Yeah well good afternoon and I want to thank the museum for hosting our talk today. So Nick and I are here. Mack is running around somewhere I think he's in DC but we're all pretty available. When we started to conceive of this project three years ago we really started off with a simple question. How and why did the United States become a superpower? And it's a little awkward in 2015 to answer that question but I think is if you if you look at the debates about the role the US should play in the world I think the question is still relevant. And in particular if you have if you remember small children used to play with light bright that idea and so I really like the cover that we had very little influence on on what it came out but we like this idea at some point though after World War II the United States really switched on. It switched on as an international actor and we recognize that today in the US and there's various different explanations. You know first the United States it's a large country. We're the third largest country in the world. Second population so third largest population in the world behind China and India. Third plentiful natural resources. So you see all the good news about how we're becoming energy self-sufficient with all the new gas and and oil reserves discovered. So that also helps feed this idea how did the US become a superpower. Others historically will point to well the US was really the last country standing after World War II and then you throw on the rise of the Soviet Union and the US played in countering communist expansionism also helps explain why we became global. But what I think we argue is so if the US rise was inevitable because of size, population, historical chance of being left after World War II with a super strong economy and military we didn't have to be a liberal power. And by liberal power what we mean is the US promoted decolonization after World War II. So we didn't use US power to claim territories. So you often hear the US inherited the British order kind of because the British were able to be liberal at home where Britain's had liberal rights, free speech, press, assembly, voting, but the empire was not very liberal at all. And in fact after World War II the US promoted decolonization for UK, France and others to get rid of colonies and to promote national self-determination. And we think this is a really important point because it also breaks from the historical precedent of what great powers do. When you win a war you're supposed to get the spoils to the war. But the US doesn't do that. And so you can start going back from your World War II period with the Marshall Plan. We didn't act like the Soviets where they went into their part of occupied Germany and took home factories and equipment and people. Instead the US, we did have a generous visa program to bring German scientists to the US and among other things. But the US also spent billions of dollars of taxpayer money to rebuild Western Europe. We didn't attempt to kind of keep Germany down. We didn't attempt to kind of steal from their future by exacting war, retribution or anything. In fact we supported a independent and aided with the development and reconstitution of Europe. And that's very different from how past powers behaved. The US also has very limited territorial ambitions. And so you do know the United States it's a global power. And certainly being here at the Naval War College I think we appreciate how the Navy enables that power by being able to operate anywhere in the world. And to me being a superpower means that. Being able to deploy forces 8,000 miles away and sustain them indefinitely. And that's really what we've been doing in Afghanistan, you know, for example, in Iraq previously to that. And the idea that countries that are on the world they don't fear US power US ships. They often welcome them. And so you could look at Japan is probably the easiest example where Japan provides billions of dollars a year to host the US Navy and Marine Corps in Japan. That's again unprecedented. We don't force ourselves on other countries. We seek to to be able to treat other countries on an equal playing field with the idea by working together will make things better for everyone. Now to be sure the international system does speak with an American accent. So the international system is born in the USA. So the United Nations, for example, begins with the San Francisco California Treaty. Now Putin I saw in his recent speech at the UN General Assembly, he says it all began in Potsdam and therefore it speaks with a Russian accent. But I think that's a we don't even need to debate that point. It's a San Francisco Treaty. The UN is headquartered in New York City. It's not headquartered in Moscow, not London, not Paris, not Tokyo. And that gives us some distinct advantages. Likewise, the modern international economic system was born in New Hampshire at Bretton Woods, New Hampshire. And so as we start thinking about, you know, for example, the International Monetary Fund to help stabilize currency and enable currency flows, the idea of World Bank to promote infrastructure around the world. Though that's an American sort of at least conceived idea. And then what becomes the World Trade Organization as well conceived in the United States, of course, the importance of our allies. In a more mundane example, if we think about the Internet, for example. So we think of the Internet as essential today for social, commercial interaction born in the United States. And we get some special privileges of that. So the domain name system, for example, it still has been a subsidiary of the Department of Commerce. But a simple example is, so CNN, if you want to go to it, CNN.com, it's not CNN.co.us. But if you look at the BBC, for example, it's not BBC.com, because it's British, it's BBC.co.uk. So if anything, being an American, we get to save a few keystrokes by not having the type .co for country and then the name of our country. And that's one of the benefits we get. There's also more tangible benefits that we get. You know, first is we're a target for foreign direct investment, which means we garner more foreign investment than any other country, even China. We typically go back one and two. But when Toyota builds a factory in the United States, that's foreign direct investment. When Mercedes builds a factory, the Hyundai Sonata, you know, for example, is built at Montgomery Alabama. That's foreign direct investment. People in other countries, other governments, want to put their money inside the United States. And we benefit tremendously from that. The dollar is a global reserve currency. You know, dozens of countries peg their currency to the U.S. dollar, so there's more stakeholders in the dollar because of that. And many countries use the dollar as their own national currency. My favorite example is Ecuador, for example, which politically the relationship between the U.S. and Ecuador is not great. But yet the Ecuadorian government uses the U.S. dollar as its currency. So everything occurs in U.S. dollars. It's not even a it's very open. It's official. And I'm sure politically that hurts the Korea administration, but he understands that there's value in that we get value in that because we're able to borrow more freely. And we don't have to relive the debate about is debt good or bad, our deficits good or bad. I'll say at least our government has the ability to borrow against its future. Not every government does. Not every government has the ability of foreign countries and banks and individuals to put money and investment in the United States. And so we benefit from that. But we would say all of this didn't happen because there was a grand vision or a grand plan. We argue and that's why the we use the word incidental. This is again one of one of those inside publisher story where they kept arguing the editor kept arguing don't you guys mean accidental? And and we had this conversation over several months and we said no, no, no, we really mean incidentally. We didn't have to become a superpower. There was a series of small steps. And given our audience, the one I like, you know, on the military side is because our notion that we would fight wars abroad, we would reinforce Europe or would fight in Asia. We didn't build a territorial defense. We didn't build a military like that. We built a military that could deploy in a forward way and then sustain others. So then when the Cold War ends, all of a sudden now, the US government has this expeditionary capability where we could even conceive of the idea of putting 150,000 troops in Iraq. And we don't have to debate whether that was a good idea or not. But it is something that just kind of happened incidentally, because we thought that's how we would fight abroad. The other thing I just want to highlight before I turn it over to my colleague who's going to look at some continuities is you know, from a defense perspective. So the example I like is Churchill's war bunkers disappeared after World War Two. The Pentagon, which was built in a very hurried fashion didn't disappear. And in fact, the Pentagon becomes what we know of today as a permanent military establishment. And that's a break from US history. Because prior to this period, there was a boom and bust cycle with defense, that we had a very small standing military. And if you look back at the Constitution, you know, it says Congress shall, you know, provide and maintain a Navy and raise armies. So we should always have a permanent Navy armies should come and go. And we live that more way, you know, for about 150 years of our history, that started to change after World War Two. So the Pentagon didn't disappear like Churchill's war bunkers. And instead, we put in place a series of policies that gave us where we are today. So the all volunteer force, for example, which comes into effect in the 70s, and really probably doesn't mature until the 90s. And then I would say today, the equivalent is how we treat the reserves. So the military reserves today are an operational reserve. They're no longer that strategic reserve that you see today. You know, I know in the Navy community, so 70% of Navy intelligence deployed in Iraq and Afghanistan came from the reserves. And that's unheard of. And if you look on today, I think there's about 20,000 reserve and guard on active duty. And that's a huge change. And as we start to look at kind of declining budgets in DoD, the active component is going to continue to rely more on the reserves to augment any sort of capability downslide. And that again, I would add is, you know, becomes an incidental thing, how we transform the reserves from a strategic reserve to an operational reserve. But that's kind of the defense strategy sort of overview. But I wanted to invite my colleague up, Nick Vozda, to really talk about continuities in foreign policy. I wanted to go back to point that Derek raised about our fight with the publisher about accidental versus incidental, because I think as Derek noted, it was