, it is possible to get a polylogarithmic approximation to EDP in undirected graph. So we really, the truth here really was closer to the hardness results. So this result builds very strongly on number of developments that happened over the last six, seven years. And then adds to those developments a very powerful machinery of its own. So in the remaining time, what I would like to do is there are many, many technical details and I can't, I won't have time to get into many of those technical details. But what I would like to do in the remaining time is to give you a flavor of the various ideas that are put together in getting this result. Okay, so the rest of the talk, I'm going to divide into four parts. And I'm going to start by talking about a framework for solving the EDP problems called the Well-Linked Decomposition Framework, which is the starting point for all the recent results. And at a high level, what the framework allows you to do is to take an arbitrary instance of EDP and reduce it to an instance of EDP, where all the sourcing pairs have very high connectivity to each other. Once you have these instances of EDP with this special property that the sourcing pairs have very high connectivity to each other. Remember in the original problem, all you care is to connect S1 to T1, S2 to T2 and so on. You don't care about the connectivity of S1 to T2 or S2 to T1. Here, we would care about the connectivity of even the sources and sinks which are not involved in any pair. So the second step after that is once you have these instances where sourcing pairs have very high connectivity to each other, we would like to exploit this connectivity to show existence of some interesting routing structures in the graph. And in particular, we will end up showing that you can embed expanders in such instances. And in order to do this embedding of expanders, we are going to use a beautiful recent approach for embedding expanders, which was highlighted in the work of Kandekar, Rav and Vazirani, which breaks us down into a cut matching game that I will talk about. And this view of embedding expander turns out to be very useful for the EDP framework. So the third thing here is EDP in graphs with large minimum cut. That was really the first result which combines both these two ideas together and shows that you can get a polylog approximation for EDP with actually even I think the result was just congestion one provided the graph you start with has a large minimum cut. That is, it's reasonably well connected to begin with. So that was the proof of concept that there is some hope that EDP may, after all, be approximable to be in a polylog factor. And finally, I will talk about how Julia Shozoi extends this approach to arbitrary graphs which do not obey the large min cut condition. So let's start with the well linked decomposition. So what's the idea of well linked decomposition? As before, we're going to start with the multi-commodity flow solution. But this time, we'll look at the solution and use it only to partition the original instance into a collection of smaller instances. Where these smaller instances will have property that all the sources and sinks in them are going to be well connected. So key point of departure from the earlier approaches is in doing this decomposition, I'll totally ignore the flow paths that are used by the LP solution. The only information we will carry forward from the multi-commodity flow solution is what was the fraction for which a pair was routed. And from this point onwards, I wouldn't care once I've done the decomposition. I wouldn't even care about the original multi-commodity flow solution. The second step of this framework is to show that once you have these well linked instances, and I'm going to define this more precisely in a moment. Once you have these well linked instances, you can embed in them routing structures which I'll call cross parts. And these are basically structures on which the EDP problem is easy to solve. And if you could do that, then you're in good shape. Because now you started with an arbitrary instance. You reduced it to well linked instances. Well linked instances have cross parts on which EDP you already know how to solve. And now you will just use these cross parts to route your original instance inside them, okay? So that's the idea of the framework. So let's define these, just a few definitions. And then I'll also show you right away a quick, simple application of this framework. So what's a well linked set? So suppose you have a graph G and a subset X of special vertices in this graph. I'll say that the set X of vertices in the graph is well linked if they satisfy the following property. If you wanted to separate some K vertices in this set X from the remaining vertices in X, then you must delete at least K edges. So in other words, with respect to set X, the graph looks like an expander, okay? Just with respect to the subset X, okay? The whole graph is not an expander but it satisfies this expander like condition for this set X, okay? So once I know what's a well linked set, I can now define what's a well linked instance of EDP. So first, what's an instance of EDP once again? It consists of a graph G along with a collection of sourcing pairs. And from here on, I'm going to refer to the sourcing vertices as terminals, okay? I will refer to them as terminals and I'll denote them by the set X. Whenever I use the set X, it refers to these terminals, okay? And I can assume without loss of generality that all SATIs are distinct, okay? There's a simple trick which can allow you to do that. So if a vertex was occurring multiple times, you can just replicate it, okay, in a suitable way. So in this view, an instance of EDP is actually the following. You're given a graph G. You're given a set X of terminals and the instance gives you a matching M on the terminals and tells you route that matching, okay? It just pairs up these terminals in some fashion and says, give me a routing of them, okay? What's a well-linked instance of EDP? Well, it's just an instance of EDP with the property that the set of terminals is well-linked. So here is a useful result for our purposes. Given any instance of EDP, you can convert it into a collection of well-linked instances with only a polylog factor loss in the solution value. So you start with some multi-instance with some multi-commonity slow solution value. Let's say this value was opt. You will be able to convert this instance into collection of well-linked instances such that in the remaining, the well-linked instances, the flow value is at least opt over polylog, okay? Once you have that, we'll see how this could be very useful for solving the problem. So now the second word phrase that I was talking about these crossbar structures. So let me just briefly define what's a crossbar. If you give me a graph page, I'll say that it is crossbar. It serves as a crossbar with respect to some special subset of vertices i that I'll call the interface of this crossbar. If you have the following property, give me any matching on this interface i. I can route it on edge-to-joint paths using inside this crossbar graph, integrally, okay? So here is an example of a crossbar, a complete graph. It's a crossbar. You give me any matching and I just have a one-hop path. It's simple, trivial integral, right? But complete graphs are not, they're not very interesting and they are not the only crossbar structures. It is a slightly more interesting crossbar structure, a grid graph. A grid is a crossbar with respect to the first row here. Why?  And you ask me to route them. So S1 wants to go to T1, S2 to T2 is some arbitrary collection. I could do this routing. S1 will move up to the second row. Just use the second row to go all the way up to T1 and then come straight down. S2 would use the next row and so on. It's a crossbar. I did this routing and it was easy, right? This already gives us one new result as the direct application of the framework, which is a result on how well EDP can be solved in planar undirected graphs. There is an old result of Robertson, Seymour and Thomas, which says that if you gave me a planar graph G, which has K well-linked terminals, then with congestion two, you can embed in that graph essentially a K by K grid. Combined with the well-linked decomposition framework, you now can show that EDP in planar graph is approximable to be in an order log n factor with congestion two. So this already was a strong improvement over what we knew before because at that point, even for planar graphs, only a polynomial factor approximation was known with constant congestion and you get it very quickly from this framework. So here is how the picture looks. You have your terminals. You have this crossbar structure sitting somewhere in the graph. You will route these terminals to the first row, the interface of the crossbar, and then pair them up at the crossbar. What about general graphs? That's our agenda for today, EDP in general graphs. So here's a natural conjecture which emerges from this framework and from this approach which I'll just refer to as a crossbar conjecture and says the following. Suppose you give me a well-linked instance of EDP. You give me a graph G with a set X of terminals which are well-linked. Then the conjecture says then give me any matching M on this set of terminals. I can integrally route one over poly log fraction of the pairs with only constant congestion. Okay? Not only the specific pairing you were interested in to begin with initially at time zero when the game began. You give me a well-linked instance, give me any matching. It is possible to route. And in a way what this is saying is that the whole graph G, if you have a well-linked instance, the whole graph G serves as a crossbar whose interface are the terminal. So if the crossbar conjecture is true, it's clear that the integrity gap of the flow relaxation is only poly log N with constant congestion. That direction is easy. The converse is also true. If the integrity gap of flow relaxation is poly log N with constant congestion, then the crossbar conjecture holds. And why is that? For any well-linked instance given any matching M on the terminals, there is a fraction flow of value at least cardinality of X by log N. Why? Because these terminals, they satisfy the cut condition for routing any matching. And there is a flow cut gap is log N. So you would be able to route at least this much flow. But she told me that the integrity gap is only poly log N with constant congestion. So then I will be able to integrally route one over poly log N fraction of pairs in M. So this means this integrity gap question, what is the integrity gap of the flow relaxation with constant congestion? It's equivalent to understanding or settling the crossbar conjecture. It's not just one approach, okay? It's essentially, so here is the plan for the rest of the talk, okay? So here is the plan for the rest of this talk. So we're going to try to prove this crossbar conjecture. And the specific way we're going to try to prove it is as follows. We're going to try to show that given any well-linked instance on K terminals, we can embed with constant congestion a low degree expander of size K over poly log N, okay? Once we have this embedding, we are in good shape, okay? I won't go over this again, but I won't go over this right now. But it's just a well-known fact that routing on expanders on edge congestion paths is an easy thing to do. In fact, a greedy routing scheme works, okay? And intuitively, the reason is this, pairs can be connected by short paths. Each time you route a pair of sati, the damage you're going to cause is roughly the length of this path, even if you were not very clever in choosing your path. If paths are of length only order log N, the damage you cause each time is only order log N, okay? In fact, if the expander is low degree, you can even go ahead and do vertex disjoint routing, and the same would be true. And this is a fact which is useful to Julia's result, okay? Okay, so now we move to part two, which is we want to embed an expander. How could we possibly try to do that? And this is where the cut matching game of Kandekar Ravan Vazirani comes into play. So in this game, you start with a graph, empty graph. And let's say you start with an empty graph on N vertices. You want to build an expander on these vertices. There are two players who are going to play this game. There is a cut player who wants to build an expander as quickly as possible. And there is a matching player whose goal is to delay the construction of this expander, and the game goes as follows. At step one, the cut player is going to give an equal size partition of the vertices of the graph to the matching player. Matching player's job is to return some perfect matching between these two sets, A1 and B1. And he's going to figure out the worst possible matching he could give to you to delay the construction of the expander. You take those edges, you put them on your vertices in the, initially the graph was empty, now you put these set of edges. At this point, the cut player will look at what it has got and will identify another set A2B2, and you will repeat this process. And the beautiful result is that after order log square and iteration of this game, you do get an expander. So no matter how these edges were given, you would get an expander after log square and iteration. We could use this to solve the ADP problem now, as follows. To prove the crossbar conjecture, we have our graph G, and we are going to build an expander on the terminals in this graph G. This is a well linked instance. When you compute a partition of the terminals A1B1, and you want a perfect matching between them, all I will do is ask the graph for you to give