very clear that the United States was going to become a major power because of our geography, because of our economic and military potential. But the way we became a superpower was not foreordained. And it was a result of choices that we made after World War Two. If we had stuck to the Rooseveltian vision that he had envisioned in 1944 and 1945, the United States would have been the chairman of the Board of Great Powers. We would have been the predominant power in the Western Hemisphere, but much of the rest of the world would have been managed by the other great powers, China, Soviet Union, Britain, France, they were supposed to take that leading role. And we were just going to be the offshore balancer that would provide necessary capabilities to back them up in keeping order in the rest of the world. When that vision does not play out because Britain and France and China are not able to play those roles and the Soviet Union makes it clear it is not interested in partnership, it would prefer to move for domination in Europe and in Northern Asia, we have to adjust. So that's where the incidental nature begins to emerge. And that begins to develop a series of interests which then become continuities in how the US approaches the world. So in the late 40s, we begin to develop for the first time and against the advice of George Washington, entangling binding alliances with other countries, giving them security guarantees that if they are attacked, the United States will respond to their defense. Starting with NATO, we attempt to do it in other parts of the world with some lesser degrees of success. We do it with countries like Japan and South Korea. We move to this expeditionary approach. We don't just simply base our military at home. We develop the idea of combatant commands. So we retain some of our combatant command structure from World War II, and then eventually we expand it so that the entire globe, every square inch of the globe today is covered by a US combatant command. No other country does this. And then, of course, we develop the capabilities to project and sustain power around the world. And we make it clear that we identify our own domestic interests with the preservation of this global order. So we create international institutions. We say that free trade and keeping trade lines open is not just simply a benefit for the world, but it benefits the United States. And so this helps to develop a certain degree of continuity from the late 1940s to the present day. As administrations change, yes, administrations will change their priorities when presidents come in. They may have a different part of the world that they focus on. Some presidents prefer to emphasize the military dimension of power. Others may look at the diplomatic side or the economic side. But we've had this continuity of interest that says that the United States must remain globally engaged, not simply because it's good for the world and we're doing it out of the goodness of our hearts, but because this is what benefits American peace and prosperity. So that starting with things like the Marshall Plan in the late 1940s, we were not just simply giving money to the Europeans because we felt sorry for Europeans who were living in the ruins of World War II. This was directly benefiting American businesses, American companies, American farmers. We develop a whole network of providing food aid around the world. Again, not simply because we see starvation in other parts of the world and want to help, but it becomes a boon to our own agricultural industry. At various points, we were one of the few countries in the world that we didn't completely avoid the trap. We mitigated it, the guns versus butter trap, which the Soviet Union fell into, so that every ruble of Soviet defense spending was a ruble that was not spent on the domestic economy, was not spent on domestic production. Whereas in the United States, we have generally had a spillover that every dollar that we spend on defense spending generally returns 60 cents in economic growth back to the U.S. economy. That ranges everything from putting a base in a particular area of the country and having the spillover effect of small businesses around that base benefiting from having a serviceman. Of course, we all know the stories of issuing a serviceman with two-dollar bills so that local merchants would know precisely how much their benefit, they benefited from the presence of that military facility, but also our ability to allow for military technologies to be licensed for commercial use. The Soviet Union actually had more advances in computers and lasers at various points in its history. They never allowed that to spill over to the domestic economy. Whereas we look at defense spending and NASA spending in the 1960s and 70s, the allowing of that to spill over into the domestic economy, whether it's the internet, whether it's microprocessors, we're seeing it now that things we've developed to deal with say battlefield combat wounds, how can we bring that into the civilian health sector. Nanotechnology is a promising field, advances in cybernetics which started in the military sphere and now we're looking for civilian applications. So what happened is that over the last 60 years, the projection of this international, forward international position of the United States was something that the US political system would justify because we benefited from it. Our engagement in the world, we mitigated our isolationist tendencies over the last 60 years because more and more Americans said we drive concrete benefit from being involved in the world, whether it's because we're drawing on foreign sources of oil or trade or natural resources or things like that. Where we are today and where we end our book is we say are we now at a new inflection point. That is we've had, we've evolved as an incidental superpower over the last 60 years. We have developed a way of looking at the world, looking at foreign policy, looking at national security through the Cold War and immediately into the post-Cold War period. But are we now at an inflection point where that incidental superpower is no longer meeting or the American public no longer believes that it meets their needs and interests. And this can be from a variety of things. And for example, if we do become truly energy self-sufficient we can source all of our energy needs from certainly US sources but maybe just from within the hemisphere. So our Canadian oil sands, Brazilian ethanol, the new discoveries off the coasts of Brazil and Cuba, rejuvenation of the Mexican oil industry. Does that change our commitment to keeping the Persian Gulf open? Do we suddenly say we no longer need to the Carter Doctrine and Reagan Corollary which said keeping that part of the world secure and safe and stable was a core US interest. If we're not pulling our energy from it anymore do we say it's no longer our responsibility. Let China handle it, let India handle it. If more manufacturing returns to the United States and as we have this revolution of 3D printing where you no longer buy 10,000 widgets being produced in a factory in China but you have a local facility that can give you a very specialized product that you need that is produced locally. Do we lose our emphasis on wanting to keep those sea lanes open? Is it as important to sell goods and services abroad? We also argue have we reached a certain sclerosis in our national security system. We were very nimble in the 1940s and the 1950s in responding to crises in the world. When you look at how quickly the Marshall Plan got through, how quickly the NATO alliance was ratified, how quickly we were able to respond and you look today at a much slower pace. We have all of these institutions that have built up over time. Are they now a drag on us? In other words, we're still responding to the world of the 21st century with the institutions that evolved over the last 60 years and now they're slowing us down rather than being a way for us to move forward. That's a concern that we have and I think we will see this these will be the issues that we will continue. They'll be debated obviously in the presidential race and we'll see this continue as we move forward in the next decade, which is what will be our role as a superpower, what will be our role as other powers begin to acquire these capabilities that for so long and certainly for the last 20 years we've gotten used to exercising in a sole capacity. So as Derek said, we were up to this point we've been the only country that can sustain a large military force thousands of miles from our home base. We've gotten used to certain freedom of action in our ability to dominate airspace and particularly in places like Iraq and Afghanistan where insurgents don't have a fifth generation aircraft and don't have sophisticated capabilities. Now as we start to move into a world where adversaries, potential adversaries, rising powers can inflict damage on us and raise the cost for us to act when we continue to do so as that gap narrows and as other countries can say well we can send forces. Obviously the Russian intervention in Syria is still very small, not that far from core Russian bases, but a reminder that other powers are now beginning to redevelop in the case of Russia and in the case of China when Chinese ships show up in the Mediterranean to do an exercise in a part of the world we kind of thought of going back to the old Romans as our RC, our area of operation and suddenly you have a Chinese ships in the Mediterranean, we're in the Caribbean where we often have thought of that as our backyard, that may change our issues and so that I guess what I'll leave you with to conclude my section of the remarks is are we going to see another period now of incidental evolution of what it means for the United States to be a superpower in the 21st century and what changes might that bring to the types of institutions and policies that for the last 70 years have defined how the U.S. has approached its national security and foreign policy. Yeah, I think we wanted to reserve time for your questions so we do have about a half hour or so, so yeah, please. To the last point you made, in this evolution whether we're at the inflection point or not, which you consider the most disruptive and dangerous, the fact that perhaps we may not be able to any longer sustain such a force overseas or the fact that somebody else can. Let me have, you want to have. I think that the fact that others can sustain raises our raises our temperature because for the last 20 years we've gotten so used to being able to operate in most theaters with no opposition and where we could go in with not having to take many risks or the risks were very low and so that now that other countries are showing their ability as we've seen now with Syria that our calculus suddenly changes once there's Russian airplanes flying out of Syria and we no longer have uncontested ability to fly over Syrian airspace and we now have to think about doing it. So I think the