me a flow, a unit flow on terminals from A1 to B1. And that is possible, why? Because the instance is well linked. So the edges of the matching now correspond to path, flow path in the graph. And this is integral flow, okay? You get this flow path routing, and here is the expander being built on the left side. Second round, some other partition comes. You will once again use the well linked property to find me a matching, which is actually finding me flow path, which connect the terminals on the two sides of the partition. You continue this game, after log square k iterations, you're going to get an expander on the terminals embedded in your graph, okay? So that's the good news, right? What's the bad news? These paths will intersect each other, so yes, and so what is the bad news? Just that, yeah, the congestion, because at each step, I am using these edges afresh, okay? I have no way of separating them, right? So problem is it gives you log square k congestion, okay? But the plan is clear at this point, okay? So this is where Rob and you came and they made a really clever observation. They showed that if the minimum cut in your graph was large, and how large? Not too large, it's just something like log cube n. Then you can embed an expander with congestion one by playing this exact game, and how do they do that? Here is a very quick summary of their approach. They're going to take the graph G, and they're going to randomly partition this graph into log square k, edge disjoints graph. So for every edge in the graph, you assign it a number at random between one and log square k. And edges with number i go to the copy g i of the graph. The fact that you started with a graph which had a large min cut to begin with, they're able to use this fact to show that even after this random partition, each g i is well linked with respect to the terminals, okay? And now you play each round of the cut matching game in the private copy g i, okay? That's it, okay? There is work in step two, okay? Which is, you start with the large min cut condition, and then you turn that into showing that each g i is still well linked. But it's technically involved, but it's not too difficult, okay? To do this. So after this result, there was a lot of excitement and it really seemed to suggest that people should try to get the polylog approximation result for EDP with constant congestion. This condition seems not too daunting, log cube n, right? That's not a very high cut requirement. Right, but that just means, since you have some congestion at play, maybe with constant congestion you could turn your graph to satisfy a condition like this, and indeed that's what was tried next, okay? So I'll just briefly say a few words about another very exciting result which came last year, and which was the final, which was the final word on this problem until Julia's result. That's a result due to Matthew Andrews, which took this framework of raw and shoe and you can get around the min cut condition. And here is the high level plan which was used by Matthew Andrews. You're given a graph J which doesn't satisfy the min cut condition. You contract regions in this graph which are violators of this min cut condition. And in this contracted graph, these regions are collapsed down to a single note. And you boost the connectivity of this graph, okay? After you do these contractions. You boost it to satisfy the log cube and min cut condition. And at this point, you invoke the raw and shoe framework. But there is a problem. You contracted regions of graph into nodes, paths which are just going through these nodes. When you uncontract, they have to actually go through the complicated graph contained inside. And what Matthew was able to show is that with polylog log n congestion, he can manage the routing inside these contracted regions, okay? And intuitively, the amount of flow the contracted regions are dealing with is roughly polylog n, okay? And if the congestion you create inside is log of the amount of flow they are dealing with, okay? But that's a very simplified, okay? This is quite non-trivial to make it all work. Okay, so where does finally to Julia shows us the approach. How does she take care of this problem by using only constant congestion? So she, at a high level, she's just going to sidestep from the plan of boosting the min cut of the graph, okay? So this approach of completely relying on the raw shoe approach and only focus on turning your initial graph into a high min cut graph. She's going to move away from that. What she does is, she's able to identify in the graph log square k vertex disjoint subsets of vertices. These are vertex disjoint subsets such that each one of these subsets SJ is well connected to the terminals. And I'll make precise what this well connectivity means. But for now, just imagine that all the terminals could reach without causing congestion to each one of these sets SJ. Each SJ is well linked inside with respect to its boundary. So if you view its boundary as terminal vertices, each SJ is a well linked instance with respect to its boundary. Boundary is just the edges crossing SJ to the rest of the graph, okay? I'll make it all of this more precise in just a minute. And then the idea now is, when you want to implement the jth round of this cut matching game, you will bring your terminals to SJ. SJ is well linked inside.  That's the idea. Julia calls this a good family of sets. I would have called it really good family of sets. So this is a very powerful construct, okay? And the hard part of our work is really showing that such sets exist and you can find them, okay? So let's look at this in bit more detail. So these good sets are sitting up there, S1, S2, SR. And the way you should view this picture is as follows. Look at S1 and look at the edges which are just leaving the boundary of S1. The number of edges which are leaving the boundary of S1 is exactly equal to the number of terminals you have. So if you have k terminals, there will be exactly k edges leaving the boundary of S1. Every single terminal will have a private edge assigned to it on this boundary, okay? So the set S1 has a representative for every terminal. It's private and unique, same for S2, same for SR. And now if I look at a terminal, so let's look at the blue terminal. It has this additional property that it can connect to all its representatives in these R sets by a spanning tree, okay? So there is a spanning tree which allows it to reach all of them, okay? And not in an edge-to-short fashion, it's just a tree, okay? But it's able to connect. It is connected to all its representative, that's all. So, STs are well-linked with respect to their boundaries. Terminals are well-linked to the boundaries. That is, each terminal can reach one represented in boundary of each one of these SRs, that is the structure. And now once you have this, you can play the game of embedding an expander as follows. So those are my terminals, and I want to build an expander. I play the first round of the cut matching game, and that gives me this partition of the terminals, and it says match them. I go to my set S1. This partition has an image in the set S1 because terminals have a representation in each set. And the set S1 is well-linked, and I will now say, play the game in there, find me a matching, okay? I get those edges here, I go to the next round. This time, I go to the set S2, play the game. I continue, in log square k iterations, we will obtain an expander embedded in G, okay? Just as before. So here is the picture, okay? So this embedding is more complicated than the embeddings of the expander we looked at earlier. Why, before each vertex of the expander corresponded to a single terminal in the graph, this time, each vertex, for each terminal, the vertex I have in the graph is not a single vertex. It is actually a connected component. What is a connected component? It's the tree which was spanning that terminal. What's an edge in the expander? Well, an edge connecting T i and T j now corresponds to a path connecting a vertex in the component of T i to a vertex in component of T j. So like this. So if you look at an edge on the right-hand side which connects those two terminals, that really just corresponds to some path connecting some vertex in the tree of T i. To some vertex in the tree of T j. But routing on vertex which we show in paths on x is still a good thing for us. In that it will give us a low congestion routing in G. Let's look at a path from S to T on which you wanted to route in the expander. Let's see how it looks in the embedding. The expander edges appears here as paths between some pairs of vertices in their corresponding component. But each one of these blocks is a connected component by itself is a tree. I can now use the tree to hook up to the right points and go through all these intermediate vertices to reach all the way at T. And I'm going to use vertex ratio and routings. So these components, once I've used them, once I throw them and that's it. As I said, the hard part is in finding these sets and just a high level one sentence intuition as to why such structures should exist. If you start with an instance which has K well linked terminals. So that means, well linked means there is a lot of connectivity among these K guys. You scale down your goal of building an expander sufficiently down. You don't want to build an expander on K terminals. You would be happy to build it on K over poly log K terminals. So since you have this huge connectivity and capacity in the graph, if you scale down your goal by a large poly log K factor, in principle, you could identify dedicated regions which are well connected, well linked and are of size only K over poly log K. The difficulty is in showing that not only you have these nice dedicated regions, but they satisfy all these additional constraints, which is the terminals can reach them and you have this nice property of well-linkedness in each one of these regions which terminals can arrive at. Okay, that's all I'm going to say about this result. And I conclude with a couple of open questions which still remain. I mean, I think this result is really like it cleans up lots of things. But there is still stuff to be done on understanding EDP of undirected graphs. So I think there are only two questions which I would like to highlight. So the first question is, we started with EDP defined in a very strict manner that the routing had to be on an H-dashwine path. And then we relaxed it to EDP with congestion and we get these nice results. But let's now return, now that we understand the power of congestion. Let's return to the basic question. What happens to EDP with no congestion? Here is the state of affairs. The best-known approximation algorithm is a square root n approximation. The best-known hardness is square root log n. Pretty much the state of affairs we had for EDP with congestion up until Julia's result, right? Except in this case, the upper bound of square root n matches the integrality gap result. So you couldn't start with the, or you couldn't entirely rely on the multi-commandative flow relaxation at your benchmark. You would not get past the root n barrier, okay? The second problem is something I didn't talk about directly much is, but it's just really the natural analog of the EDP question. It's the congestion minimization problem. Same input as in EDP, but this time I tell you, you must route all SITI pairs, everything has to be routed. Your goal is to minimize the maximum congestion you will cause at any edge. So I pointed out a result of Raghavan and Thompson from 1987 already tells you how to do this with log n over log log n congestion. For directed graphs, that's the best possible. But for undirected graphs, the hardness is really a level below. It sits at around log log n, okay? So it's a very interesting question. If it turns out, even for congestion minimization, the right answer turns out to be in the log log n regime. That's all I wanted to say, thank you.


Please be seated. It is my distinct honor as president of Gustavus Adolphus College to welcome you to this, the 49th Nobel Conference at Gustavus. As we officially open the conference, I would like to introduce one of the college's chaplains, Reverend Ciri Erickson, for the invocation. But before I do so, I would like Chaplain Ciri to stand along with Chaplain Brian Conkel. We have two new chaplains. This is quite a tradition at the Nobel Conference. In fact, the first director of the Nobel Conference was Chaplain Elvie. And what a pleasure it is to welcome these two new chaplains to this great institution. Chaplain Ciri is a graduate of Carlton College, where she was Phi Beta Kappa and majored in chemistry. She received her master of Divinity degree from the Claremont School of Theology. And before coming to Gustavus, Reverend Erickson served as pastor for lifelong learning at Trinity Lutheran Church in Stillwater. Chaplain Brian is a graduate of Viterbo University in La Crosse, Wisconsin. And he graduated from Luther Seminary and has served on two different occasions as a missionary, first in South America and then for seven years in South Africa. Most recently, he served as a parish pastor in Madison, Wisconsin. We welcome both of you. Chaplain Ciri, would you please join me at the podium as we welcome you? Let us join our hearts and our minds together in a moment of gratitude. Compassionate and creative God, we give thanks for the beauty and magnificence of this universe and for our human capacity to explore its deepest mysteries. As we journey together in an epic adventure of truth seeking, may we be challenged to expand our vision of the world. May we be dazzled by the wonders of scientific knowledge and may we remain curious and open to a future of continued