second is the is the bigger issue because that raises our, it changes our calculus to say well what are we willing to lose and this formula that Derek likes to use in foreign policy is what are we willing to die for what are we willing to kill for what are we willing to pay for and what are we willing not to do any and I think for the last 20 some years we could inflict a great deal of killing and damage without having to do a lot of dying ourselves comparatively speaking based on when you look at World War II or Korea and we've gotten used to that also means that our politicians have a much lower tolerance for risk so I think we're now in that face we're having to say this matters to us but we may need to think about losing more ships, more aircraft, more people changes our calculus and how that plays out over the coming years I think will be interesting and it could then tie into this neo-isolationism that we're seeing emerge at least in some segments of the American electorate saying you know the rest of the world we did our we did our bit for keeping the world safe and secure now someone else can take on this burden yeah and I'm not quite sure it's an either or either yeah because if you look at kind of the nature of warfare I would say at least probably forever but at least the last 20 years it's coalition warfare is the norm so it's rare the US does things unilaterally I mean I kid my class that the last great war the US fought was Panama you know in the sense of it was it was unilateral it was overwhelming force 30 years later it's stuck right democratic capitalist friendly country to the United States we can't claim that with any other country uh the last war and and so there is a sort of frustration you know on the one hand I think we're happy that great power tensions are relatively low of course we have differences with Russia and China but they're also partners in many respects and so for example if we take Russia the US can't get to space without Russia today sustainment in Afghanistan is dependent on Russia uh if we look at on the China side uh it's easy to point to the negative but then we could also point out you know on the on the positive side uh any sort of issue with North Korea China is essential we look at the Iran question it was the p5 plus one uh Russia and China included that helped us you know got the Iran nuclear agreement which we think is important uh and so sometimes I think what we try to do is is we confuse normal diplomatic friction that we see today and we try to put it back in this old cold war sort of thing and so jokingly again I'll tell my students if you really want to hurt the Chinese just close the port of Long Beach all right China's growth and rise is dependent on US imports the economies are intertwined whether we like it or not and I would argue we like it this is part of the US plan and uh to to raise China I mean this is why Nixon went to China and every US president since has gone and enabled that we benefit tremendously from that I know that's not popular to say but our standard of living as Americans is higher because of China and and so we have to learn to kind of reconcile with that ambiguity and I think at least the last 15 years have taught us we've we we've struggled to translate tactical victory into strategic victory and and I think a lot of that has to do not necessarily with the US military but with the nature of conflict which is primarily internal these days I mean that's something we should be celebrating I mean the right I don't think we're terribly worried about nuclear war today but if we go back to the 1980s absolutely well absolutely sir wonder if you can share some insight you might have for foreign policy and defense strategy on what looks like the 21st century version of invasion which is immigration uninvited people coming into the country not with tanks and infantry anymore and attending to stay but with the in large numbers is there any insights from your analysis that you can help with us what kind of a policy strategy can we cope with that yeah I mean I would say you know the US has largely benefited from legal and illegal immigration I mean really when it comes down to it and we we still haven't reconciled this notion of yeah it's a violation of law however they're right we it's US companies it's US individuals offering illegal immigrant immigrants jobs and I you know again and as I globally think about why the US does so well in the world is because we have this unique ability to integrate populations from all around the world and we don't suffer certainly in New England I don't think we suffer from nationalism I think if we went we're in southwestern border there you know there would be a different sense but we don't I don't know I mean I don't I don't share the same seems to be a different thing these are not folks who want to assimilate but that's different very different and and these are folks that could be controlled by an outside power you you may reference or alluded to the fact that security is an internal thing yeah or an internal thing and this will certainly amplify that well it is an interesting question as well I'm just thinking about the larger you know the the global picture which is that it raises questions about how permanent the current map of nation states is which is that we kind of we look at the world we kind of look at the snapshot and think well that's permanent so we see you know migration changes in the European Union and not you know and and we just finished we had the the Ruger conference here which was looking at Ukraine but then also be that situation is tied to the migration crisis but is also tied with the number of smaller European countries particularly those that had just escaped from Soviet domination now saying well wait a minute are we going to have you know we fought hard to preserve our identity and culture but we're you know two million people and if the European Union wants us to take you know a hundred thousand or two hundred thousand migrants and then the question is is our people say going to learn like Lithuanian or Hungarian probably not though speak English it kind of changes the dynamic then that that produces tensions because you have people say I want to hold on to national identity and not not have it just be changed and you know the question in you know the big migration questions in paycom in the next 50 years which is you have Russia and Australia to resource rich countries to land rich countries to what well Russia water rich countries and lots of populations that look at that land and say well there's five million Russians here and four hundred million Chinese across the border so why not just just shift so I think that that will become an issue and the question is you know do countries assimilate which is do they bring people in and are those people wanting to be assimilated do countries export their populations and then hope that that creates levers of influence so that you know you send your population and you make sure they still have passports and you still say that you're there your citizens but now you have a reason to and you know the Russians use this and parts of the former Soviet Union to say well those people are Russian passport holders so they weren't migrants in the same way but the the principle is there and then what it does for the cohesiveness of current allies and even within the US I mean as we see as our demographics change you know will we focus less on Europe we have more immigration from the south and east you know do we come more of an Asia Pacific and hemispheric power and therefore what happens in Europe doesn't matter because you have more people who then say you know what happens in Europe I don't care I don't my family doesn't come from there I don't think of them as being connected to us and the same thing in Europe which is we've seen the impact of changes in demographics in Europe of European countries willing to partner with the US in the Middle East saying well you know the US has a particular approach so I think that that that does become this question of you know and it actually if I may just it touches on a larger question about the changes in the nature of war and conflict because you know our old model our Cold War model is here's my border you cross it with tanks that's an invasion we had 2007 the cyber attack on Estonia right which crippled their crippled their banking system crippled their government system cost hundreds of millions of dollars in economic damage probably occurred from Russia of course couldn't be conclusively proven and the Estonian said we were attacked NATO do something and people said well but you know NATO is you know invasion means somebody has to come with a uniform and a tank and cross your border but there's a cyber attack count the little green men count migration I mean all of these then begin to change the nature of what is war what is conflict and then what is the nature of your obligation if you're in a treaty relationship with the country to protect them and the Hungarians didn't quite make that appeal to NATO but they were on the verge of saying well you know we're being overrun by migrants coming in from Serbia NATO maybe you better say you know they didn't they didn't they decided not to make that NATO appeal they went through the EU but that would have been a very interesting discussion if the Hungarians had gone to Brussels and said you know we need the deployment of you know NATO countries need to provide forces to stand on our border to keep people out and whether or not NATO would have honored that as an article five I don't know so you've you've opened up an interesting yeah because the whole nature of war in the 21st century changing and in the North American context you know a point to prominent Americans like Dave Petraeus and Bob Zelek former World Bank president deputy of secretary of state they've argued we should think about NAFTA in a political context I mean NAFTA are largest trading partners Canada Mexico China's number two but Canada and Mexico are one in three respectively think start evolving NAFTA to think about it in a political context we're partly there are militarily because of NORAD with Canada and so these you know Petraeus and Zelek they chair the Commission for the Council on Foreign Relations about a year or so ago yeah and this is one of their conclusions is look if we want to compete globally we need to start talking about the NAFTA just like we talk about the European Union or as an honor yeah sir I just want to poke a little bit at your use of the word incidental again I would think that President Truman Eisenhower Senator Bannonberg and these this collection of people that decided that it was better not to return Germany to pastoral or even the same thing the same thing in Japan but that was not incidental this was an absolute reversal of the public policy to now support an international order as defined by by Truman and Eisenhower he just strikes me as being kind of counterfactual but