discovery. With gratitude for the scientists who are presenting at this conference, for their passionate pursuit of knowledge about the universe and for their dedication to teaching and learning, we pray today with full hearts. Amen. Thank you, Chaplain Ciri. This year's Nobel conference theme, the universe at its limits is, I believe, especially illustrative of the college's commitment and the commitment of our faculty to tackle cutting-edge topics from an interdisciplinary perspective and explore their philosophical and their theological implications. This year's theme and focus has generated tremendous excitement in an unusually high demand for tickets, as well as a significant interest on the web streaming of the conference. On Sunday evening, we had the largest attendance ever for the preview dinner and lecture done by Dr. James Gates, held at the Science Museum of Minnesota to introduce the conference to the business leaders, the non-profit executives, educational leaders, and media representatives, and our alumni and friends in Minneapolis and in St. Paul. Gustavus' annual national Nobel conference was the first educational conference of its kind in the United States and continues to be the only such conference of its magnitude at an undergraduate liberal arts college today. This year's conference marks the fourth year of a very special year-long outreach program for high school students and teachers throughout the state of Minnesota. The program was first funded through a grant from the Howard Hughes Medical Institute and this year it is funded by the Catherine B. Anderson Fund of the St. Paul Foundation. We are taking advantage of this year's conference topic to enhance high school senior curriculum in the state and to better prepare participating teachers and their students for the conference. Engaging high school students and teachers has long been a hallmark of the conference. Of the over 5,000 individuals who will attend the two-day conference here in St. Peter, approximately 1,700 will be here from high schools all over the region, Minnesota and contiguous states. This year we have eight teachers from eight different high schools in this program in the Minnesota program that we have and many of those students are attending the Nobel conference today and others are joining us tomorrow as well as many other students from all over the state. I want to direct your attention to the students here. I believe they're seated in the balcony area and I'd like to add them stand so that we can welcome them to this their first Nobel conference. Would you please stand? As we approach the 50th Nobel conference at Gustavus, I think it is important to remind ourselves of how the conference began. The college was planning to build a new science building during its Centennial year. For some of you alums, you will remember that. It was in 1962. Then President Edgar Carlson traveled to Sweden to ask the Nobel Foundation if when a new science building is completed whether we could name the building the Alfred Nobel Hall of Science and they agreed we have the Nobel Hall of Science. He was bold enough to ask the foundation then that when the building would be completed in 1964 if we could possibly invite all of the living Nobel laureates to St. Peter here on a hill in a small town in Minnesota looking over the river valley. That was pretty visionary wasn't it? 26 Nobel laureates came to St. Peter for what was the first such gathering of science scholars and is now the Nobel conference at Gustavus. Today we are celebrating the fact that we have now had a total of 100 Nobel laureates visit our campus since that first conference. After conferring the honorary degrees here in a short while over 100 laureates will have received an honorary degree from the Gustavus. I think that's pretty special. You might look at the banners along the wall that are from the earlier conferences so when you have time between the lectures you might want to walk around and remind yourself of those. I'm always amazed of how many people attend year in and year out and how many new ones we have coming. So a simple test here let's just raise our hands if this is our first Nobel conference. That's great. Wow you're in for a great experience and please come back. For those who have been here for more years than one please raise your hand. That's really great and now the real test and I know there are a few here of those seated how many have been to every Nobel conference please stand so we can recognize you. They're right over here right over here. Isn't that great thank you. I also think it is important to point out that the Nobel conference at Gustavus has been made possible over the years through very significant and generous support. I call your attention to the descriptive materials in the program that outline the fact that the Nobel conference endowment fund was originally created in July of 1978 and has been permanently secured now as a result of the generous support of the Reverend Drell and Adline Bernardsen. Other gifts to the endowment fund are listed in the program and I hope you'll look through that. We also want to acknowledge the 2013 sponsors of the Nobel conference and they are listed in the program. One of our sponsors is Heroic Productions owned by Gustavus Alums John and Anita Young. Heroic Productions is truly heroic. They provide the extraordinary media production you are enjoying in this arena today and thousands more will be able to view the conference remotely and because of their tremendous work we thank you John and Anita for all that you do for the college. At Gustavus we believe the Nobel conference represents all that is good about a liberal arts education in an undergraduate residential college environment. Today more than ever before questions are being asked about the value of a liberal arts education. Many are wanting to quantify education by comparing the value of education at one institution versus another by looking solely at what many call the return on investment ROI. You've read it in the news print. You've seen it on television. Education cannot be quantified by simply looking at the jobs graduates receive or the salaries they are paid. We believe Gustavus is a place where there's return on investment but we need to look at much more than the simple economics being discussed around the country. We believe we need to be talking about ROI but also ROE the return on a Gustavus education for a lifetime. The Nobel conference and other opportunities for our students provide them with a deeper understanding of their place in the world and how they can make a difference. The learning outcomes of liberal arts education demonstrates how that education will be lived out over a lifetime by our students. Our alumni are the living proof of the real return on investment the return on a Gustavus education. Thank you for being here to take