that was a deliberate move to make us something of an incidental power but a world power that had real control and not just this reading what they did I think what we meant by incidental was that in the absence of certain factors not being in place say like the Soviet Union had collapsed in 1945 that as a result of the war you know you had an uprising and you know the army says enough with communism we're going to march on the Kremlin and take out Stalin and the Soviet Union falls apart we may not have done those things then we would not maybe we would have said we would have gone with the Morgenthau plan and said hey and then Germany can be pastoral Japan can be so for us I think incidental was that there were these we were reacting to things we didn't we didn't come in in 45 with the plan saying we're going to rebuild Germany we're going to create NATO we're going to sign a defense treaty with Japan it was incidental reactions to things that were happening that otherwise we maybe would have gone back to so in some ways it was being driven by these events rather than by an American no small I think too I we use it as a series of small decisions that led to this and so I have to take both words at the same time back to why did the US become a superpower it was incidental certainly decisions were made but if you look back at the plan and the easiest one to see without digging deep into history is why the Soviet Union ended up on the UN Security Council the US was in a position to dictate in 1945 the composition and I think in retrospect we would look at that as like ah what a horrible decision I mean we ended up with 50 years of heartburn who in the right mind would put the Soviets on the Security Council but the original idea as Nick mentioned is the world would be governed the US would be kind of this chairman of the board and this sort of the I always want to say the four horsemen but it's the this idea is for policemen thank you but the idea you know the idea China at the time Taiwan would kind of manage Asia and and the Soviet Union would manage Europe you know Eastern Central and and the Brits would manage Western Europe and we can kind of focus on our own hemisphere and not worry about it and then in we saw the impact so the rapid demobilization after world war two and then you can look at the Korean war as the consequence you know of that and there was a bit of it right there was a bit of naive I mean people did make some naive assumptions you know about how the world was going to unfold after 1945 and then we kind of shifted along the way but I think we ended the war the but even before the war ended we started off in a very different spot we thought we're going to be able to share power with the Soviets and the Chinese to manage global affairs in 1950 when I first went to sea we would be we were highly respected with one world war two and people wanted to do business with us and we had good products to sell and when we would enter say Africa with a rusty old tanker they would dip the ensign to us and you go buy an old tug that was half dead they would do the same thing so now we've lost that ability in fact when we go into the Persian Gulf we go into Rastunora Saudi Arabia and if there were 50 tankers there they look at the flam red horse and we went right in and one of our captains had a big limousine come down and he was a friend of the king and he had done that when they 1930s when they were building Saudi Arabia into an oil producing company so trade with our 42 percent of autonomous carried and merchant ships had friends worldwide yeah u.s. flagged yeah we all know I mean there are very few u.s. flagged merchant ships that travel outside of territorial waters and yet all right the u.s. Navy still views it is important is keeping the oceans open freedom of navigation and if you want to be negative or cynical you know the idea is we keep the the straight of our moves open so the Iranians can export oil to China is that a good use of taxpayer dollars you know the people are you know and that's where we start saying is are we at an inflection point where you can think of that or does the u.s. continue to derive value by kind of enabling the international system and it's not all you know the all peace love for the united states because you know part of its own actions and and we devote a whole chapter in the book about the u.s. goes to war every three years and I can I can walk you back chronologically we're at war a new war every three years 2014 it was Syria Iraq again 2011 it was Libya and then you have right Afghanistan Iraq 2001 to present you know and so on keep keep going back so the u.s. doesn't where there's an important peaceful dimension of what the u.s. does it's very easy for other countries that have been on the receiving end of that to kind of paint another picture and that's part of u.s. history and the challenge for our diplomats around the world is to be able to explain u.s. actions like these in a way that says we are attempting to make the situation better and that can't always be easy so if you see a foreign service officer out there make sure you thank them for their service to no well you see that with you know that the shift when we talk about this it and and certainly this was also a book that Charles cuption wrote about our predilection for wanting to turn former enemies into friends where we believe we did not and again going back to Derek's point about not that Americans are necessarily more moral than others but we identified we made a change in our security where most countries identified that when they go to war they have to ground the enemy down so that the enemy can never challenge them after that war the whole you know we're going to take carthage and burn it to the ground and salt the earth whereas we feel that where our security is enhanced if we go and rebuild uh... develop those relationships uh... and so that for you know nineteen ninety nine montenegro was being bombed by nato air forces and now it's on the verge of entering a nato member it's going to become a nato member and part of the alliance so in nineteen fifty i was invited to a fourth of july celebration in alexandria egypt and uh... when we got there i never saw a booze flowing in such quarters and uh... they had a french general walked across the floor and collapsed sounds sounds like good times yes sir minute maybe to this uh... business of the cyber threat is the subtle changed invasion not people who are coming in as migrants legal or uh... illegal but rather computer viruses yeah that can pose a threat an increasing threat there's a poem that's coming out now about the vulnerability and the danger of the electrical grid yeah yeah yeah ten ten couple and we built our own progenitor force and stocked it with the uh... real threats you're the emc chair this is your uh... uh... yeah so the one the one good so the book has been reviewed a few times already and the one criticism uh... that we got was like you guys didn't mention cyber and i talked to the reviewer i'm like yeah you're right you know why because at the same time i published a book on china and cyber security and so i think i had compartmentalized and i didn't want to get wrapped up and i think we both didn't want to get wrapped up in specific threats we we were looking more broadly you know the challenge for these threats that don't resemble traditional things is we don't know how to deal with them and it goes back to you know on the cyber it's i assume you're talking about ten couples new book and there's a either there's a big debate cyber war no cyber war you know we're we're all wake up you know one morning with no electricity or not you know all i could say at least so far is we think about cyber it's really kind of in a criminal perspective people stealing identity credit cards some financial it's done in an espionage way secrets now the u.s and china recently i don't know if they signed anything at least they agreed publicly that we will not target each other's intellectual property because the u.s is splitting hairs the u.s says look you know espionage is kind of a historical way of doing things just don't go after economic data and and that's really where the chat you know we're pressuring the chinese along those front maybe at some point you know partly i go back to the willy satan idea or he robbed banks because that's where the money was you know that the u.s is where the intellectual property is and it's not only targeted by china but you know many many other countries you know does that trigger war you know i go back to well what at what point can you no longer discuss and and the frustrations that some people have as you as you look at you know chinese behavior on cyber and you say wow we need to do something okay we'll we'll do what do you want to jeopardize chinese buying u.s treasuries to finance u.s government operations do you want to jeopardize chinese role in controlling north korea and participating with iran do you want to china you know compromise your second largest trading partner it you know from an administration perspective i don't think it makes the big list it's on the list but it's not at the top of the list because the u.s china relationship is so complex you know i will say i'm also on the rhodes island state cyber commission and so the governor has been you know working very strongly to understand the nature of the threat and how it fits to individual citizens because you know the the u.s government only deals really security at the national external level but most of our security is done at the state and local level through the police and so the governor is really trying to get her uh her arms around this and seeing how it goes source of tension absolutely we're still talking yes because there's a lot of the relationship is really complex yes in the back i have a question about the book you mentioned the subject about rediscovering the intensity of national interest and redefining national interest as a response to the whole changing geopolitical sphere like what could it be what could be different about our national interest as like to me for my research we discovered that national interest is very connected with national identity and national identity us of us the united states is like in leadership in free trade in democracy and human rights and freedoms so that's always going to be pinnacle of everything we do in ensuring that this is met like what is your perspective and what could be different like how do we readjust rediscover our national interest in the current affairs well let me give you two examples and i've already alluded to one which is a redefinition of our national interests as they relate to the middle east and the persian gulf which is to say Saudi Arabia you're an autocratic monarchy we don't like your monarchy we don't like what it's doing you're selling most of your oil to china we don't need your oil you and the chinese figure out how to get your oil out of Saudi Arabia to asian markets we're not going to base anyone there we're going to close our bases down and we're going to come home and we're going to kind of on the lines of what derrick said we're going to kind of create a super western hemispheric community and we're going to say you know this is where our energy and trade is and you know lots of luck to you so that could be a redefinition because for ever since the 1970s even before going back to when Roosevelt met with the king in 1944 we have said the security of this part of the world is a core national interest of the united states that could be a redefinition if we have more of our and we could say not our concern anymore on the we have this definition of ourselves as democracy and human rights but the question is is that are we missionaries or are we sitting on the hill which is that is we're here to spread it to the rest of the world or we suddenly go back to saying you know what this is how we do it and you want to follow what we do great but we're not going to spread it anymore so the impact of kind of the Arab winter now not the Arab spring anymore and we say you know we're done with trying to transform societies Afghanistan we'll see what happens in the aftermath of Afghanistan but you know we can't really look in 2015 and say that you know liberalism has taken real root or hold there and so we may we may redefine our national interest back to the way you know back to a John Quincy Adams approach which says yeah human rights and democracy matter but they matter to us as an example a light to the rest of the world not for us to as he said we don't seek monsters out in the rest of the world so that could feed back in there's a new type of American exceptionalism which is that yeah America is exceptional and it's exceptional because it's America and the rest of the world is not like America so it's useless to make the rest of the world try to look like America come home America you know secure our borders secure our area and you know so that could be a that could be a redefinition and we sort of you know we're going to see what happens in the presidential race we had we saw some of that being articulated seems to be diminishing now but last year when people were looking at some of the candidates were saying well we can see this isolationist redefinition emerging but that that strand is in our political DNA as well I mean the missionary DNA has been active for the last since Wilson and definitely since World War II but the isolationist DNA is there too which says you know yeah I like the city on the hill versus missionary I would add referee versus spectator I think the one thing we don't appreciate as Americans is we get to be a referee because we have the distance we don't have if you start thinking about I mean there's historic nationalist rivalries I can't think of one with the United States I mean the U.S. tends to even the Brits they burned down the Capitol they burned down the White House in the War of 1812 but we would write the Brits are our strongest ally and best friend we get over things and so the one thing I think the world looks to us so because sometimes this sort of discussion gets you in it well let the Chinese and the Saudis figure it out and then we become spectators and I would say I think the role the U.S. has been playing is more of a referee and maybe if we want to stay with nationalist examples maybe the Suez crisis where the French and British jumped in tried to take this re-nationalize the Suez Canal and the U.S. said no that's Egyptian and so the U.S. does get to play this role of referee and I think maybe that's where I think his current policy makers struggle to try to figure out well we can't solve that problem there for or for we should do nothing now there's some there's a there's a role to play and I think you know to me it's more of the referee and somewhere that's in between yes gentlemen in the back if I look at the last two comments looking forward in natural interest cyber threats whereas when I look at the title not to go back on the play on the nuance of words evolution of an incidental superpower I'd be interested to hear going forward is it going to be the evolution from an incidental superpower are you looking at the United States still wanting to be a superpower especially with regard to foreign policy and defense strategy we talked about national interests cyber securities straighter homos do we want to be a superpower and how would that relate to our foreign policy and defense strategy yeah that's a great question and that would be a nice follow-up book wouldn't it evolution well I mean one of the things the reality that we're facing with is that for the first time since world war two America most Americans increasing number of Americans don't perceive superpower status as benefiting them anymore in contrast to the 50s or the 60s or the 70s where people said America's a superpower and I benefit from that because whether it's trade or security people say today superpower status means we get bled we have to go into all these everyone always expects us to do the heavy lifting and then someone else gets the reward I mean this and what happens I think in Afghanistan may help set that narrative because if the end result of Afghanistan is going to be the China benefits that we kind of set the table and then China benefits from all the resources and the contracts and kind of the same thing we heard after Iraq we were promised in 2003 that we would go in we would liberate Iraq and then there would be all of this economic benefit we were going to have lower oil prices we were going to have and then you look at the contracts and other things that didn't quite work out that way so I think you have that sense and that's why I think the question then moving forward is is that does that sense grow in the American body politic that is do we need to be a superpower to be secured do we need to be a superpower to protect our interests you see that in the Pew polling data increasingly Americans do too much in the world we should pull back not you know not go complete isolationist not disarmed let other people handle it we see it in the the reaction the polling data on the Syria crisis where Americans say that's too bad what's happening but you know what I don't want my sons and daughters going there if the Turks don't want to do it and the Saudis don't want to do it then we shouldn't do it so I can't give you a definitive answer yet I just that's where but we're in that point where for the first time since the end of world war too you have more people beginning to question does this superpower status matter and then this question of well maybe it matters to elites in New York and Washington but it doesn't matter to Main Street anymore and you see that rhetoric coming out well you know New York bankers benefit from this because they're selling deals with the Chinese but you know Main Street is boarded up and shuttered and and the like and so that maybe and then the the question about the de-evolution or the new evolution will have to do a lot with the institutions that we now have we look at what by all accounts is a very bloated national security apparatus you know more than a million people now holding security clearances how many different duplication of intelligence and security agencies how many people work at the Pentagon how sustainable is that and are people going to say well now we have to we have this sclerotic national security establishment that has evolved and it's now time to really take the meat cleaver and you know for me a bell whether will be does is african still here in 10 years do people say well we don't need african anymore we don't need maybe we don't need south com they can just be folded into you back into you come and back into north com because we don't need to have that presence and we're going to start cutting back on these things and we have a point in the book where we think we say at the end the real challenge we're facing is you know we have a relate we have a defense or security relationship with some 150 countries right now and a few years ago you would ask people in Washington so which of these matter and it's all 150 matter no one gives you that answer what the debates are beginning to emerge is we all agree that it's going to be about 20 to 30 but right now the debate is which 20 and 30 and that's where the knives come out of okay well who gets to be the 20 or 30 countries that are the key partners of the U.S. one reason why we see this uptick in foreign lobbying in Washington and why are so many governments paying hundreds of thousands of dollars now for lobbyists because they know that the cuts are coming and everyone wants to make sure that I'm not going to my country isn't going to be the one that's cut and that factors into this you know de-evolution re-evolution of what it means to be a superpower and in terms of what the American commitments are and the high point in the mid-2000s where you had a bunch of countries that had these virtual what they thought were virtual guarantees from the U.S. so Georgia Georgia where the Georgians kind of basically felt that they were basically members of NATO discovered in August of 2008 that if you haven't signed on the dotted line and then Ukraine discovering that you know a throwaway memoranda that was kind of propagated in 1994 to kind of keep them off but you know keep them from asking you know well that's great you know the president went to his lawyers and they said it's you know it's maybe a moral obligation to help Ukraine but it's certainly not a legal one and so now we're beginning to see that you know we're starting to take stock and inventory of who has a commitment who doesn't and yeah I would pose it so the rise of China is an important phenomenon and we'll all live with it for the next 30 years is being important feature I would I always love the contrast between when the Chinese president arrives in Washington State and has dinner with with Bill Gates and and everyone else from kind of the IT and Boeing sector and then you contrast that with how the Chinese president is treated in Washington DC and so when we start looking at tensions for example either on China or South China Sea I mean I would almost go back again to US history to look at US business and US economic policy used to be the leader in the US government we're only just really within the last 30 years we we tend to look at everything through a military lens that if we're going to be active in the world it means we must solve X crises in military means and so there might be something to be learned along those lines is you know how was China dealt with in Washington State versus Washington DC and will we see that you know on on the IP loss how does Apple manufacture in China if it is really so bad how do they they manufacture it and I think the short answer is you know their their key to success is they their they the innovation cycle they cut the key to American manufacturing or say American business is really innovation