part in this significant learning opportunity for all of us that will help enrich our lives as we expand upon our education and live out our lives meaningfully in an ever-changing world. I would hope that all of us as we learn about the universe at its limits would be mindful of the opportunities we have had as individuals and we have had collectively to stretch to stretch beyond our limits because of the education we have received. Now it is my pleasure to introduce three outstanding Gustavus faculty who help students stretch beyond the limits. First I want to introduce Dr. Steve Melema, professor of physics. Steve would you please stand. Steve is the chair of this year's conference and you will meet him later. He will be moderating some of the discussion. He and his colleagues have worked tirelessly for more than a year now to organize this year's conference. Thank you Steve for all that you and your colleagues have done. Secondly I would like to introduce and have Dr. Chuck Niederiter stand. Chuck is a professor of physics. He has served for the last five years as director of the Nobel conference and is stepping down this year from the director's position a role that he has served admirably and brought significant strength to this program and to this college. In the conference's 49th year we have had only three Nobel conference directors. Chuck on behalf of all of us at Gustavus including the board of trustees the faculty staff and students and I might add the thousands that have attended the Nobel conferences over the past five years we say thank you. Finally I would like to ask Dr. Scott Burdistan. Scott is the associate professor of chemistry and he will serve as the next director. Pretty big shoes to fill Scott. He will serve as the director this next year. He has been working with Chuck and with Steve and all of their faculty colleagues over the last year to think about ways we can continue to build upon the strong traditions of the past 49 years. Next year as I mentioned will be the 50th year for the Nobel conference. You will be receiving information and I think there's actually some flyers in the back about the 50th Nobel. We will be looking retrospectively over the last 49 years as we begin to look at the next 50 years of the Nobel conference and the tradition that we have. We will be you will be delighted when you hear more about the programs from Scott and his colleagues. Scott, thank you for accepting this responsibility. I now ask before we recognize three distinguished Nobel laureates with honorary degrees to have Provost Mark Braun come to the podium. Provost Braun is in his third year now at Gustavus's provost and he is leading a tremendous faculty. He is an individual that served on this faculty for 17 years before he left here for a little time away as the chief academic officer at Augustana College in Sioux Falls. We are so pleased to have him here and he will be making his remarks and introducing Dr. Niederreiter for his conference overview. Mark, thank you President Oly. Could I ask the faculty to please rise? On behalf of the faculty of Gustavus Adolphus College, we welcome all of you to this 49th Nobel conference. Thank you faculty. It is consistent with our mission as a liberal arts college that we annually invite to the conference speakers and panelists who approach the subject from many perspectives. The process begins with conversations on campus designed to identify and refine a topic and assemble a Gustavus faculty committee to explore the best scholars in the world to address that topic. The conversation then expands to include our invited speakers who present their unique perspectives as the talks are designed and coordinated. And now that we are all assembled here, the conversation really takes wing. We will come to a deeper appreciation of the topic through the presentations, through the dialogue among the panelists following each lecture, and through the questions from our audience. I invite all of you, the on-campus audience and the online viewers worldwide to actively join in the conversation on the universe at its limits. Now it's my pleasure to invite to the podium to launch our conversation, the director of the Nobel conference, Gustavus physics professor Dr. Charles Niederreiter. It is my pleasure to welcome everyone to this, the 39th 49th installment of the Nobel conference, the universe at its limits. For those of you who are with us for the first time a special welcome, for nearly 50 years the Nobel conference has specialized in important scientific issues and their relevance to contemporary society. For myself and my colleagues in physics, this is our dream conference. What could be more noble than attacking the questions of the origins, constituents, and evolution of our universe? Or what could be more challenging? Leave it to the physicists. Those of us who made it to the end of an introductory astronomy course realized that the seemingly opposite lines of inquiry that began in ancient Greece over 2,000 years ago, astronomy and the study of what is inside manner, both provide answers to the questions of the origin, constituents, and evolution of the universe. Indeed, we need both astronomy, the study of what is outside beyond the boundaries of earth, and the study of the realm of subatomic particles and the fundamental forces in nature in order to put together a coherent picture of our universe and how it got this way. The Nobel conference 49 committee has put together a panel of experts in both areas to help us answer questions about dark energy and the acceleration of the universe to candidates for dark matter and its role in holding the whole thing together. Embedded in all of this are questions about how it all got started that initiate a discussion of the relationships between science and faith. At this time, let's meet our speakers. Dr. Frank Wilczek, Hermann Feschbeck Professor of Physics at Massachusetts Institute of Technology and a 2004 Nobel Laureate in Physics, will get us started thinking about the connections between the very large and very small and the basic rules of our universe. Dr. Tarrish Shears, Professor of Physics at the University of Liverpool and Royal Society University Research Fellow at CERN, will tell us about research at the Large Hadron Collider and perhaps about the discovery of the Higgs boson. All right, we have a little problem with order here. Okay, I think I figured it out. Alex Filipinko is the Richard and Rhoda Goldman Distinguished Professor in the Physical Sciences in the Department of Astronomy at the University of California Berkeley. And Dr. Alex Filipinko will talk to us about his research in the accelerating expansion of the universe. We'll hear about the quest to identify dark matter from Dr. Samuel Ting, Thomas Dudley Cabot Institute Professor of Physics at MIT and a 1976 Nobel Laureate in Physics. Dr. George Smoot is Professor