so you can copy it and steal it and that works great for a couple months and then the next one comes out and the next one comes out and but at some point maybe the Chinese can absorb this IP intellectual property more and we can start seeing some truly Chinese products but I I don't know I mean your question I like the contrast between Washington State and DC to think about that did you want to keep going or you want to go a couple more yeah yeah yeah let me let me start here just because he doesn't have to grade that's right we shift your your view far away from United States is flexible in the innovation we now are seen as honest broker by it seems India and China but the dominance of oil coming through there is is India China Japan Diego Garcia is is the major source of our influence throughout the Indian Ocean is this changing both because of our lack of interest in needs and the in the strengthening of China not now but eventually to really control it if they wanted to what's our future there the 50 year agreement comes to an end next year it's going to be continued we're pouring billions still into Diego Garcia is it going to continue yeah I mean I think inertia tends to take over in these sorts of situations so I think yes I mean the administrations committee certainly the navy and I think the year for 60 percent of the forces will be in Asia in that theater to include the Indian Ocean so no I mean I think we're we're a Pacific power too and so I think we see that is an important role to play but I'll also note to the frustration with the administration they want to focus more on Asia can't get out of the Middle East and then of course Russia makes it hard to to rethink your Russia forces a rethink of U.S. foreign policy in Europe as well no I would agree with that mm-hmm yeah back here sir yeah uh another specific the uh trans-specific trade which is now up for ratification if that's not ratified whatever one may think about the features of it are we in the future likely to deal with a trade environment dictated by the Chinese I think the the TPP was one of those ways so part of our are they one of our strong threads in the book is showing that the U.S. got to write the rules of the international system mainly and we benefited and I think with TPP that's kind of version too of being able to write these rules so you know that China doesn't does it make any economic sense to include your second largest trading partner from TPP I'm not an economist I mean I tend to think probably not I know why we're doing that but you know I'm not at some point my guess would be China would be incorporated into TPP on some level because they are the second largest trading partner for the United States so you know most of these agreements the U.S. market is pretty open most of these agreements tend to benefit U.S. companies in those other countries so I tend to think we would try to push along those lines yeah I mean the thing about TPP that's two things that are important the first is that as Derek said about writing rules and who writes the rules because you can go with us and the TPP or you can go with the Chinese and their free trade agreement for Asia you can join a U.S. crafted Asia Bank or you can now join a China bank and in some cases you know for the most part our strategy has been look if countries want to do both more power to you but you kind of get to see the benefit it allows you to put the two glasses of water and to compare which is a better deal and which has a better a better what you know in terms of the rules and particularly you know the risks that you run with Chinese institutions as with their currency is capricious shifts that hey we've decided that our currency is worth half of what it was yesterday by fiat you know that generally investors and others don't like that whereas we are we're more transparent so that that's a benefit that we have and so that is part of this but it is part of this competition of who gets to set institutions who's trusted I think your point about the U.S. is a referee you know do you want the U.S. to be the referee do you want Beijing to be the referee um maybe at some point China will be in that role maybe it will grow in trust and we'll see what it does but right now they don't they don't enjoy that same level of of trust for our perspective what I find fascinating about the TPP and the fact that you know it could fail I mean it may not be ratified it may not make through the Congress is that it does speak to back to the earlier question the the point that you know 30 years ago free trade agreements most Americans said all right there might be winners and losers but it benefits the country as a whole so you would found that there was generally support now you see more and more people saying this doesn't benefit us TPP does not benefit me the administration and and the Republicans have not who support both who supported have not crafted I think the argument in a way that appeals to Main Street they craft arguments that play well at CFR and in DC think tanks but that they don't they're not flying in other parts of the country's to why TPP matters why Americans benefit from it and with it as with other agreements you have to there's a domestic political side of there are going to be winners and losers and you have to have a strategy that will assuage the losers that their interests that they'll be taking care of and I think some of the opposition to TPP now is segments of America will lose and you know well too bad you're the losing side and but that losing side still has considerable political resources and they're going to be capable of blocking it and then the risk we run is TPP fails and that pretty much is the end of the pivot because that's our really only non-military part of the pivot to Asia and then it just becomes we can put more aircraft carriers we can have Diego Garcia and then you're going to have countries in the region saying why do the Americans solve everything only through hard power so and it'll never be enough in our allies part of the a key tenant of US foreign policy and defense strategy is promoting our allies you know we we empower our allies through weapon sales and transfers we enable our allies by doing joint exercises and coalition operations and all of this benefits the United States because we're supporting the defense industrial base at the same time and so you can think of a situation for every F-35 for example you know we sell to Japan you get jobs in the United States and you get one more fighter aircraft in theater that you wouldn't you that you don't have to pay for and there's some real advantages of that and that's one of the advantages that we really try to draw out in the book


So this lecture is part of an online algebraic geometry course about schemes, and we'll be about how you move quasi-coherent schemes from one quasi-coherent sheaves from one scheme to another. So suppose you've got a map between schemes X and Y, and we've got a sheaf F on Y. We might want to get a sheaf F on X, which we will denote by F star of F. And if we've got a sheaf G on X, then we will get a sheaf lower star G on Y. And furthermore, these maps will be sort of adjoints in the sense that the set of morphisms from this sheaf to this sheaf and the set of morphisms from this sheaf to this sheaf are more or less the same. So we'll say that F opposite star is going to be left adjoint to F lower star. Well, earlier on we defined some maps F to the minus one and F star for sheaves of Abelian groups. And the F lower star that we're about to define for quasi-coherent sheaves will be more or less the same as this one, but the F opposite star has to be modified from this one for reasons we will see in a moment. So we first look at the affine case. So here we've got a morphism A to B of rings. And we can ask, suppose we've got a module M over A, how do we get a module M over B? So a module over B. Well, that's obvious because we can just make M into a B module by just using the map from B to A. So turning an A module into a B module is kind of easy. So M is also a B module. On the other hand, if we've got a B module N, there's no obvious way in which it's an A module. So B module N is not an A module. But there's a way to turn it into an A module. We can take N tensor over B of A.  And this is a sort of left adjoint. If we look at morphisms from N tensor A to M as A modules and morphisms like this. So these are going to be B module homomorphisms. And these are going to be A module homomorphisms. Then the B module homomorphisms here are more or less the same as the A module homomorphisms here. There's a sort of canonical isomorphism between them. So the map taking N to N tensor over B A is left adjoint to the map taking M to M, where this one is an A module and this one is as a B module. Well, now let's examine whether or not these maps preserve exactness. Because obviously if we're transferring sheets from one ring or one scheme to another, then knowing whether exactness is preserved is going to be really useful. Well, the map taking M to M. So here we're taking M as an A module to M as a B module is obviously exact. More or less because we haven't really done anything to M except pretend we're working over a different ring. On the other hand, the map taking N to N tensor over B A, well, the exactness is a bit more subtle. Map taking N to N is obviously exact, but tensuring with something doesn't always preserve exactness. You remember, tensuring with something is only right exact. So you remember if you've got an exact sequence say nought goes to Z goes to Z goes to Z over 2Z goes to zero. Let's just tensor with Z over 2Z. Well, we get Z over 2Z goes to Z over 2Z goes to Z over 2Z goes to nought and this bit is exact. But this map here is not injective. So it's a really important point that tensuring with something is only right exact, it's not exact. So there's one case in which it is exact. It's exact if A is a flat B module. And that's true because this is more or less the definition of what it means for A to be a flat B module. It just means that tensuring with A preserves exactness. So this is one of the reasons why flatness occurs so much in algebraic geometry. It means that this map here that we're going to define extended schemes is exact. The concept of flatness is very unintuitive. It was sort of introduced by Seher and growth and Dick discovered it had central importance in algebraic geometry. However, it's very hard to explain what it means geometrically and there's probably no really easy explanation because people have been doing algebraic geometry and commutative algebra for about a century before Seher discovered flatness was important. So there probably isn't any obvious reason for it. So let's translate all this into the language of affine schemes. So what we do is we have a morphism from the spectrum of A to the spectrum of B. I hope I've got all these arrows the right way around. So let's call this X. Let's call this scheme Y. And if we've got a sheaf over F, we can pull it back to a sheaf F to the minus one of F over A. So this isn't necessarily a sheaf over A for the same reason that if we've got a module over the ring B, there's no reason why it should be a module over the ring A. And what we remember what we had to do with rings was tensor it with something. So we need to tensor this with something as well. So we tensor it with over F minus one O Y of O X. And this is really just what we did with modules. We just took n tensor over B of A. And if you translate everything into scheme theoretic language, it looks like this rather slightly complicated mess. On the other hand, if we've got a module over A, in other words, a sheaf over spectrum of A, then it's very easy to convert it into a module over B. And this is just the map G goes to F star G where F lower star F to the minus one of the other maps we defined earlier for sheaves of abelian groups. So and as we saw the maps from this sheaf to this sheaf are essentially the same as the morphisms from this sheaf to this sheaf. So these are the same.   