of Physics at the University of California Berkeley, Senior Scientist at Lawrence Berkeley National Laboratory and Professor of Physics at Paris Diderot University and he won the Nobel Prize in Physics in 2006. Professor Smoot will help us understand what we can learn about the early universe from leftover radiation from the Big Bang. Dr. Lawrence Krause, Foundation Professor of the School of Earth and Space Exploration and Director of the Origins Project at Arizona State University, will give us an idea what science can tell us about the origin of the universe. The Emeritus Director of the Vatican Observatory, Father George Coyne, who is currently McDivitt Chair of Religious Philosophy at Lemoine College, will help us explore the relationships between the religious view of the origin of the universe and that of science. Dr. Sylvester James Gates Jr is the Regents Professor, John S. Toll Professor of Physics and Director of the Center for String and Particle Theory at the University of Maryland. As this year's Rydell Professor, Ika Stavis, he has already started getting us to think about the underlying symmetry of the universe and I hope that he will continue with his lecture at our banquet tomorrow evening. I also would like to acknowledge one of the leaders in exploration of the universe, Dr. Vera Rubin. Dr. Rubin was the first to recognize the existence of dark matter in her studies of rotational velocities of stars and galaxies. We invited her to be with us and after initially accepting, she later informed us that her health wasn't good enough for her to travel to St. Peter. We wish her well and hope that she enjoys watching the conference on her computer. Our panel of speakers was put together by a committee chaired by my colleagues, Steve Mila, as President Oli said. Steve had help from our, had help from our colleagues in physics, Tom Huber and Jesse Patrika, as well as colleagues in math and computer science, Tom LaFarro and Mike Vidsden, and from chemistry, Steve Mila and Larry Potts. You will meet them and other faculty hosts over the next, over the course of the next two days. I need to also acknowledge the assistance of a myriad of students who have helped or are helping in various ways. At this time I'd also like to call your attention to other events taking place on campus with the Nobel conference. At 6 p.m. tonight our art at the Nobel conference reception at the Hillstrom Museum of Art featuring string theory and the superconducting super collider series, paintings by Lucinda Mason, just to name a few. And at 8 p.m. this evening the Nobel conference concert, Dark Energy, in Christchapel. Professor Yumiko Oshima Ryan has put together a real treat for us. As we continue to evaluate the Nobel conference at Gustavus we ask you to take a little time to fill out a survey to help us in this endeavor. A link to this survey will appear on the Nobel conference website on Thursday and will be emailed out to those for whom we have email addresses. So once again welcome to all of you. We're looking forward to an exciting two days. If you've been with us before you probably know of the Gustavus tradition of bestowing honorary degrees on Nobel laureates who visit campus. So at this time I'd like to call to the platform Professor Samuel Ting and citator Professor Huber for the conferral of the first honorary degree. President Oli, Provost Braun, Deans Goodin O'Loughlin, distinguished panelists, faculty, and Nobel conference guests. Today Gustavus Adolphus College honors Nobel laureate Samuel Ting, the Thomas D. Cabot Professor of Physics at MIT. Dr. Ting has dedicated his career to experiments exploring the fundamental constituents of the universe. His ability to identify challenging areas for research and then assemble a large international collaboration to achieve difficult physical physics goals is remarkable. His experiments have been critical in the development of the standard model and exploring physics beyond the standard model. In the early 1970s Dr. Ting assembled a collaboration with a nearly unprecedented goal to build a high-resolution electron-positron spectrometer that could operate with the intense proton beam at Brookhaven National Lab. As with all of his subsequent experiments construction of this detector took tremendous creativity and attention to details. In 1974 this persistence was rewarded with their discovery of the J particle which provided direct experimental evidence for the existence of the Charm Quark. Dr. Ting shared the Nobel Prize in 1976 for this discovery. Dr. Ting was the leader of the L3 collaboration at the LEP accelerator at CERN. From 1989 until LEP shut down in 2000 to make room for the LHC the L3 collaboration involved hundreds of scientists from 50 institutions worldwide. Under Dr. Ting's leadership the L3 collaboration performed high resolution studies of the standard model predictions and performed searches for physics beyond the standard model. Dr. Ting's most recent and possibly most ambitious project was the construction, launch, and operation of the alpha magnetic spectrometer on the International Space Station. Only a physicist with Dr. Ting's stature and tenacity could have navigated the complicated technical and political challenge of this project. Design and construction of the one and a half billion dollar detector involved 500 scientists from 16 countries. Even after it was fully constructed it took an intensive lobbying effort by Dr. Ting to convince NASA, the president, and Congress to add one final space shuttle flight of of the of endeavor to transport the detector to the space station. Although it has been in operation for only two years this detector has provided tantalizing hints about the nature of dark matter in the universe. President Oli, for his contributions in experimental particle physics the faculty of Gustavus Dolphus College recommends that Samuel Ting be awarded the honorary degree Doctor of Science. Now by the virtue of the authority vested in me by the Board of Trustees of Gustavus Dolphus College and upon the recommendation of the faculty and approval of the Board of Trustees I hereby confer upon you Dr. Samuel Ting the degree of Doctor of Science, honoris causa, with all the rights privileges and honors pertaining thereto. Now I'd like to call to the platform Professor Frank Wilczek and citator Professor Vison for the conferral of the second honorary degree. President Oli, Provost Brown, Dean's Good and Elafin, distinguished panelists, faculty and Nobel guests. Today Gustavus Dolphus College honors Nobel Laureate Frank Wilczek, the Hermann Feshbach Professor of Physics at MIT. Frank Wilczek received the Nobel Prize in 2004 for work he did as a graduate student at Princeton University when he was only 21 years old. He along with his advisor David Gross developed the theory of quantum chromodynamics also known as QCD. Their theory independently developed by David Politzer who also shared the prize in 2004 describes the strong interactions which govern the behavior of quarks ever so tiny particles that combine to make protons and neutrons the basis for all of the matter that we see around us. The Nobel Foundation in presenting this award stated the discovery which is awarded this year's Nobel Prize is of decisive importance for our understanding of how the theory of one of nature's fundamental forces works. The force that ties together the smallest pieces of matter the quarks. David Gross, David Politzer and Frank Wilczek have through their theoretical contributions made it possible to complete the standard model of particle physics the model that describes the smallest objects in nature and how they interact. At the same time it constitutes an important step in the endeavor to provide a unified description of all the forces of nature regardless of the spatial scale from the tiniest distances within the atomic nucleus to the vast distances of the universe. Dr. Wilczek has received many awards and honors for outstanding work in theoretical physics. He was named a MacArthur Foundation Fellow in 1982. He was elected to the National Academy of Sciences in 1990 and is awarded the Lorentz Medal by the Royal Netherlands Academy of Arts and Science in 2002. He holds honorary degrees from the Ohio State University and the Maria Curie Sklodowska University among others. Frank Wilczek has worked on an unusually wide range of topics including condensed matter physics astrophysics and particle physics. He has helped to reveal and develop axions anions asymptotic freedom the color superconducting phases of cork matter and other aspects of quantum field theory. He is an active writer not only of scholarly papers in theoretical physics but also of works aimed at translating this sometimes overly dense language of mathematics and physics into stories and adventures to which we can all relate. He has published three popular books Longing for the Harmonies written with his wife Betsy Fantastic Realities and the Lightness of Being. President Oli for his contributions to developing the theory of quantum chromodynamics the faculty of Gustavus Adolphus College recommends that Frank Wilczek be awarded the honorary degree Doctor of Science. Now by the virtue of the authority vested in me by the Board of Trustees of Gustavus Adolphus College and upon the recommendation of the faculty and the approval of the Board of Trustees I hereby confer upon you Dr. Frank Wilczek the degree of Doctor of Science Honoris Causa with all the rights privileges and honors pertaining thereto. Finally I'd like to call to the platform Professor George Smoot and Citator Professor Patrika for the conferral of our last honorary degree. President Oli, Provost Braun, Dean's Good and Olafin distinguished panelists faculty and Nobel conference guests. Today Gustavus Adolphus College honors Nobel laureate George F. Smoot III Professor of Physics at the University of California Berkeley and Paris Diderot University. Professor Smoot shared the 2006 Nobel Prize in physics with John Mather for quote their discovery of the black body form and anisotropy of the cosmic microwave background radiation end quote. In the mid 1970s Professor Smoot and his collaborators developed a proposal for a satellite to study the cosmic microwave background the radiation left over from the Big Bang. This mission known as the Cosmic Background Explorer or COBIE was launched into orbit on November 18th 1989 and contained three instruments. One was an instrument to measure the spatial variations or anisotropies of the microwave background. A second instrument was to measure precisely the spectrum of this background and a third instrument was to measure the infrared background. Professor Smoot was the principal investigator of the instrument used to search for anisotropies. This instrument spent a number of years mapping the temperature across the sky a task made more difficult by the need to remove nearby galactic sources and the Doppler effect produced by the motion of the earth. This was done to a resolution of better than 50 micro kelvin in temperature and 10 degrees spatially in the sky. In April 1992 the COBIE team announced that their map had for the first time seen density variations that could serve as seeds for galaxies and galactic clusters to the then evolving universe as temperature variation seen now directly correlates with the density variation of the early cosmos. Professor Smoot continues his research in cosmology and is involved in the Planck mission a third generation experiment to map the cosmic background. In addition he's the author of more than 200 scientific articles and co-authored the book Wrinkles in Time which detailed his efforts. His other honors include the 1991 NASA Medal for Exceptional Scientific Achievement, the 1995 Lawrence Award, the 2003 Einstein Medal, and the 2009 Orsted Medal. President Oley for his contributions to observational astrophysics and cosmology the faculty of Gustavus Dolphus College recommends that George Smoot be awarded the honorary degree Doctor of Science. Now by the virtue of the authority vested in me by the Board of Trustees of Gustavus Dolphus College and upon the recommendation of the faculty and approval of the Board of Trustees I hereby confer upon you Dr. George Smoot the degree of Doctor of Science honoris causa with all of the rights privileges and honors pertaining thereto. What a wonderful opportunity to recognize three outstanding scholars. Let's give all three a round of applause again. As we close this opening ceremony of this magnificent 49th Nobel Conference at Gustavus it is my pleasure to welcome to the podium Reverend Brian Conkel to close the ceremony with a blessing. Following his blessing we will leave the podium go down take a break get everything set up we're not going to leave the auditorium we're going to start right into the first presentation so you can stand and rest and relax and meet some of the folks that are next to you. This truly is a great day at Gustavus Dolphus College and it's a wonderful opportunity to invite and to have these individuals here at our institution for this great day. Dr. Chuck Chaplin Bryant received the blessing spirit of life subject of many possibilities object of many identities is the wheel of stars move above us the plates of the earth shift below us the web of neurons reposition within us we give thanks for those beautiful moments in time when cosmic possibilities become our experienced realities may we all be so blessed that we may honor this time together in the spirit of integrity and intrigue so that our collective gifts may be animated facilitated and agitated so we may remember who we are lift up what matters most and be set free to explore the many possibilities of life in its fullness so let it be so so let us be blessed