And we see that F star and F lower star are adjoints. More precisely F upper star is left adjoint to F lower star. So these are going between categories of quasi coherent sheaves on these two schemes. So all of this is just exactly the same as what we wrote down here except we're writing it in geometric language using sheaves and schemes instead of talking about modules and rings. So although this this only looks a bit of a mess but it's just saying you tensor a module with another module. Now we need to study. Now we just recall exactness properties of these. So for affine schemes. We see that F lower star is exact. And F upper star is right exact. That's because we showed these for modules over a ring and affine schemes are more or less the same as rings. And we also saw that this is exact. If something is flat, some flatness condition holds and I want to really emphasize the word affine here. Because when we look at none affine schemes we will see in a moment that F lower star is no longer exact. So now look at general schemes, not necessarily affine. So we've got a map F from X to Y. And we've got a sheaf F on Y and we've got a map F star of F on X. And we've got a map taking G to F star of G. And you can check for general schemes of jointness still holds. F upper star is defined by exactly the same formula as before. And what F upper star looks like is F upper star F looks locally like N tensor over B of A. We're going to take an open affine subset whose coordinate ring is A and an open affine subset whose coordinate ring is B and so on. And this map here is really just locally taking a tensor product. But we know that F upper star is left adjoint to F lower star. And left adjoints are always right exact. And we saw earlier that F upper star became exact if some sort of flatness condition holds. And the same thing holds for general schemes. F star is exact if some flatness condition holds. It's not difficult to write out this flatness condition explicitly, but it's a bit of a mouthful. We have to sort of cover Y with open affine subsets and then cover X with open affine subsets mapping to them. And then for each coordinate ring here, the corresponding ring here has to be flat over it and so on. But it's easier just to remember this as some vague flatness condition. And similarly F star is always left exact because right adjoints are always left exact. F lower star is no longer exact in general. And we've seen an example of this before when we looked at invertible modules over P1. Let's just take F to be the map from P1 of K, one-dimensional projective line to a point, the spectrum of K. And then we notice that F star for this map is just the same as taking global sections of a sheaf. And now we look at this map O minus one plus O minus one that we saw last lecture and it maps on to O zero. And we noted that the global sections of this or F star of this was just zero. Whereas for this, the global sections were just K. So this map here is not on to. So F lower star is left exact for, sorry, it's exact for morphisms of affine schemes, but it's no longer exact for general morphisms of schemes. What happens in general is over a scheme, if we've got an exact sequence, nought goes to A, goes to B, goes to C, goes to nought, we will later see that in fact we get a long exact sequence, nought goes to F star of A, goes to F star of B, goes to F star of C. And then instead of getting nought, we get something called the right derived functor of F applied to A and goes to the right derived functor of F applied to B and that goes to the right derived functor of F applied to C and that goes to the second right derived functor of F applied to A and so on. Anyway, that's all coming later. There's one more topic I would just want to finish this lecture with. There's one other way, well, actually there are several other ways to get between sheaves on schemes, but one other way in particular that sometimes turns up is if you've got an open immersion from U into X. So informally U is an open subset of X or at least isomorphic to one. And now we've got a map F lower star taking sheaves on U to sheaves on X, but there's another one who sometimes encounter F with a sort of exclamation mark. This is called extension by zero. So I'll just say a little bit about this. The way it works is as follows, if we've got a sheaf on U, we can think of it as being an etal map from an etal space to U. Remember etal means it's a local homomorphism. Well, as U is an open immersion in X, the map from U to X is also etal. So we can just compose these and get a map from E to X. And this is the etal space representing F exclamation mark of whatever sheaf we started with. So if we're taking a sheaf A on U, then F lower star of F will be here. So this is the etal space of F. And if we just compose it, this will be the etal space of F shrink of F. So what is happening is easy to see at the level of stalks. So the stalk of this at each point of X is zero if the point isn't in the image of U. And it's just the same as the stalk of F if it isn't the image of U. So that's what's meant by extension of zero. All the stalks outside U are just zero. Well, next we should note that F star of a quasi-coherent sheaf is not quasi-coherent in general. Well, I mean, sometimes quasi-coherent, but usually not. And let's see an example of this. So let's just take F to be the map from the spectrum of K to the spectrum of R where R is a discrete valuation ring. So you remember the spectrum of R looks something like an open point and a closed point. And the spectrum of K just looks like the open point being included into it. And let's take the sheaf corresponding to the module K. So you remember we indicate the corresponding sheaf by just put a twiddle on it. And let's work out what F star of K on this is. Well, F lower star of K is just the sheaf K. So that's a perfectly good quasi-coherent sheaf on R. On the other hand, F lower sheet of K twiddle is kind of funny sheaf because the stalk at the closed point is just zero. So it has no global sections other than zero. I mean, it's a tall space kind of looks like this. Here we've got the spectrum of R. And then above it, you've got the zero section and you've got all these other sections which just can't be, which just don't, which can't be extended to this point. So the only global section is the zero section. So it's not quasi-coherent because any quasi-coherent sheaf is determined by its module of global sections. So it is a module over the ring, over the sheaf of rings of the spectrum of R, but it's not a quasi-coherent module. So this is one natural way in which modules over sheaves of rings arise which aren't quasi-coherent. The exact relation between F lower star and F lower shriek is F lower shriek is left adjoint to F star, which in this case is F minus one, and F lower star is right adjoint to it. For most morphisms, F opposite star doesn't actually have a left adjoint. However, the special case when the morphism is an open immersion, it does happen to have a left adjoint and it's given by this funny sort of extension by zero. Anyway, because of this, the extension by zero isn't often used for quasi-coherent sheaves, although it's used a bit more for non-quasi-coherent ones. In the next lecture, we're going to discuss coherent sheaves and try and explain why we ended up with such a horrible name quasi-coherent for quasi-coherent sheaves.


Hi, this is Christian. So in this video, we'll talk about Laravel. Now, do any coding here, just going over what Laravel is and how we use it in the program. So Laravel, as you can see, is a back-end open-source PHP, I should say, full-stack web application framework that uses PHP as the source language. It embraces what uses the MVC, the Model View Controller, architecture pattern. You'll see that when we start coding. It has a lot of built-in application features, things I list here, as you can see, and many more. But these are some of the most important or relevant ones. You will get to use quite a lot. So in this demo, in the next video, we're going to do the following. It will install Laravel, create a application, a very simple Hello, World application in Laravel. We're going to look at the Model View Controller and the routes, files, and photo structures. And we're going to create a simple templated syntax system by watching a template. And then we're going to render the content using the language syntax to the browser. And these are some really nice readings about Laravel, some documentations here. They have an OK documentation. It's still not the best. In my opinion, the best online documentation is still php.net. But indeed, they do assembly and nice examples as well. So the tools you need are as follows. You will need at least a PHP 8 or higher, right recommended. You can still go with 7. I'm pretty sure, but it may cause some issues. And the best way to do that is basically install XAMP on your system. Because XAMP is a program that installs a stack of other application you need already, right? The X here stands for cross-platform. The A is for Apache. M is for MariaDB or MySQL. And the P's here are for Perl and PHP. And if you are on a Mac, you want to use it. That's only for a Mac. You will use the one that says MEMP. And the windows will still WAMP instead. But I use them because it's cross-platform. Now, you also need a Composer, which is the package installer. This is not only used only for Perl. It's for the entire PHP framework. So this is synonymous to MPM when you talk about Node. So you need a Composer to do that and an IDE of your choice. There are a lot of IDEs. Any IDE will work, whichever you feel most comfortable with. You don't have to change IDE. But I'm using Visual Studio Code. I will stick with this one here. It's free open source. You already know that. The other one is the PHP Storm, which is really powerful. It's not free, but it's really robust, provided by the JetBrains team. So if you want to get a free version of that, you can follow this link here and sign up as a student or educator and some other license to give you a free for one year, OK? But in this example, I will be using just if we just do the code so that everybody can use it as well. OK, and then you also need to install the Laval CLI. It's recommended after you install Composer, right? So once you do that, just install the Laval select globally by running this command right here, OK? So that's that. Right, so Composer is really simple. I'm going to go right there right now just to show you what it looks like. So I'm using Windows. So if you're on a Windows system, just download the executable files and run the installer that way. It's very easy. You can also run in the command terminal like you see here. Just copy one of these and run it directly, OK? If you're a Mac, they all have different ways to do that as well. Mac or Linux systems, OK? So install that first. And then now down here, just a little bit history of Laval. As you can see, it's still quite young compared to other frameworks, I guess, especially the .NET. But it's been around for the last decade or so. We are now using version 9 at the time this recording. So version 10 is coming up next couple of months or so. So versions are important to understand because they can break some changes or the photo structures might change a little bit. But the framework will still be the same, OK? So just be aware of that. So down here is how you create a Laval project. Just follow these same steps. Yeah, again, I'm using the composer as opposed to the Laval. You can also create a project using the Laval command at the level of CLI itself. But for our example, we'll be using Composer to create that for us, OK? So this is the command here to run the application. Once it's installed, you use the PHP artisan command and followed by the serve function, OK? And then by default, I think it's the local host port number 8,000 is the default port number. You can use local host or you can use the <IP_ADDRESS>, which is the same thing, OK? So here is the structure for Laval 9, the photo structure, I should say. Now, if you're using the older version of Laval or a newer version, these folder directors may change or may not be exactly what you see here. So on the left side here is the root directory. The root directory means it's the root project, right? So for example, up here, if I create my project called my app, inside my app folder, I'm going to see these folders in addition to some other files. Here, we're just looking at the directories. So there is about 10, 11 directories in here for Laval 9, all right? You will see this by default. The one I'm putting in blue here means that they will be created and scaffolded for you automatically when you install or create your project, OK? So it's important here. On the right side is what's inside this app directory. We only focus on this app directory here. So if you open the app directory, you will see these directories as well. The one I put in blue here, again, are the default ones. The one in black are only as neat basis. So if you want to create the black ones here like this, you would use the artisan command make, colon, whatever that is, and it will create these folders for you automatically in here, OK? So chances are, we're not going to probably using many of these one here, other than just the default ones. And down here is what each of these directories do, right? What do they provide and what's their purpose? So if you read about it here, you understand maybe better. But most importantly, we're going to focus mainly on the app directory, the public directory here, resources, and the routes, OK? Or mainly just mostly these up here, OK? We're not going to focus too much on the bottom ones down here. So these will be touched quite extensively, especially if you want to config and do some database activities, which we'll probably not do in this class. OK, so down here are some of the, again, information about the other directory. It's an app directory here, what these folders are. The important ones we'll be using are the HTTP, the providers, maybe just those two, OK? The other ones, we're not going to do them until when we later, but I think just those two here, right? OK, so Laravel uses a template and syntax system called BLADE. So it's called a BLADE syntax called sometimes used for the view as a BLADE view, then we mean a BLADE file. A BLADE file must have the extension dot BLADE dot PHP attached to it, OK? If you don't have that attached to the file name, it's not going to be rendered by the BLADE system. Yeah, you can still use a view, just a regular HTML PHP file, which is OK, but you're not going to be to inject BLADE syntax. So that's what it looks like. And these are stored inside the resources slash views directory, which is the one I mentioned up here. The views directory, that's from here, way up here. Inside of resources, OK? We'll see as we code. And then inside that file, open up, it will look just like this, just like a regular HTML document, or if you will, if you have a PHP document, and you will see some of these curly braces in there, these are very similar or should be very familiar. If you have been using the mustache tags for Express or Flask or Angular others, OK? So BLADE also uses this syntax here. This is for text or string interpolation. This is actually incorrect. The syntax here, I think it's incorrect because the name here should have a dollar sign. OK, I could be mistaken, but it's probably incorrect. We'll take a look. OK, so that means you're going to inject the data you're into here, and it will be parsed, and we render to the view. You see this is a hello, whatever this name is. OK, this is how a function called get is used. This is part of the HTTP protocols or HTTP verbs, how you can receive data or requests from the browser. And they're going to use to render data to the view. So to get will be a request type. You have this post, a put, a deleting options, and the patch, and so forth. OK, so based on the type of request you receive, you're going to match this pattern. This is the pattern that needs to be matched in the URL. Once it matches this pattern, then it's going to call this function here from here to here. This is, as you can see, it's a callback function or referred to as a closure in Laravel and PHP. Also known as just anonymous function, basically. So this function here returns a view. It is a view function that you pass data to it. The required parameter is the view name. OK, these are just some data parameters you pass to the component or the view to be rendered. So if you want to pass the name variable to this template here, you would pass it this way. There are a couple ways to do this, but the easier way is to use an array of key value pairs or also known as the associative array. Or I guess you can also refer to as object, right? So you do that, and when you run this to the view, you can see a message that looks like this. OK. All right, so and here are just some examples where you can use blade view versus just a PHP view file. So here is an example of a regular PHP code, right? If you have that PHP file, you have, you know, this is the HTML area. And if you want to inject PHP code in there, you can put the PHP tags and then run some code in here. I'm using here, for example, it's a 4-H loop. The loops do a variable called users, and then you loop that through here using just PHP code. OK. And if you're using the blade syntax using this as opposed to this, right? I mean, down here, this is the blade syntax. It looks kind of similar, as you can see. You're basically changing the PHP here to the add symbol, right? Pretty much that's it. And then you will use the curly braces here as opposed to the PHP echo command. So you can see it's like a replacement. So this is a blade syntax, and you will be using this as opposed to the PHP code, right? The rule is that, again, a blade file can only allow you to use the blade syntax in here, OK? Like the add symbol, the curly braces. If you do not use the blade template, if you try to inject these data into your blade template, you're going to see these just like regular text. So do not do that. Don't mistake by doing that because you will be exposing some sensitive data to the user, to the view people, right? But PHP can exist in both templates. So as you can see, in either a .php file or a blade PHP file, PHP is still that PHP. It doesn't really care, right? So therefore, if I have a file called index.php, I can render my variable using the PHP syntax. If I'm using the blade template, I can use the blade syntax, OK? But if you were to use the index PHP, and if you try to use blade syntax, then this is what you're going to see in the browser as opposed to the interpolated variable values, right? So do not do that. But PHP exists in both states. So here is that blade PHP file. I can put both blade code and PHP code, right? And here again, PHP code and blade code. So that's it's PHP's world. But I recommend not to use PHP code because that's the whole idea. Otherwise, it defeats the purpose of the blade syntax. So use it only if you must. If you don't use it, then try not to use it. You do everything in the source, right? And then just do some blade syntax here. Down here is for creating routes. We do that as well, as you can see. It takes to get, put, pose, delete, patch options in here. This is the request type that's in the route class. Use the colon, colon here. And then you pass in URL. And a callback function or again, a closure. The URL here is the pattern. The backslash is usually we reserve for the route directory. And then others will be like, for example, users and then slash and then you're an ID or something like that, right? Or about whatever. And then you have to provide a callback function to perform when the user gets to this route. What happens? And that occurs inside this event function here. So this is an event-driven function, right? That means it will not fire until you actually navigate to this URL, okay? This is an example of what crowd operation will look like. So you can see there's a get, a pose, a put, a delete. Okay, just the foremost common operations here. And for the get, you can use a get, a single ID by passing the ID variable here. Notice the curly braces followed by the ID or the field you wanna pass to that URL is what the ID here. There are other ways to do this as well. You can, we'll learn this later, but this is how you pass variable to that. And here it posts, you don't need ID. So you just basically add the data from the body of your form to that data set. Okay, and then the put. The put, you're just updating in existing ID. So that's what you need ID here. And delete a similar, you're deleting a single record, you put ID, if you delete all, you don't need ID. Okay, so these are just how it is set up. All right, so that is pretty much the very high overview of Laravel. And in the next video, we're going to go ahead and create our project and Laravel.